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<li><a rel="nofollow" href="https://wiki.tcl-lang.org/history/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis">History</a></li>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#2aa26ec155ca4fb6e2f231f267093b904d885ca8713a6740eae10266e8c9a9ad"> Chinese Horse Race Problems from Suanshu, Double False Position Algorithm, and eTCL demo example calculator, numerical analysis</a>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#1d00da22e97df80a90de5abd3c37e68785a90864a496afb02e50c5068b502b59">Pseudocode Section</a>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#1e716c6ec7b20517217d4f8985661caa379aa38f44d8f15277bdbf870204a4df"> Testcases Section</a>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#b00907904f84621888320aae2e88b576be44e91787db940ac4ec901aafd25ad2"> Testcase 1 </a>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#7f6724c630d2d4c5dcdf9906c9a50a02ba82b95094a63daea8729d7e99f73c24"> Testcase 2 </a>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#bf46ab89ae3dcb44d3b1eea653984d980aaeac7bcd3a30d1092e506f631dd431"> Testcase 3 </a>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#8376fd2a3e444ff463387ca863c37edc212b9272b2cfe4a95c9100c1dccfea3f"> Screenshots Section</a>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#1da4244b5ee5f30b64e852cb4fcd75ba574fcc429ecf3f0b5690b307bed62de6"> figure 1.</a>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#c71281d1e05df1a958631120547cfd0604672207b45312b087aca23f98d99fdb"> figure 2.</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#fd2c249d8a6107be6666d1735107cb471a12f310cae0032d116569f289417095"> figure 3.</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#d36a34541d015e77f2eca3bccbc8555ed1b568c39f5fb69f73ff85be99d02d82"> figure 4.</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#c433a06ad32c6d67c8a646c003c2d28145b8865449395c2b692aecf85b1f560e"> figure 5.</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#4f7b232da525e0f481341b70b237ee2ebc8148b9fdbd2da8a5332a4424038b40"> figure 6.</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#3d3a074d573e9749137ac430048d53e3783fe7eced95639f6cf8be0a8eeef217"> References:</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#fe390e3262f2848ba3988afd719b455ae1e7b257ceda9fbc8d674acb64d61fa7">Appendix Code</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#91e97000326748d418926ea0203dd16d3a12b9374f57bf8e4747e4d0308486f9"> appendix TCL programs and scripts </a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#e7fbfe54a6ce2d05f5b0e0f0913edc280ca6661b149b0d208e772883ce790e39"> Pushbutton Operation</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#e344c236ce314deb2c0e8f794ed535f3ea908ffeafabc611fc7ed059865d9a24"> Chinese Horse Race Problem from Nine Chapters (commentary c.260 CE ) </a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#a959b851a3c6c7d581ffc4791b38d29804521afc2d6e12c95709ff5ce67a2283"> CVS Spreadsheet for Charted Graphical Solution</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#ee552cc643bd97fe0620f002d6895142e73f697c85016a4be520fc10b71767e3"> test of Chinese font for Suanshu horse problem 19 of section 7 </a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#28470a55913727ab7417a6bac398038c8f028b89017505501ffc9d52d69670cf">Comments Section</a>
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<li><a rel="nofollow" href="https://wiki.tcl-lang.org/history/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis">History</a></li>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#2aa26ec155ca4fb6e2f231f267093b904d885ca8713a6740eae10266e8c9a9ad"> Chinese Horse Race Problems from Suanshu, Double False Position Algorithm, and eTCL demo example calculator, numerical analysis</a>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#1d00da22e97df80a90de5abd3c37e68785a90864a496afb02e50c5068b502b59">Pseudocode Section</a>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#1e716c6ec7b20517217d4f8985661caa379aa38f44d8f15277bdbf870204a4df"> Testcases Section</a>
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<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#b00907904f84621888320aae2e88b576be44e91787db940ac4ec901aafd25ad2"> Testcase 1 </a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#7f6724c630d2d4c5dcdf9906c9a50a02ba82b95094a63daea8729d7e99f73c24"> Testcase 2 </a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#bf46ab89ae3dcb44d3b1eea653984d980aaeac7bcd3a30d1092e506f631dd431"> Testcase 3 </a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#8376fd2a3e444ff463387ca863c37edc212b9272b2cfe4a95c9100c1dccfea3f"> Screenshots Section</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#1da4244b5ee5f30b64e852cb4fcd75ba574fcc429ecf3f0b5690b307bed62de6"> figure 1.</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#c71281d1e05df1a958631120547cfd0604672207b45312b087aca23f98d99fdb"> figure 2.</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#fd2c249d8a6107be6666d1735107cb471a12f310cae0032d116569f289417095"> figure 3.</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#d36a34541d015e77f2eca3bccbc8555ed1b568c39f5fb69f73ff85be99d02d82"> figure 4.</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#c433a06ad32c6d67c8a646c003c2d28145b8865449395c2b692aecf85b1f560e"> figure 5.</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#4f7b232da525e0f481341b70b237ee2ebc8148b9fdbd2da8a5332a4424038b40"> figure 6.</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#3d3a074d573e9749137ac430048d53e3783fe7eced95639f6cf8be0a8eeef217"> References:</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#fe390e3262f2848ba3988afd719b455ae1e7b257ceda9fbc8d674acb64d61fa7">Appendix Code</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#91e97000326748d418926ea0203dd16d3a12b9374f57bf8e4747e4d0308486f9"> appendix TCL programs and scripts </a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#e7fbfe54a6ce2d05f5b0e0f0913edc280ca6661b149b0d208e772883ce790e39"> Pushbutton Operation</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#e344c236ce314deb2c0e8f794ed535f3ea908ffeafabc611fc7ed059865d9a24"> Chinese Horse Race Problem from Nine Chapters (commentary c.260 CE ) </a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#a959b851a3c6c7d581ffc4791b38d29804521afc2d6e12c95709ff5ce67a2283"> CVS Spreadsheet for Charted Graphical Solution</a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#ee552cc643bd97fe0620f002d6895142e73f697c85016a4be520fc10b71767e3"> test of Chinese font for Suanshu horse problem 19 of section 7 </a>
</li>
<li><a href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#28470a55913727ab7417a6bac398038c8f028b89017505501ffc9d52d69670cf">Comments Section</a>
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<h2>Chinese Horse Race Problems from Suanshu, DFP, and example eTCL demo calculator, numerical analysis</h2>
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<h2 id="2aa26ec155ca4fb6e2f231f267093b904d885ca8713a6740eae10266e8c9a9ad" class="mkup_h1"> Chinese Horse Race Problems from Suanshu, Double False Position Algorithm, and eTCL demo example calculator, numerical analysis</h2><p class="mkup_p">This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Aside from your courtesy, your wiki MONIKER and date as a signature and minimal good faith of any internet post are the rules of this TCL-WIKI. Its very hard to reply reasonably without some background of the correspondent on his WIKI bio page. Thanks, <a class="mkup_a mkup_known" href="https://wiki.tcl-lang.org/page/gold">gold</a> 12dec2018</p><hr class="mkup_hr"><ul class="mkup_UL"><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#2aa26ec155ca4fb6e2f231f267093b904d885ca8713a6740eae10266e8c9a9ad">Chinese Horse Race Problems from Suanshu, Double False Position Algorithm, and eTCL demo example calculator, numerical analysis</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#1d00da22e97df80a90de5abd3c37e68785a90864a496afb02e50c5068b502b59">Pseudocode Section</a><ul class="mkup_UL"><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#1e716c6ec7b20517217d4f8985661caa379aa38f44d8f15277bdbf870204a4df">Testcases Section</a><ul class="mkup_UL"><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#b00907904f84621888320aae2e88b576be44e91787db940ac4ec901aafd25ad2">Testcase 1</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#7f6724c630d2d4c5dcdf9906c9a50a02ba82b95094a63daea8729d7e99f73c24">Testcase 2</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#bf46ab89ae3dcb44d3b1eea653984d980aaeac7bcd3a30d1092e506f631dd431">Testcase 3</a></li></ul></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#8376fd2a3e444ff463387ca863c37edc212b9272b2cfe4a95c9100c1dccfea3f">Screenshots Section</a><ul class="mkup_UL"><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#1da4244b5ee5f30b64e852cb4fcd75ba574fcc429ecf3f0b5690b307bed62de6">figure 1.</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#c71281d1e05df1a958631120547cfd0604672207b45312b087aca23f98d99fdb">figure 2.</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#fd2c249d8a6107be6666d1735107cb471a12f310cae0032d116569f289417095">figure 3.</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#d36a34541d015e77f2eca3bccbc8555ed1b568c39f5fb69f73ff85be99d02d82">figure 4.</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#c433a06ad32c6d67c8a646c003c2d28145b8865449395c2b692aecf85b1f560e">figure 5.</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#4f7b232da525e0f481341b70b237ee2ebc8148b9fdbd2da8a5332a4424038b40">figure 6.</a></li></ul></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#3d3a074d573e9749137ac430048d53e3783fe7eced95639f6cf8be0a8eeef217">References:</a></li></ul></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#fe390e3262f2848ba3988afd719b455ae1e7b257ceda9fbc8d674acb64d61fa7">Appendix Code</a><ul class="mkup_UL"><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#91e97000326748d418926ea0203dd16d3a12b9374f57bf8e4747e4d0308486f9">appendix TCL programs and scripts</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#e7fbfe54a6ce2d05f5b0e0f0913edc280ca6661b149b0d208e772883ce790e39">Pushbutton Operation</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#e344c236ce314deb2c0e8f794ed535f3ea908ffeafabc611fc7ed059865d9a24">Chinese Horse Race Problem from Nine Chapters (commentary c.260 CE )</a></li></ul></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#a959b851a3c6c7d581ffc4791b38d29804521afc2d6e12c95709ff5ce67a2283">CVS Spreadsheet for Charted Graphical Solution</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#ee552cc643bd97fe0620f002d6895142e73f697c85016a4be520fc10b71767e3">test of Chinese font for Suanshu horse problem 19 of section 7</a></li><li class="mkup_li"><a rel="nofollow" class="mkup_a" href="https://wiki.tcl-lang.org/page/Chinese+Horse+Race+Problems+from+Suanshu%2C+DFP%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis?R=0#28470a55913727ab7417a6bac398038c8f028b89017505501ffc9d52d69670cf">Comments Section</a></li></ul><p class="mkup_p"><a class="mkup_a mkup_known" href="https://wiki.tcl-lang.org/page/gold">gold</a> Here is some eTCL starter code for Chinese Horse Race Problems from Suanshu and double false position algorithm (DFP) in calculator shell. </p><p class="mkup_p">The Chinese used double false position (DFP) to interpolate the solution of a horse race problem in the Suanshu or Nine Chapters (commentary c. 260 CE). For the eTCL console program below, the Chinese miles (li) were converted to kilometers, using the modern .5 km per li constant (since there is some uncertaincy about the Suanshu equivalent miles). The paraphrased horse race problem largely follows the account of Swartz and Shen. A race was staged between a racehorse and a cart horse with a two wheeled cart to Qi City and return. The distance between the Changan home to Qi City is 1500 km. The racehorse has a pace of 96.5 km on the first day and has an increment of 6.5 km each day. The pace of the cart horse is 48.5 and has a decrement of 0.25 km each day. The race horse reaches Qi City first and turns home. Meanwhile the cart horse continues on the road. On what day will the very tired cart horse and returning racehorse meet?</p><p class="mkup_p">To reach the same solution as the Suanshu, considerations are dependent on how the Suanshu counts days, nightwatches, and daily travel. For timing around the day interval of the horse race solution, it is convenient to use sunrise and sunset as watches or interval breakpoints. Each 24 hour day, the horses start about 1/4 or 0.25 day and rest beginning about 3/4 or 0.75 day. At sunset of day 15, the cart horse is 701.25 km from home and the returning racehorse is 870 km from home. The separation of the cart horse and racehorse is 870-701.25 or 168.75 km apart. Whether considering alone the current pace of the racehorse 193.5 km over the 15th day interval or the combined pace of both horses on the 15th (193.5 km and 44.25 km over the interval), the solution can be expected on the next day or the 16th interval. In other modern terms, the horse race solution is bounded 15 > solution < 16 days, calling for a piecewise linear solution to estimate the fraction. </p><p class="mkup_p">The Suanshu solution was 15+ 135/191 or decimal 15.7068 days, ref Shen et al. At sunrise of day 16 (~ 16.25), the horses wake up and continue the race from the conditions of the previous sunset, the cart horse is 701.25 km from home and the returning racehorse is 870 km from home. Both horses have a different and separate paces for the 16th day, but at sunset (~ 16.75) the returning racehorse is 676 km from home and the cart horse is 746 km from home. Clearly, the horses have passed each other between sunrise and sunset on the 16th day interval. On the 16th, the separation of the cart horse and racehorse is 746-676 or 70 km apart. The days 15 and 16 are loaded as the false positions. The error1 is 168.75 km and error2 is 70 km. As a trial calculation, the DFP solution approximates (fp1*e2+ fp2*e1) / (e2+e1), substituting expr (15.*70.+ 16.*168.75) / (168.75+70.) 15.7068 days.</p><p class="mkup_p">Since the preparations for the DFP solution involve adding and subtracting over 16 intervals of fractions, there is ample chance for miscues on the exact solution. The increment on the racehorse is expr((96.5+6.5))/96.5-1 or 0.06735, about 6.7 percent each day. The decrement on the cart horse is exp r((48.5+.25))/48.5-1 or 0.00515, about 0.5 percent each day.The combined error on the eTCL solution, DFP, and hand calculations for the horse race problem would probably be about +- 3 percent relative error. The horse race problem has some analogies to the some lunar eclipse problems, ie. the apparent position of the moon "chasing" and eclipsing the sun etc. Since loading the specific false positions and DFD formula is critical for the Chinese problems, maybe the eTCL logic switch should be modified to allow direct loading of the false positions or errors.</p><p class="mkup_p">The Suanshu uses an indirect stage from direct questions (leap frog) or black boxes the error terms in modern terminology. Since this indirect stage of DFP problems is tricky, one can see why the some much later European works and even translations copied the easy stuff and dropped the indirect DFP methods in the Suanshu. Clearly, the available problems in the Suanshu show the versatility of the double false position method from joint purchases to horse races.</p><p class="mkup_p">In the eTCL calculator, two false positions are supplied as guesses.</p><p class="mkup_p">The DFP logic switch is usually set to 1. Set DFP logic switch 1 for ++ false position errors, 2 for +-, 3 for --, or 4 for negative false position (override) entries. The DFP logic switches 2,3,4 check the calculator results for the Chinese and Arabian variant problems, which may generate negative e1&e2 and negative error sums. The eTCL seems to be working very well, getting a correct solution even with (override) negative entries.</p><hr class="mkup_hr"><table class="mkup_data"><tbody><tr class="mkup_tr"><th class="mkup_th">Mixed Signs and Logic Switches for DFP errors e1&e2</th><th class="mkup_th"></th><th class="mkup_th"></th><th class="mkup_th"> tcl wiki format</th></tr><tr class="mkup_trodd"><td class="mkup_td"> quantity</td><td class="mkup_td"> value</td><td class="mkup_td"> comment, if any</td></tr><tr class="mkup_treven"><td class="mkup_td"> ++ :</td><td class="mkup_td">double surplus</td><td class="mkup_td"> condition +e2>+e1, gets positive error </td></tr><tr class="mkup_trodd"><td class="mkup_td"> +-:</td><td class="mkup_td">mixed surplus deficit </td><td class="mkup_td"> condition +e2>(-e1), gets positive error </td></tr><tr class="mkup_treven"><td class="mkup_td"> -+:</td><td class="mkup_td">mixed deficit surplus </td><td class="mkup_td">condition (-e2)>+e1, gets negative error </td></tr><tr class="mkup_trodd"><td class="mkup_td"> --:</td><td class="mkup_td">double deficit </td><td class="mkup_td"> condition -e2>-e1, gets negative error </td></tr><tr class="mkup_treven"><td class="mkup_td"> ++ :</td><td class="mkup_td">double surplus</td><td class="mkup_td"> set false_position_1 (int (* $side_length (/ 4. 5. )))</td></tr><tr class="mkup_trodd"><td class="mkup_td"> ++ :</td><td class="mkup_td">double surplus</td><td class="mkup_td"> set false_position_1 (int (* $side_length (/ 3. 5. )))</td></tr><tr class="mkup_treven"><td class="mkup_td"> +-:</td><td class="mkup_td">mixed surplus deficit </td><td class="mkup_td"> set false_position_2 (int [* $side_length (/ 6. 4. )))</td></tr><tr class="mkup_trodd"><td class="mkup_td"> +-:</td><td class="mkup_td">mixed surplus deficit </td><td class="mkup_td"> set false_position_2 (int [* $side_length (/ 3. 4. )))</td></tr><tr class="mkup_treven"><td class="mkup_td"> --:</td><td class="mkup_td">double deficit </td><td class="mkup_td"> set false_position_1 (int (* $side_length (/ 8. 4. )))</td></tr><tr class="mkup_trodd"><td class="mkup_td"> --:</td><td class="mkup_td">double deficit </td><td class="mkup_td"> set false_position_2 (int (* $side_length (/ 6. 4. )))</td></tr><tr class="mkup_treven"><td class="mkup_td"> note :</td><td class="mkup_td">calculator works if negative errors generated</td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> </td><td class="mkup_td">but neg e1&e2 and error sum caused terminology & varients in early times</td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> </td><td class="mkup_td">eTCL logic can be changed for generating neg e1&e2 </td><td class="mkup_td"> </td></tr></tbody></table>
<hr class="mkup_hr"><h2 id="1d00da22e97df80a90de5abd3c37e68785a90864a496afb02e50c5068b502b59" class="mkup_h1">Pseudocode Section</h2><div class="sh_sourceCode"><button class="copybtn btn pull-right" data-clipboard-target="#mkup_code_0" title="Click to copy code snippet to clipboard"><span class="glyphicon glyphicon-copy" aria-hidden="true"></span></button><pre id="mkup_code_0" class="sh_tcl sh_sourceCode"><span class="sh_comment"> # using pseudocode </span>
<span class="sh_comment"> # possible problem instances, </span>
initialize algorithm_result <span class="sh_symbol">=</span> <span class="sh_number">1</span><span class="sh_symbol">.</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> false1 <span class="sh_symbol">[</span><a href="https://wiki.tcl-lang.org/page/expr" class="sh_keyword">expr</a> guess <span class="sh_symbol">*</span> <span class="sh_number">3</span><span class="sh_symbol">/</span><span class="sh_number">5</span><span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> false1 <span class="sh_symbol">[</span><a href="https://wiki.tcl-lang.org/page/expr" class="sh_keyword">expr</a> guess <span class="sh_symbol">*</span> <span class="sh_number">4</span><span class="sh_symbol">/</span><span class="sh_number">5</span><span class="sh_symbol">]</span>
calculate f<span class="sh_symbol">(</span>false1<span class="sh_symbol">)</span> and f<span class="sh_symbol">(</span>false2<span class="sh_symbol">)</span>
error1 <span class="sh_symbol">=</span> product <span class="sh_symbol">-</span>f1
error2 <span class="sh_symbol">=</span> product <span class="sh_symbol">-</span>f2
<span class="sh_symbol">[</span><a href="https://wiki.tcl-lang.org/page/expr" class="sh_keyword">expr</a> <span class="sh_symbol">(</span>e2<span class="sh_symbol">*</span>f1<span class="sh_symbol">-</span>e1<span class="sh_symbol">*</span>f2<span class="sh_symbol">)/(</span>e2<span class="sh_symbol">-</span>e1<span class="sh_symbol">)]</span>
check algorithm
f<span class="sh_symbol">(</span>solution<span class="sh_symbol">)</span> <span class="sh_symbol">=?</span> initial product
check_sum <span class="sh_symbol">=</span> a<span class="sh_symbol">+</span>b<span class="sh_symbol">+</span>c<span class="sh_symbol">+</span>d<span class="sh_symbol">+</span>e <span class="sh_symbol">=</span> original real estate
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> answers and printout with resulting values
pseudocode<span class="sh_symbol">:</span> need test cases <span class="sh_symbol">></span> small<span class="sh_symbol">,</span>medium<span class="sh_symbol">,</span> giant
pseudocode<span class="sh_symbol">:</span> need testcases within range of expected operation<span class="sh_symbol">.</span>
pseudocode<span class="sh_symbol">:</span> are there any cases too small or large to be solved<span class="sh_symbol">?</span></pre></div><h3 id="1e716c6ec7b20517217d4f8985661caa379aa38f44d8f15277bdbf870204a4df" class="mkup_h2">Testcases Section</h3><p class="mkup_p">In planning any software, it is advisable to gather a number of testcases to check the results of the program. The math for the testcases can be checked by pasting statements in the TCL console. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the capacity functions (subroutines). </p><h4 id="b00907904f84621888320aae2e88b576be44e91787db940ac4ec901aafd25ad2" class="mkup_h3"> Testcase 1 </h4><table class="mkup_data"><tbody><tr class="mkup_tr"><th class="mkup_th">table 1</th><th class="mkup_th">printed in</th><th class="mkup_th"> tcl wiki format</th></tr><tr class="mkup_trodd"><td class="mkup_td"> quantity</td><td class="mkup_td"> value</td><td class="mkup_td"> comment, if any</td></tr><tr class="mkup_treven"><td class="mkup_td"> 1:</td><td class="mkup_td">testcase_number </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 15.0 :</td><td class="mkup_td">false position fp1 days</td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 16.0 :</td><td class="mkup_td">false position fp2 days </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 168.75 :</td><td class="mkup_td">error1 meters </td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 70.0 :</td><td class="mkup_td">error2 meters </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 1.0 :</td><td class="mkup_td">optional logic switch </td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 15.7068 :</td><td class="mkup_td">answers: days </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 15.7068 :</td><td class="mkup_td">days </td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 15.7068 :</td><td class="mkup_td">days </td><td class="mkup_td"> </td></tr></tbody></table><h4 id="7f6724c630d2d4c5dcdf9906c9a50a02ba82b95094a63daea8729d7e99f73c24" class="mkup_h3"> Testcase 2 </h4><table class="mkup_data"><tbody><tr class="mkup_tr"><th class="mkup_th">table 2</th><th class="mkup_th">printed in</th><th class="mkup_th"> tcl wiki format</th></tr><tr class="mkup_trodd"><td class="mkup_td"> quantity</td><td class="mkup_td"> value</td><td class="mkup_td"> comment, if any</td></tr><tr class="mkup_treven"><td class="mkup_td"> 2:</td><td class="mkup_td">testcase_number </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 10.0 :</td><td class="mkup_td">false position fp1 days</td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 20.0 :</td><td class="mkup_td">false position fp2 days </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 100.0 :</td><td class="mkup_td">error1 meters </td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 120.0 :</td><td class="mkup_td">error2 meters </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 1.0 :</td><td class="mkup_td">optional logic switch </td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 14.545 :</td><td class="mkup_td">answers: days </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 14.545 :</td><td class="mkup_td">days </td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 14.545 :</td><td class="mkup_td">days </td><td class="mkup_td"> </td></tr></tbody></table><h4 id="bf46ab89ae3dcb44d3b1eea653984d980aaeac7bcd3a30d1092e506f631dd431" class="mkup_h3"> Testcase 3 </h4><table class="mkup_data"><tbody><tr class="mkup_tr"><th class="mkup_th">table 3</th><th class="mkup_th">printed in</th><th class="mkup_th"> tcl wiki format</th></tr><tr class="mkup_trodd"><td class="mkup_td"> quantity</td><td class="mkup_td"> value</td><td class="mkup_td"> comment, if any</td></tr><tr class="mkup_treven"><td class="mkup_td"> 3:</td><td class="mkup_td">testcase_number </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 15.0 :</td><td class="mkup_td">false position fp1 days</td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 25.0 :</td><td class="mkup_td">false position fp2 days </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 120.0 :</td><td class="mkup_td">error1 meters </td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 150.0 :</td><td class="mkup_td">error2 meters </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 1.0 :</td><td class="mkup_td">optional logic switch </td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 19.444 :</td><td class="mkup_td">answers: days </td><td class="mkup_td"> </td></tr><tr class="mkup_trodd"><td class="mkup_td"> 19.444 :</td><td class="mkup_td">days </td><td class="mkup_td"> </td></tr><tr class="mkup_treven"><td class="mkup_td"> 19.444 :</td><td class="mkup_td">days </td><td class="mkup_td"> </td></tr></tbody></table><hr class="mkup_hr"><h3 id="8376fd2a3e444ff463387ca863c37edc212b9272b2cfe4a95c9100c1dccfea3f" class="mkup_h2">Screenshots Section</h3><h4 id="1da4244b5ee5f30b64e852cb4fcd75ba574fcc429ecf3f0b5690b307bed62de6" class="mkup_h3">figure 1.</h4><p class="mkup_p"><img class="mkup_img" alt="Chinese Horse Race Problems from Suanshu, DFP, and example eTCL demo calculator screenshot" src="./Chinese Horse Race Problems from Suanshu, DFP, and example eTCL demo calculator, numerical analysis_files/Chinese+Horse+Race+Problems+from+Suanshu,+DFP,+and+example+eTCL+demo+calculator+screenshot"></p><h4 id="c71281d1e05df1a958631120547cfd0604672207b45312b087aca23f98d99fdb" class="mkup_h3">figure 2.</h4><p class="mkup_p"><img class="mkup_img" alt="Ancient Egyptian Double False Position Algorithm and eTCL demo example calculator horse 1" src="./Chinese Horse Race Problems from Suanshu, DFP, and example eTCL demo calculator, numerical analysis_files/Ancient+Egyptian+Double+False+Position+Algorithm+and+eTCL+demo+example+calculator+horse+1"></p><h4 id="fd2c249d8a6107be6666d1735107cb471a12f310cae0032d116569f289417095" class="mkup_h3">figure 3.</h4><p class="mkup_p"><img class="mkup_img" alt="Ancient Egyptian Double False Position Algorithm and eTCL demo race horse increments" src="./Chinese Horse Race Problems from Suanshu, DFP, and example eTCL demo calculator, numerical analysis_files/Ancient+Egyptian+Double+False+Position+Algorithm+and+eTCL+demo+race+horse+increments"></p><h4 id="d36a34541d015e77f2eca3bccbc8555ed1b568c39f5fb69f73ff85be99d02d82" class="mkup_h3">figure 4.</h4><p class="mkup_p"><img class="mkup_img" alt="Ancient Egyptian Double False Position Algorithm and eTCL demo example cart horse decrements" src="./Chinese Horse Race Problems from Suanshu, DFP, and example eTCL demo calculator, numerical analysis_files/Ancient+Egyptian+Double+False+Position+Algorithm+and+eTCL+demo+example+cart+horse+decrements"></p><h4 id="c433a06ad32c6d67c8a646c003c2d28145b8865449395c2b692aecf85b1f560e" class="mkup_h3">figure 5.</h4><p class="mkup_p"><img class="mkup_img" alt="Ancient Egyptian Double False Position Algorithm graphical solution" src="./Chinese Horse Race Problems from Suanshu, DFP, and example eTCL demo calculator, numerical analysis_files/Ancient+Egyptian+Double+False+Position+Algorithm+graphical+solution"></p><h4 id="4f7b232da525e0f481341b70b237ee2ebc8148b9fdbd2da8a5332a4424038b40" class="mkup_h3">figure 6.</h4><p class="mkup_p"><img class="mkup_img" alt="Ancient Egyptian Double False Position Algorithmhorse race detail" src="./Chinese Horse Race Problems from Suanshu, DFP, and example eTCL demo calculator, numerical analysis_files/Ancient+Egyptian+Double+False+Position+Algorithmhorse+race+detail"></p><hr class="mkup_hr"><h3 id="3d3a074d573e9749137ac430048d53e3783fe7eced95639f6cf8be0a8eeef217" class="mkup_h2">References:</h3><ul class="mkup_UL"><li class="mkup_li"><a class="mkup_a mkup_known" href="https://wiki.tcl-lang.org/page/Horseracing+in+Tcl">Horseracing in Tcl</a> by <a class="mkup_a mkup_known" href="https://wiki.tcl-lang.org/page/RS">RS</a></li><li class="mkup_li"><a class="mkup_a mkup_known" href="https://wiki.tcl-lang.org/page/Ancient+Egyptian+Double+False+Position+Algorithm%2C+and+example+eTCL+demo+calculator%2C+numerical+analysis">Ancient Egyptian Double False Position Algorithm, and example eTCL demo calculator, numerical analysis</a></li><li class="mkup_li">Les neuf chapitres : le classique mathématique de la Chine </li><li class="mkup_li">ancienne et ses commentaires , in French and Chinese</li><li class="mkup_li">author(s) Karine Chemla, Guo Shuchun </li><li class="mkup_li">historia mathematica 1 (1974), 47-64 </li><li class="mkup_li">yang hui's commentary on the increase and decrease chapter of Suanshu </li><li class="mkup_li">by lam lay yong, university of singapore </li><li class="mkup_li">Suanshu English translation: Florian Cajori: Arithmetic in Nine Sections, 1893.</li><li class="mkup_li">Suanshu English translation: Lam Lay Yong: Jiu Zhang Suanshu,</li><li class="mkup_li">A Suanshu Overview, Archive for History of Exact Science, 1994 </li><li class="mkup_li">Nine Chapters and Liu Hui's commentary, </li><li class="mkup_li">Nine Chapters on the Mathematical Art, Shen, Oxford 1999</li><li class="mkup_li">The Suanshu, Notes on Nine Chapters, Draft Notes. C. Cullen 2004 </li><li class="mkup_li">Issues in the Origin and Development of Hisab al-Khataâayn</li><li class="mkup_li">(Calculation by Double False Position), Randy K. Schwartz ,</li><li class="mkup_li">Eighth North African Meeting on the History of Arab Mathematics </li><li class="mkup_li">Analysis of ancient Chinese horse race problem,</li><li class="mkup_li">Mingming Leng, Mahmut Parlar1,</li><li class="mkup_li">DeGroote School of Business, McMaster University, Hamilton, Ont., Canada </li><li class="mkup_li">10 December 2004</li><li class="mkup_li">On Generalized Tian Jiâs Horse Racing Strategy, </li><li class="mkup_li">Jian-Jun SHU School of Mechanical & Aerospace Engineering, </li><li class="mkup_li">Nanyang Technological University, 50 Nanyang Avenue, Singapore </li><li class="mkup_li">A Remarkable Collection of Babylonian Mathematical Texts, Joran Friberg,</li><li class="mkup_li">Chalmers University of Technology, Gothenburg, Sweden</li><li class="mkup_li">(major work on Babylonian inheritance problems)</li><li class="mkup_li">Muroi, Kazuo (1988). Inheritance problems of Babylonian mathematics. </li><li class="mkup_li">Historia Scientiarum , 34, 11-19</li><li class="mkup_li">Chabert, J. "Methods of False Position." Ch. 3 in A History of Algorithms: From the Pebble to the Microchip. , 1999. </li><li class="mkup_li">John Hannah , False position in Leonardo of Pisa's Liber Abbaci,Historia Mathematica Volume 34 issue 3 2007 </li><li class="mkup_li">Eugene C. Boman,False Position, Double False Position and Cramer's Rule, College Mathematics Journal</li><li class="mkup_li">Howard Eves ,On the practicality of the rule of false position, Mathematics Teacher Volume 51 </li><li class="mkup_li">Joy B. Easton, the rule of double false position, Mathematics Teacher Volume 60 </li><li class="mkup_li">Vera Sanford, the rule of false position, Mathematics Teacher Volume 44 issue 5 1951 </li><li class="mkup_li">Karine Chemla, Reflections on the World-wide History of the Rule of False Double Position, or: How a Loop Was Closed </li><li class="mkup_li">Thomas G. Edwards -- Using the Ancient Method of False Position to Find Solutions, Mathematics Teaching in the Middle School Volume 14 issue 4 2008 </li><li class="mkup_li"><a class="mkup_a mkup_known" href="https://wiki.tcl-lang.org/page/Oneliner%27s+Pie+in+the+Sky">Oneliner's Pie in the Sky</a> </li><li class="mkup_li"><a class="mkup_a mkup_known" href="https://wiki.tcl-lang.org/page/One+Liners">One Liners</a> </li><li class="mkup_li"><a class="mkup_a mkup_known" href="https://wiki.tcl-lang.org/page/Category+Algorithm">Category Algorithm</a></li><li class="mkup_li"><a class="mkup_a mkup_unknown" href="https://wiki.tcl-lang.org/_new?newpagename=Babylonian+Number+Series+and+eTCL+demo+example+calculator">Babylonian Number Series and eTCL demo example calculator</a></li><li class="mkup_li"><a class="mkup_a mkup_known" href="https://wiki.tcl-lang.org/page/Brahmagupta+Area+of+Cyclic+Quadrilateral+and+eTCL+demo+example+calculator">Brahmagupta Area of Cyclic Quadrilateral and eTCL demo example calculator</a></li><li class="mkup_li"><a class="mkup_a mkup_known" href="https://wiki.tcl-lang.org/page/Gauss+Approximate+Number+of+Primes+and+eTCL+demo+example+calculator">Gauss Approximate Number of Primes and eTCL demo example calculator</a></li><li class="mkup_li">Land surveying in ancient Mesopotamia, M. A. R. Cooper</li><li class="mkup_li"><a class="mkup_a mkup_unknown" href="https://wiki.tcl-lang.org/_new?newpagename=Sumerian+Approximate+Area+Quadrilateral+and+eTCL+Slot+Calculator+Demo+Example+%2C+numerical+analysis">Sumerian Approximate Area Quadrilateral and eTCL Slot Calculator Demo Example , numerical analysis</a> </li><li class="mkup_li">Thomas G. Edwards, Using the Ancient Method of False Position to Find Solutions</li><li class="mkup_li">Joy B. Easton, rule of double false position</li><li class="mkup_li">Vera Sanford, rule of false position</li></ul><h2 id="fe390e3262f2848ba3988afd719b455ae1e7b257ceda9fbc8d674acb64d61fa7" class="mkup_h1">Appendix Code</h2><h3 id="91e97000326748d418926ea0203dd16d3a12b9374f57bf8e4747e4d0308486f9" class="mkup_h2">appendix TCL programs and scripts </h3><div class="sh_sourceCode"><button class="copybtn btn pull-right" data-clipboard-target="#mkup_code_1" title="Click to copy code snippet to clipboard"><span class="glyphicon glyphicon-copy" aria-hidden="true"></span></button><pre id="mkup_code_1" class="sh_tcl sh_sourceCode"><span class="sh_comment"> # pretty print from autoindent and ased editor</span>
<span class="sh_comment"> # Approximate Chinese horse race calculator</span>
<span class="sh_comment"> # written on Windows XP on eTCL</span>
<span class="sh_comment"> # working under TCL version 8.5.6 and eTCL 1.0.1</span>
<span class="sh_comment"> # gold on TCL WIKI, 20feb2017</span>
<a href="https://wiki.tcl-lang.org/page/package" class="sh_keyword">package</a> require Tk
<a href="https://wiki.tcl-lang.org/page/package" class="sh_keyword">package</a> require math<span class="sh_symbol">::</span>numtheory
<a href="https://wiki.tcl-lang.org/page/namespace" class="sh_keyword">namespace</a> path <span class="sh_cbracket">{</span><span class="sh_symbol">::</span>tcl<span class="sh_symbol">::</span>mathop <span class="sh_symbol">::</span>tcl<span class="sh_symbol">::</span>mathfunc math<span class="sh_symbol">::</span>numtheory <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> tcl_precision <span class="sh_number">17</span>
<a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a> <span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a> <span class="sh_symbol">-</span>relief flat <span class="sh_symbol">-</span>bg aquamarine4
<a href="https://wiki.tcl-lang.org/page/pack" class="sh_keyword">pack</a> <span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a> <span class="sh_symbol">-</span>side top <span class="sh_symbol">-</span>fill y <span class="sh_symbol">-</span>anchor center
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> names <span class="sh_cbracket">{{}</span> <span class="sh_cbracket">{</span>false position fp1 days <span class="sh_symbol">:</span><span class="sh_cbracket">}</span> <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/lappend" class="sh_keyword">lappend</a> names <span class="sh_cbracket">{</span>false position fp2 days<span class="sh_symbol">:</span><span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/lappend" class="sh_keyword">lappend</a> names <span class="sh_cbracket">{</span>error1 meters<span class="sh_symbol">:</span> <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/lappend" class="sh_keyword">lappend</a> names <span class="sh_cbracket">{</span>error2 meters<span class="sh_symbol">:</span> <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/lappend" class="sh_keyword">lappend</a> names <span class="sh_cbracket">{</span>optional<span class="sh_symbol">:</span><span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/lappend" class="sh_keyword">lappend</a> names <span class="sh_cbracket">{</span>answers<span class="sh_symbol">:</span> days<span class="sh_symbol">:</span> <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/lappend" class="sh_keyword">lappend</a> names <span class="sh_cbracket">{</span>days<span class="sh_symbol">:</span> <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/lappend" class="sh_keyword">lappend</a> names <span class="sh_cbracket">{</span>days<span class="sh_symbol">:</span> <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/foreach" class="sh_keyword">foreach</a> i <span class="sh_cbracket">{</span><span class="sh_number">1</span> <span class="sh_number">2</span> <span class="sh_number">3</span> <span class="sh_number">4</span> <span class="sh_number">5</span> <span class="sh_number">6</span> <span class="sh_number">7</span> <span class="sh_number">8</span><span class="sh_cbracket">}</span> <span class="sh_cbracket">{</span>
<a href="https://wiki.tcl-lang.org/page/label" class="sh_keyword">label</a> <span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span><a href="https://wiki.tcl-lang.org/page/label" class="sh_keyword">label</a><span class="sh_variable">$i</span> <span class="sh_symbol">-</span><a href="https://wiki.tcl-lang.org/page/text" class="sh_keyword">text</a> <span class="sh_symbol">[</span><a href="https://wiki.tcl-lang.org/page/lindex" class="sh_keyword">lindex</a> <span class="sh_variable">$names</span> <span class="sh_variable">$i</span><span class="sh_symbol">]</span> <span class="sh_symbol">-</span>anchor e
<a href="https://wiki.tcl-lang.org/page/entry" class="sh_keyword">entry</a> <span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span><a href="https://wiki.tcl-lang.org/page/entry" class="sh_keyword">entry</a><span class="sh_variable">$i</span> <span class="sh_symbol">-</span>width <span class="sh_number">35</span> <span class="sh_symbol">-</span>textvariable side<span class="sh_variable">$i</span>
<a href="https://wiki.tcl-lang.org/page/grid" class="sh_keyword">grid</a> <span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span><a href="https://wiki.tcl-lang.org/page/label" class="sh_keyword">label</a><span class="sh_variable">$i</span> <span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span><a href="https://wiki.tcl-lang.org/page/entry" class="sh_keyword">entry</a><span class="sh_variable">$i</span> <span class="sh_symbol">-</span>sticky ew <span class="sh_symbol">-</span>pady <span class="sh_number">2</span> <span class="sh_symbol">-</span>padx <span class="sh_number">1</span> <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/proc" class="sh_keyword">proc</a> about <span class="sh_cbracket">{}</span> <span class="sh_cbracket">{</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> msg <span class="sh_string">"Calculator for Chinese Horse Race </span>
<span class="sh_string"> from TCL WIKI,</span>
<span class="sh_string"> written on eTCL "</span>
tk_messageBox <span class="sh_symbol">-</span>title <span class="sh_string">"About"</span> <span class="sh_symbol">-</span><a href="https://wiki.tcl-lang.org/page/message" class="sh_keyword">message</a> <span class="sh_variable">$msg</span> <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/proc" class="sh_keyword">proc</a> calculate <span class="sh_cbracket">{</span> <span class="sh_cbracket">}</span> <span class="sh_cbracket">{</span>
<a href="https://wiki.tcl-lang.org/page/global" class="sh_keyword">global</a> answer2
<a href="https://wiki.tcl-lang.org/page/global" class="sh_keyword">global</a> side1 side2 side3 side4 side5
<a href="https://wiki.tcl-lang.org/page/global" class="sh_keyword">global</a> side6 side7 side8 flag
<a href="https://wiki.tcl-lang.org/page/global" class="sh_keyword">global</a> testcase_number
<a href="https://wiki.tcl-lang.org/page/incr" class="sh_keyword">incr</a> testcase_number
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> side1 <span class="sh_symbol">[*</span> <span class="sh_variable">$side1</span> <span class="sh_number">1</span><span class="sh_symbol">.</span> <span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> side2 <span class="sh_symbol">[*</span> <span class="sh_variable">$side2</span> <span class="sh_number">1</span><span class="sh_symbol">.</span> <span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> side3 <span class="sh_symbol">[*</span> <span class="sh_variable">$side3</span> <span class="sh_number">1</span><span class="sh_symbol">.</span> <span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> side4 <span class="sh_symbol">[*</span> <span class="sh_variable">$side4</span> <span class="sh_number">1</span><span class="sh_symbol">.</span> <span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> side5 <span class="sh_symbol">[*</span> <span class="sh_variable">$side5</span> <span class="sh_number">1</span><span class="sh_symbol">.</span> <span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> side6 <span class="sh_symbol">[*</span> <span class="sh_variable">$side6</span> <span class="sh_number">1</span><span class="sh_symbol">.</span> <span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> side7 <span class="sh_symbol">[*</span> <span class="sh_variable">$side7</span> <span class="sh_number">1</span><span class="sh_symbol">.</span> <span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> side8 <span class="sh_symbol">[*</span> <span class="sh_variable">$side8</span> <span class="sh_number">1</span><span class="sh_symbol">.</span> <span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> false_postion1 <span class="sh_variable">$side1</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> false_postion2 <span class="sh_variable">$side2</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> error1 <span class="sh_variable">$side3</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> error2 <span class="sh_variable">$side4</span>
<span class="sh_comment"> # initialize solution variable</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> solution_days <span class="sh_number">1</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> solution_days <span class="sh_symbol">[+</span> <span class="sh_symbol">[*</span> <span class="sh_variable">$false_postion1</span> <span class="sh_variable">$error2</span> <span class="sh_symbol">]</span> <span class="sh_symbol">[*</span> <span class="sh_variable">$false_postion2</span> <span class="sh_variable">$error1</span> <span class="sh_symbol">]]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> solution_days <span class="sh_symbol">[/</span> <span class="sh_variable">$solution_days</span> <span class="sh_symbol">[+</span> <span class="sh_variable">$error2</span> <span class="sh_variable">$error1</span> <span class="sh_symbol">]]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> flag <span class="sh_number">1</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> side6 <span class="sh_variable">$solution_days</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> side7 <span class="sh_variable">$solution_days</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> side8 <span class="sh_variable">$solution_days</span>
<span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/proc" class="sh_keyword">proc</a> fillup <span class="sh_cbracket">{</span>aa bb cc dd ee ff gg hh<span class="sh_cbracket">}</span> <span class="sh_cbracket">{</span>
<span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span>entry1 insert <span class="sh_number">0</span> <span class="sh_string">"$aa"</span>
<span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span>entry2 insert <span class="sh_number">0</span> <span class="sh_string">"$bb"</span>
<span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span>entry3 insert <span class="sh_number">0</span> <span class="sh_string">"$cc"</span>
<span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span>entry4 insert <span class="sh_number">0</span> <span class="sh_string">"$dd"</span>
<span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span>entry5 insert <span class="sh_number">0</span> <span class="sh_string">"$ee"</span>
<span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span>entry6 insert <span class="sh_number">0</span> <span class="sh_string">"$ff"</span>
<span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span>entry7 insert <span class="sh_number">0</span> <span class="sh_string">"$gg"</span>
<span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span>entry8 insert <span class="sh_number">0</span> <span class="sh_string">"$hh"</span>
<span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/proc" class="sh_keyword">proc</a> clearx <span class="sh_cbracket">{}</span> <span class="sh_cbracket">{</span>
<a href="https://wiki.tcl-lang.org/page/foreach" class="sh_keyword">foreach</a> i <span class="sh_cbracket">{</span><span class="sh_number">1</span> <span class="sh_number">2</span> <span class="sh_number">3</span> <span class="sh_number">4</span> <span class="sh_number">5</span> <span class="sh_number">6</span> <span class="sh_number">7</span> <span class="sh_number">8</span> <span class="sh_cbracket">}</span> <span class="sh_cbracket">{</span>
<span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a><span class="sh_number">.</span><a href="https://wiki.tcl-lang.org/page/entry" class="sh_keyword">entry</a><span class="sh_variable">$i</span> delete <span class="sh_number">0</span> end <span class="sh_cbracket">}</span> <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/proc" class="sh_keyword">proc</a> reportx <span class="sh_cbracket">{}</span> <span class="sh_cbracket">{</span>
<a href="https://wiki.tcl-lang.org/page/global" class="sh_keyword">global</a> side1 side2 side3 side4 side5
<a href="https://wiki.tcl-lang.org/page/global" class="sh_keyword">global</a> side6 side7 side8
<a href="https://wiki.tcl-lang.org/page/global" class="sh_keyword">global</a> testcase_number flag
<a href="https://wiki.tcl-lang.org/page/console" class="sh_keyword">console</a> show<span class="sh_symbol">;</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"%|table $testcase_number|printed in| tcl wiki format|% "</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"&| quantity| value| comment, if any|& "</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"&| $testcase_number:|testcase_number | |& "</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"&| $side1 :|false position fp1 days| |&"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"&| $side2 :|false position fp2 days | |& "</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"&| $side3 :|error1 meters | |& "</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"&| $side4 :|error2 meters | |&"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"&| $side5 :|optional logic switch | |&"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"&| $side6 :|answers:days | |&"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"&| $side7 :|days | |&"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"&| $side8 :|days | |&"</span>
<span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a> <span class="sh_symbol">.</span>buttons <span class="sh_symbol">-</span>bg aquamarine4
<span class="sh_symbol">::</span><a href="https://wiki.tcl-lang.org/page/ttk::button" class="sh_keyword">ttk::button</a> <span class="sh_symbol">.</span>calculator <span class="sh_symbol">-</span><a href="https://wiki.tcl-lang.org/page/text" class="sh_keyword">text</a> <span class="sh_string">"Solve"</span> <span class="sh_symbol">-</span>command <span class="sh_cbracket">{</span> calculate <span class="sh_cbracket">}</span>
<span class="sh_symbol">::</span><a href="https://wiki.tcl-lang.org/page/ttk::button" class="sh_keyword">ttk::button</a> <span class="sh_symbol">.</span>test2 <span class="sh_symbol">-</span><a href="https://wiki.tcl-lang.org/page/text" class="sh_keyword">text</a> <span class="sh_string">"Testcase1"</span> <span class="sh_symbol">-</span>command <span class="sh_cbracket">{</span>clearx<span class="sh_symbol">;</span>fillup <span class="sh_number">15.0</span> <span class="sh_number">16</span><span class="sh_symbol">.</span> <span class="sh_number">168.75</span> <span class="sh_number">70.0</span> <span class="sh_number">1.0</span> <span class="sh_number">15.7</span> <span class="sh_number">15.7</span> <span class="sh_number">15.7</span><span class="sh_cbracket">}</span>
<span class="sh_symbol">::</span><a href="https://wiki.tcl-lang.org/page/ttk::button" class="sh_keyword">ttk::button</a> <span class="sh_symbol">.</span>test3 <span class="sh_symbol">-</span><a href="https://wiki.tcl-lang.org/page/text" class="sh_keyword">text</a> <span class="sh_string">"Testcase2"</span> <span class="sh_symbol">-</span>command <span class="sh_cbracket">{</span>clearx<span class="sh_symbol">;</span>fillup <span class="sh_number">10.0</span> <span class="sh_number">20.0</span> <span class="sh_number">100.0</span> <span class="sh_number">120.0</span> <span class="sh_number">1.0</span> <span class="sh_number">14.5</span> <span class="sh_number">14.5</span> <span class="sh_number">14.5</span> <span class="sh_cbracket">}</span>
<span class="sh_symbol">::</span><a href="https://wiki.tcl-lang.org/page/ttk::button" class="sh_keyword">ttk::button</a> <span class="sh_symbol">.</span>test4 <span class="sh_symbol">-</span><a href="https://wiki.tcl-lang.org/page/text" class="sh_keyword">text</a> <span class="sh_string">"Testcase3"</span> <span class="sh_symbol">-</span>command <span class="sh_cbracket">{</span>clearx<span class="sh_symbol">;</span>fillup <span class="sh_number">15.0</span> <span class="sh_number">25</span><span class="sh_symbol">.</span> <span class="sh_number">120.0</span> <span class="sh_number">150.0</span> <span class="sh_number">1.0</span> <span class="sh_number">19.5</span> <span class="sh_number">19.5</span> <span class="sh_number">19.5</span> <span class="sh_cbracket">}</span>
<span class="sh_symbol">::</span><a href="https://wiki.tcl-lang.org/page/ttk::button" class="sh_keyword">ttk::button</a> <span class="sh_symbol">.</span>clearallx <span class="sh_symbol">-</span><a href="https://wiki.tcl-lang.org/page/text" class="sh_keyword">text</a> clear <span class="sh_symbol">-</span>command <span class="sh_cbracket">{</span>clearx <span class="sh_cbracket">}</span>
<span class="sh_symbol">::</span><a href="https://wiki.tcl-lang.org/page/ttk::button" class="sh_keyword">ttk::button</a> <span class="sh_symbol">.</span>about <span class="sh_symbol">-</span><a href="https://wiki.tcl-lang.org/page/text" class="sh_keyword">text</a> about <span class="sh_symbol">-</span>command <span class="sh_cbracket">{</span>about<span class="sh_cbracket">}</span>
<span class="sh_symbol">::</span><a href="https://wiki.tcl-lang.org/page/ttk::button" class="sh_keyword">ttk::button</a> <span class="sh_symbol">.</span>cons <span class="sh_symbol">-</span><a href="https://wiki.tcl-lang.org/page/text" class="sh_keyword">text</a> report <span class="sh_symbol">-</span>command <span class="sh_cbracket">{</span> reportx <span class="sh_cbracket">}</span>
<span class="sh_symbol">::</span><a href="https://wiki.tcl-lang.org/page/ttk::button" class="sh_keyword">ttk::button</a> <span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/exit" class="sh_keyword">exit</a> <span class="sh_symbol">-</span><a href="https://wiki.tcl-lang.org/page/text" class="sh_keyword">text</a> <a href="https://wiki.tcl-lang.org/page/exit" class="sh_keyword">exit</a> <span class="sh_symbol">-</span>command <span class="sh_cbracket">{</span><a href="https://wiki.tcl-lang.org/page/exit" class="sh_keyword">exit</a><span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/pack" class="sh_keyword">pack</a> <span class="sh_symbol">.</span>calculator <span class="sh_symbol">-</span>in <span class="sh_symbol">.</span>buttons <span class="sh_symbol">-</span>side top <span class="sh_symbol">-</span>padx <span class="sh_number">10</span> <span class="sh_symbol">-</span>pady <span class="sh_number">5</span>
<a href="https://wiki.tcl-lang.org/page/pack" class="sh_keyword">pack</a> <span class="sh_symbol">.</span>clearallx <span class="sh_symbol">.</span>cons <span class="sh_symbol">.</span>about <span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/exit" class="sh_keyword">exit</a> <span class="sh_symbol">.</span>test4 <span class="sh_symbol">.</span>test3 <span class="sh_symbol">.</span>test2 <span class="sh_symbol">-</span>side bottom <span class="sh_symbol">-</span>in <span class="sh_symbol">.</span>buttons
<a href="https://wiki.tcl-lang.org/page/grid" class="sh_keyword">grid</a> <span class="sh_symbol">.</span><a href="https://wiki.tcl-lang.org/page/frame" class="sh_keyword">frame</a> <span class="sh_symbol">.</span>buttons <span class="sh_symbol">-</span>sticky ns <span class="sh_symbol">-</span>pady <span class="sh_cbracket">{</span><span class="sh_number">0</span> <span class="sh_number">10</span><span class="sh_cbracket">}</span>
<span class="sh_symbol">.</span> configure <span class="sh_symbol">-</span>background aquamarine4 <span class="sh_symbol">-</span>highlightcolor brown <span class="sh_symbol">-</span>relief raised <span class="sh_symbol">-</span>border <span class="sh_number">30</span>
wm title <span class="sh_symbol">.</span> <span class="sh_string">"Chinese Horse Race Calculator"</span> </pre></div><hr class="mkup_hr"><h3 id="e7fbfe54a6ce2d05f5b0e0f0913edc280ca6661b149b0d208e772883ce790e39" class="mkup_h2"> Pushbutton Operation</h3><p class="mkup_p">For the push buttons, the recommended procedure is push testcase and fill frame, change first three entries etc, push solve, and then push report. Report allows copy and paste from console. </p><p class="mkup_p">For testcases in a computer session, the eTCL calculator increments a new testcase number internally, eg. TC(1), TC(2) , TC(3) , TC(N). The testcase number is internal to the calculator and will not be printed until the report button is pushed for the current result numbers. The current result numbers will be cleared on the next solve button. The command { calculate; reportx } or { calculate ; reportx; clearx } can be added or changed to report automatically. Another wrinkle would be to print out the current text, delimiters, and numbers in a TCL wiki style table as</p><div class="sh_sourceCode"><button class="copybtn btn pull-right" data-clipboard-target="#mkup_code_2" title="Click to copy code snippet to clipboard"><span class="glyphicon glyphicon-copy" aria-hidden="true"></span></button><pre id="mkup_code_2" class="sh_tcl sh_sourceCode"> <a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">" %| testcase $testcase_number | value| units |comment |%"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">" &| volume| $volume| cubic meters |based on length $side1 and width $side2 |&"</span> </pre></div><hr class="mkup_hr"><h3 id="e344c236ce314deb2c0e8f794ed535f3ea908ffeafabc611fc7ed059865d9a24" class="mkup_h2">Chinese Horse Race Problem from Nine Chapters (commentary c.260 CE ) </h3><div class="sh_sourceCode"><button class="copybtn btn pull-right" data-clipboard-target="#mkup_code_3" title="Click to copy code snippet to clipboard"><span class="glyphicon glyphicon-copy" aria-hidden="true"></span></button><pre id="mkup_code_3" class="sh_tcl sh_sourceCode"><span class="sh_comment"> # pretty print from autoindent and ased editor</span>
<span class="sh_comment"> # initial console program, Chinese horse race problem</span>
<span class="sh_comment"> # written on Windows XP on eTCL</span>
<span class="sh_comment"> # working under TCL version 8.5.6 and eTCL 1.0.1</span>
<span class="sh_comment"> # gold on TCL WIKI, 10feb2017</span>
<a href="https://wiki.tcl-lang.org/page/package" class="sh_keyword">package</a> require Tk
<a href="https://wiki.tcl-lang.org/page/package" class="sh_keyword">package</a> require math<span class="sh_symbol">::</span>numtheory
<a href="https://wiki.tcl-lang.org/page/namespace" class="sh_keyword">namespace</a> path <span class="sh_cbracket">{</span><span class="sh_symbol">::</span>tcl<span class="sh_symbol">::</span>mathop <span class="sh_symbol">::</span>tcl<span class="sh_symbol">::</span>mathfunc math<span class="sh_symbol">::</span>numtheory <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> tcl_precision <span class="sh_number">17</span>
<a href="https://wiki.tcl-lang.org/page/console" class="sh_keyword">console</a> show
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> race_distance <span class="sh_number">96.5</span>
<span class="sh_comment"> #set china_distance 1500.</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> china_distance <span class="sh_number">1500</span><span class="sh_symbol">.</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> good_horse_pace <span class="sh_number">96.5</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> good_horse_increment <span class="sh_number">6.5</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> cart_horse <span class="sh_number">48.5</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> cart_horse_decrement <span class="sh_number">0.25</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> good_horse_distance <span class="sh_number">96.5</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> cart_horse_distance <span class="sh_number">48.5</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> cart_horse_distance <span class="sh_number">48.5</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> good_horse_tally <span class="sh_number">96.5</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> cart_horse_tally <span class="sh_number">48.5</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> cart_horse_tallyx <span class="sh_number">0</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> horse_race_days <span class="sh_number">1</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> distance_from_home <span class="sh_number">0</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> i <span class="sh_number">25</span>
<a href="https://wiki.tcl-lang.org/page/while" class="sh_keyword">while</a> <span class="sh_cbracket">{</span><span class="sh_variable">$i</span><span class="sh_symbol">></span><span class="sh_number">0</span><span class="sh_cbracket">}</span> <span class="sh_cbracket">{</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> race_distance <span class="sh_symbol">[+</span> <span class="sh_variable">$race_distance</span> <span class="sh_symbol">[*</span> <span class="sh_variable">$race_distance</span> <span class="sh_variable">$good_horse_increment</span><span class="sh_symbol">]]</span>
<a href="https://wiki.tcl-lang.org/page/if" class="sh_keyword">if</a> <span class="sh_cbracket">{</span> <span class="sh_variable">$horse_race_days</span> <span class="sh_symbol">></span> <span class="sh_number">25</span> <span class="sh_cbracket">}</span> <span class="sh_cbracket">{</span> <a href="https://wiki.tcl-lang.org/page/break" class="sh_keyword">break</a> <span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">"$horse_race_days , $good_horse_tally, $cart_horse_tally , $good_horse_distance , $cart_horse_distance , $distance_from_home "</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> good_horse_distance <span class="sh_symbol">[+</span> <span class="sh_variable">$good_horse_distance</span> <span class="sh_variable">$good_horse_increment</span> <span class="sh_symbol">]</span>
<span class="sh_comment"> #set cart_horse_distance [- $cart_horse_distance $cart_horse_decrement ]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> cart_horse_distance <span class="sh_symbol">[-</span> <span class="sh_variable">$cart_horse_distance</span> <span class="sh_variable">$cart_horse_decrement</span><span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> good_horse_tally <span class="sh_symbol">[+</span> <span class="sh_variable">$good_horse_tally</span> <span class="sh_variable">$good_horse_distance</span> <span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> cart_horse_tally <span class="sh_symbol">[+</span> <span class="sh_variable">$cart_horse_tally</span> <span class="sh_variable">$cart_horse_distance</span><span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> cart_horse_tallyx <span class="sh_symbol">[-</span> <span class="sh_number">1500</span> <span class="sh_variable">$cart_horse_tally</span><span class="sh_symbol">]</span>
<a href="https://wiki.tcl-lang.org/page/if" class="sh_keyword">if</a> <span class="sh_cbracket">{</span> <span class="sh_variable">$good_horse_tally</span> <span class="sh_symbol">></span> <span class="sh_number">1500</span> <span class="sh_cbracket">}</span> <span class="sh_cbracket">{</span> <a href="https://wiki.tcl-lang.org/page/set" class="sh_keyword">set</a> distance_from_home <span class="sh_symbol">[-</span> <span class="sh_number">1500</span> <span class="sh_symbol">[-</span> <span class="sh_variable">$good_horse_tally</span> <span class="sh_number">1500</span><span class="sh_symbol">]]</span><span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/incr" class="sh_keyword">incr</a> horse_race_days <span class="sh_number">1</span>
<span class="sh_comment"> #incr good_horse_distance 1</span>
<span class="sh_comment"> #incr cart_horse_distance 1</span>
<a href="https://wiki.tcl-lang.org/page/incr" class="sh_keyword">incr</a> i <span class="sh_symbol">-</span><span class="sh_number">1</span>
<span class="sh_cbracket">}</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">" &|$good_horse_tally | final good_horse_tally km | | ||&"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">" &|$cart_horse_tally | final cart_horse_tally km | | ||&"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">" &|$horse_race_days | final horse_race_days | | |&"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">" &|$horse_race_days | final horse_race_days | | ||&"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">" &|$horse_race_days | upper bound is average + .5*average | | |&"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">" &|$horse_race_days | hold: lower bound is average - .5*average | | ||&"</span>
<a href="https://wiki.tcl-lang.org/page/puts" class="sh_keyword">puts</a> <span class="sh_string">" &|$horse_race_days | bound:: constant distance or slot | | ||&"</span> </pre></div><hr class="mkup_hr"><h2 id="a959b851a3c6c7d581ffc4791b38d29804521afc2d6e12c95709ff5ce67a2283" class="mkup_h1"> CVS Spreadsheet for Charted Graphical Solution</h2><div class="sh_sourceCode"><button class="copybtn btn pull-right" data-clipboard-target="#mkup_code_4" title="Click to copy code snippet to clipboard"><span class="glyphicon glyphicon-copy" aria-hidden="true"></span></button><pre id="mkup_code_4" class="sh_tcl sh_sourceCode"><span class="sh_number">0</span><span class="sh_symbol">,</span>Horse Race Problem <span class="sh_number">19</span><span class="sh_symbol">/</span><span class="sh_number">20</span><a href="https://wiki.tcl-lang.org/page/in" class="sh_keyword"> in</a> Section <span class="sh_number">7</span> of Suanshu<span class="sh_symbol">,,,,</span>
<span class="sh_number">1</span> <span class="sh_symbol">,</span> <span class="sh_number">96.5</span><span class="sh_symbol">,</span> <span class="sh_number">48.5</span> <span class="sh_symbol">,</span> <span class="sh_number">96.5</span> <span class="sh_symbol">,</span> <span class="sh_number">48.5</span> <span class="sh_symbol">,</span> <span class="sh_number">0</span>
<span class="sh_number">2</span> <span class="sh_symbol">,</span> <span class="sh_number">199.5</span><span class="sh_symbol">,</span> <span class="sh_number">96.75</span> <span class="sh_symbol">,</span> <span class="sh_number">103.0</span> <span class="sh_symbol">,</span> <span class="sh_number">48.25</span> <span class="sh_symbol">,</span> <span class="sh_number">0</span>
<span class="sh_number">3</span> <span class="sh_symbol">,</span> <span class="sh_number">309.0</span><span class="sh_symbol">,</span> <span class="sh_number">144.75</span> <span class="sh_symbol">,</span> <span class="sh_number">109.5</span> <span class="sh_symbol">,</span> <span class="sh_number">48.0</span> <span class="sh_symbol">,</span> <span class="sh_number">0</span>
<span class="sh_number">4</span> <span class="sh_symbol">,</span> <span class="sh_number">425.0</span><span class="sh_symbol">,</span> <span class="sh_number">192.5</span> <span class="sh_symbol">,</span> <span class="sh_number">116.0</span> <span class="sh_symbol">,</span> <span class="sh_number">47.75</span> <span class="sh_symbol">,</span> <span class="sh_number">0</span>
<span class="sh_number">5</span> <span class="sh_symbol">,</span> <span class="sh_number">547.5</span><span class="sh_symbol">,</span> <span class="sh_number">240.0</span> <span class="sh_symbol">,</span> <span class="sh_number">122.5</span> <span class="sh_symbol">,</span> <span class="sh_number">47.5</span> <span class="sh_symbol">,</span> <span class="sh_number">0</span>
<span class="sh_number">6</span> <span class="sh_symbol">,</span> <span class="sh_number">676.5</span><span class="sh_symbol">,</span> <span class="sh_number">287.25</span> <span class="sh_symbol">,</span> <span class="sh_number">129.0</span> <span class="sh_symbol">,</span> <span class="sh_number">47.25</span> <span class="sh_symbol">,</span> <span class="sh_number">0</span>
<span class="sh_number">7</span> <span class="sh_symbol">,</span> <span class="sh_number">812.0</span><span class="sh_symbol">,</span> <span class="sh_number">334.25</span> <span class="sh_symbol">,</span> <span class="sh_number">135.5</span> <span class="sh_symbol">,</span> <span class="sh_number">47.0</span> <span class="sh_symbol">,</span> <span class="sh_number">0</span>
<span class="sh_number">8</span> <span class="sh_symbol">,</span> <span class="sh_number">954.0</span><span class="sh_symbol">,</span> <span class="sh_number">381.0</span> <span class="sh_symbol">,</span> <span class="sh_number">142.0</span> <span class="sh_symbol">,</span> <span class="sh_number">46.75</span> <span class="sh_symbol">,</span> <span class="sh_number">0</span>
<span class="sh_number">9</span> <span class="sh_symbol">,</span> <span class="sh_number">1102.5</span><span class="sh_symbol">,</span> <span class="sh_number">427.5</span> <span class="sh_symbol">,</span> <span class="sh_number">148.5</span> <span class="sh_symbol">,</span> <span class="sh_number">46.5</span> <span class="sh_symbol">,</span> <span class="sh_number">0</span>
<span class="sh_number">10</span> <span class="sh_symbol">,</span> <span class="sh_number">1257.5</span><span class="sh_symbol">,</span> <span class="sh_number">473.75</span> <span class="sh_symbol">,</span> <span class="sh_number">155.0</span> <span class="sh_symbol">,</span> <span class="sh_number">46.25</span> <span class="sh_symbol">,</span> <span class="sh_number">0</span>
ce11 <span class="sh_symbol">,</span> <span class="sh_number">1419.0</span><span class="sh_symbol">,</span> <span class="sh_number">519.75</span> <span class="sh_symbol">,</span> <span class="sh_number">161.5</span> <span class="sh_symbol">,</span> <span class="sh_number">46.0</span> <span class="sh_symbol">,</span> <span class="sh_number">0</span>
<span class="sh_number">12</span> <span class="sh_symbol">,</span> <span class="sh_number">1587.0</span><span class="sh_symbol">,</span> <span class="sh_number">565.5</span> <span class="sh_symbol">,</span> <span class="sh_number">168.0</span> <span class="sh_symbol">,</span> <span class="sh_number">45.75</span> <span class="sh_symbol">,</span> <span class="sh_number">1413.0</span>
<span class="sh_number">13</span> <span class="sh_symbol">,</span> <span class="sh_number">1761.5</span><span class="sh_symbol">,</span> <span class="sh_number">611.0</span> <span class="sh_symbol">,</span> <span class="sh_number">174.5</span> <span class="sh_symbol">,</span> <span class="sh_number">45.5</span> <span class="sh_symbol">,</span> <span class="sh_number">1238.5</span>
<span class="sh_number">14</span> <span class="sh_symbol">,</span> <span class="sh_number">1942.5</span><span class="sh_symbol">,</span> <span class="sh_number">656.25</span> <span class="sh_symbol">,</span> <span class="sh_number">181.0</span> <span class="sh_symbol">,</span> <span class="sh_number">45.25</span> <span class="sh_symbol">,</span> <span class="sh_number">1057.5</span>
<span class="sh_number">15</span> <span class="sh_symbol">,</span> <span class="sh_number">2130.0</span><span class="sh_symbol">,</span> <span class="sh_number">701.25</span> <span class="sh_symbol">,</span> <span class="sh_number">187.5</span> <span class="sh_symbol">,</span> <span class="sh_number">45.0</span> <span class="sh_symbol">,</span> <span class="sh_number">870.0</span>
<span class="sh_number">16</span> <span class="sh_symbol">,</span> <span class="sh_number">2324.0</span><span class="sh_symbol">,</span> <span class="sh_number">746.0</span> <span class="sh_symbol">,</span> <span class="sh_number">194.0</span> <span class="sh_symbol">,</span> <span class="sh_number">44.75</span> <span class="sh_symbol">,</span> <span class="sh_number">676.0</span>
<span class="sh_number">17</span> <span class="sh_symbol">,</span> <span class="sh_number">2524.5</span><span class="sh_symbol">,</span> <span class="sh_number">790.5</span> <span class="sh_symbol">,</span> <span class="sh_number">200.5</span> <span class="sh_symbol">,</span> <span class="sh_number">44.5</span> <span class="sh_symbol">,</span> <span class="sh_number">475.5</span>
<span class="sh_number">18</span> <span class="sh_symbol">,</span> <span class="sh_number">2731.5</span><span class="sh_symbol">,</span> <span class="sh_number">834.75</span> <span class="sh_symbol">,</span> <span class="sh_number">207.0</span> <span class="sh_symbol">,</span> <span class="sh_number">44.25</span> <span class="sh_symbol">,</span> <span class="sh_number">268.5</span>
<span class="sh_number">19</span> <span class="sh_symbol">,</span> <span class="sh_number">2945.0</span><span class="sh_symbol">,</span> <span class="sh_number">878.75</span> <span class="sh_symbol">,</span> <span class="sh_number">213.5</span> <span class="sh_symbol">,</span> <span class="sh_number">44.0</span> <span class="sh_symbol">,</span> <span class="sh_number">55.0</span>
<span class="sh_number">20</span> <span class="sh_symbol">,</span> <span class="sh_number">3165.0</span><span class="sh_symbol">,</span> <span class="sh_number">922.5</span> <span class="sh_symbol">,</span> <span class="sh_number">220.0</span> <span class="sh_symbol">,</span> <span class="sh_number">43.75</span> <span class="sh_symbol">,</span> <span class="sh_symbol">-</span><span class="sh_number">165.0</span> </pre></div><h2 id="ee552cc643bd97fe0620f002d6895142e73f697c85016a4be520fc10b71767e3" class="mkup_h1"> test of Chinese font for Suanshu horse problem 19 of section 7 </h2><p class="mkup_p">listed as problem 20 by some authors</p><div class="sh_sourceCode"><button class="copybtn btn pull-right" data-clipboard-target="#mkup_code_5" title="Click to copy code snippet to clipboard"><span class="glyphicon glyphicon-copy" aria-hidden="true"></span></button><pre id="mkup_code_5" class="sh_tcl sh_sourceCode"><span class="sh_number">1</span><span class="sh_symbol">)</span>çä¸è¶³<span class="sh_symbol">:</span>
This problem deals with terms of lack and surplus<span class="sh_symbol">.</span>
<span class="sh_number">2</span><span class="sh_symbol">)</span>ä»æè¯é¦¬èé§é¦¬ç¼é·å®è³é½ãé½å»é·å®ä¸åéã
This are a good horse and unkempt mane <span class="sh_cbracket">{</span>cart<span class="sh_symbol">?</span> nag<span class="sh_symbol">?</span><span class="sh_cbracket">}</span> horse
<span class="sh_cbracket">{</span>traveling<span class="sh_cbracket">}</span> from Changan to Qi City<span class="sh_symbol">.</span>
Qi City at a distance of three thousand miles
<span class="sh_number">3</span><span class="sh_symbol">)</span>è¯é¦¬åæ¥è¡ä¸ç¾ä¹åä¸éï¼æ¥å¢åä¸éãé§é¦¬åæ¥è¡ä¹åä¸éï¼
Good horse <a href="https://wiki.tcl-lang.org/page/on" class="sh_keyword">on</a> the first day <span class="sh_cbracket">{</span>travels<span class="sh_cbracket">}</span> ninety three three units<span class="sh_symbol">,</span>
increasing thirteen units <span class="sh_cbracket">{</span>each day<span class="sh_cbracket">}</span><span class="sh_symbol">.</span>
In early day of race<span class="sh_symbol">,</span> at the beginning of the day ninety seven<span class="sh_symbol">,</span>
<span class="sh_cbracket">{</span> Additional three <span class="sh_number">3</span><a href="https://wiki.tcl-lang.org/page/in" class="sh_keyword"> in</a> Chinese
original <a href="https://wiki.tcl-lang.org/page/text" class="sh_keyword">text</a><span class="sh_symbol">,</span> but not understood here<span class="sh_cbracket">}</span>
<span class="sh_number">4</span><span class="sh_symbol">)</span>æ¥æ¸åéãè¯é¦¬å
è³é½ï¼å¾©éè¿é§é¦¬ãåå¹¾ä½æ¥ç¸é¢ååè¡å¹¾ä½ï¼
<span class="sh_cbracket">{</span>Cart horse decreases by<span class="sh_cbracket">}</span> half unit each day<span class="sh_symbol">.</span>
Good horse is first to Qi city<span class="sh_symbol">,</span>
and returns <span class="sh_cbracket">{</span>to meet the cart<span class="sh_symbol">?</span><span class="sh_cbracket">}</span> horse<span class="sh_symbol">.</span>
Ask the geometric day to meet and the geometry of each track<span class="sh_symbol">?</span>
<span class="sh_number">5</span><span class="sh_symbol">)</span>çæ°ï¼ä¸åäºæ¥ãä¸ç¾ä¹åä¸åæ¥ä¹ä¸ç¾ä¸åäºèç¸é¢ã
Answer<span class="sh_symbol">:</span> At fifteen days<span class="sh_symbol">,</span> one hundred and
ninety one one hundred and thirty and five <span class="sh_cbracket">{</span>horses<span class="sh_cbracket">}</span> meet<span class="sh_symbol">.</span>
<span class="sh_cbracket">{</span>Chinese fraction <a href="https://wiki.tcl-lang.org/page/for" class="sh_keyword">for</a> solution<span class="sh_symbol">,</span> <span class="sh_number">15</span> <span class="sh_symbol">+</span> <span class="sh_number">135</span><span class="sh_symbol">/</span><span class="sh_number">191</span> days<span class="sh_cbracket">}</span>
<span class="sh_number">6</span><span class="sh_symbol">)</span>è¯é¦¬è¡ååäºç¾ä¸ååéãä¸ç¾ä¹åä¸åéä¹ååå
ã
Good horse is four thousand five hundred thirty<span class="sh_symbol">-</span>four<span class="sh_symbol">,</span>
one hundred forty<span class="sh_symbol">-</span>one hundred forty<span class="sh_symbol">-</span>six units
<span class="sh_cbracket">{</span>Chinese fraction <a href="https://wiki.tcl-lang.org/page/for" class="sh_keyword">for</a> race horse<span class="sh_symbol">,</span> <span class="sh_number">4534</span> <span class="sh_symbol">+</span> <span class="sh_number">46</span><span class="sh_symbol">/</span><span class="sh_number">191</span> units<span class="sh_cbracket">}</span>
<span class="sh_number">7</span><span class="sh_symbol">)</span>é§é¦¬è¡ä¸ååç¾å
åäºéãä¸ç¾ä¹åä¸åéä¹ä¸ç¾ååäºã
Four thousand four hundred and sixty five hundred miles<span class="sh_symbol">,</span>
one hundred and ninety one hundred and one hundred and forty five<span class="sh_symbol">.</span>
<span class="sh_cbracket">{</span>Chinese fraction <a href="https://wiki.tcl-lang.org/page/for" class="sh_keyword">for</a> cart horse<span class="sh_symbol">,</span> <span class="sh_number">1465</span><span class="sh_symbol">+</span> <span class="sh_number">145</span><span class="sh_symbol">/</span><span class="sh_number">191</span> units <span class="sh_cbracket">}</span>
<span class="sh_number">8</span><span class="sh_symbol">)</span>è¡æ°ï¼å令åäºæ¥ï¼ä¸è¶³ä¸ç¾ä¸åä¸éåã令ä¹åå
æ¥ï¼å¤ä¸ç¾ååéã
scholar <span class="sh_cbracket">{</span>Liu<span class="sh_cbracket">}</span> said<span class="sh_symbol">:</span> leave fifteen days<span class="sh_symbol">,</span>
less than three hundred thirty<span class="sh_symbol">-</span>seven<a href="https://wiki.tcl-lang.org/page/in" class="sh_keyword"> in</a> half<span class="sh_symbol">.</span>
So that <a href="https://wiki.tcl-lang.org/page/on" class="sh_keyword">on</a> the 16th<span class="sh_symbol">,</span> more than one hundred and forty miles<span class="sh_symbol">.</span>
<span class="sh_cbracket">{</span>Chinese fraction <a href="https://wiki.tcl-lang.org/page/for" class="sh_keyword">for</a> separation distance <a href="https://wiki.tcl-lang.org/page/on" class="sh_keyword">on</a> 15th<span class="sh_symbol">,</span> <span class="sh_number">337</span> <span class="sh_symbol">+</span> <span class="sh_number">1</span><span class="sh_symbol">/</span><span class="sh_number">2</span> units <span class="sh_cbracket">}</span>
<span class="sh_cbracket">{</span>Chinese expression <a href="https://wiki.tcl-lang.org/page/for" class="sh_keyword">for</a> separation distance <a href="https://wiki.tcl-lang.org/page/on" class="sh_keyword">on</a> 16th<span class="sh_symbol">,</span> <span class="sh_number">140</span> units <span class="sh_cbracket">}</span>
<span class="sh_number">9</span><span class="sh_symbol">)</span>以çãä¸è¶³ç¶ä¹å令ä¹æ¸ï¼å¹¶èçºå¯¦ã并çä¸è¶³çºæ³ã
to surplus<span class="sh_symbol">,</span> lack of dimension by the number of instructions<span class="sh_symbol">,</span>
and <a href="https://wiki.tcl-lang.org/page/for" class="sh_keyword">for</a> the real<span class="sh_symbol">.</span> And lack of profit <a href="https://wiki.tcl-lang.org/page/for" class="sh_keyword">for</a> the law<span class="sh_symbol">.</span>
<span class="sh_number">10</span><span class="sh_symbol">)</span>實å¦æ³èä¸ï¼å¾æ¥æ¸ãä¸ç¡è
ï¼ä»¥çæ¸é¤ä¹èå½åã
the real law <span class="sh_cbracket">{</span>and <a href="https://wiki.tcl-lang.org/page/for" class="sh_keyword">for</a> the <a href="https://wiki.tcl-lang.org/page/error" class="sh_keyword">error</a> party of <span class="sh_cbracket">}</span> one<span class="sh_symbol">,</span> the number of days<span class="sh_symbol">.</span>
Not the other<span class="sh_symbol">,</span> in addition to the number of
<span class="sh_comment">#end of file</span>
English paraphrases marked with brackets <span class="sh_cbracket">{}</span>
paraphrased translation of race horse problem <span class="sh_number">19</span><span class="sh_symbol">/</span><span class="sh_number">20</span> from Suanshu
problem deals with terms of insufficient and surplus<span class="sh_symbol">:</span>
<span class="sh_number">3</span> thousands li <span class="sh_symbol">(</span>Chinese miles<span class="sh_symbol">),.</span>
Liang Ma early June<span class="sh_symbol">,</span> increasing <span class="sh_number">193</span> pace intervals<span class="sh_symbol">,</span> <span class="sh_number">13</span> li increments <span class="sh_symbol">.</span>
In the early days of the cart horse<span class="sh_symbol">,</span>
decrements are less one half li <span class="sh_symbol">(</span>Chinese mile<span class="sh_symbol">).</span> Race horse first
Whether geometry<span class="sh_symbol">,</span> reunions and the line geometry<span class="sh_symbol">?</span>
What is the <a href="https://wiki.tcl-lang.org/page/time" class="sh_keyword">time</a> of reunion<span class="sh_symbol">?</span>
answer is<span class="sh_symbol">,</span> <span class="sh_cbracket">{</span>Chinese fraction<span class="sh_cbracket">}</span> <span class="sh_number">191</span> units <span class="sh_symbol">,</span> day <span class="sh_number">135</span> and separated<span class="sh_symbol">.</span>
The starter line Lane<span class="sh_symbol">,</span> <span class="sh_cbracket">{</span>Chinese fraction<span class="sh_cbracket">}</span> <span class="sh_number">191</span> hours<a href="https://wiki.tcl-lang.org/page/in" class="sh_keyword"> in</a> <span class="sh_number">145</span><span class="sh_symbol">.</span></pre></div><p class="mkup_p">end of test</p><p class="mkup_p"><a class="mkup_a mkup_known" href="https://wiki.tcl-lang.org/page/gold">gold</a> This page is copyrighted under the TCL/TK license terms, <a rel="nofollow" class="mkup_a" href="https://www.tcl-lang.org/software/tcltk/license.html">this license</a>. </p><h2 id="28470a55913727ab7417a6bac398038c8f028b89017505501ffc9d52d69670cf" class="mkup_h1">Comments Section</h2><p></p><button class="mkup_button" type="button" id="togglediscussionbutton0" onclick="toggleDiscussion(0);">Show discussion</button><div class="mkup_discussion" id="discussion0"><p class="mkup_p">Please place any comments here, Thanks.</p>
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