*** Stonehenge Circle Accuracy Slot Calculator Example *** This page is under development. Comments are welcome, but please load any comments in the comments section at the middle of the page. Thanks,[gold] ---- [gold] Here is an eTCL script on to estimate Stonehenge Circle Accuracy. For the push buttons, the recommended procedure is push testcase and fill frame, change entries , push solve, and then push report. Report allows copy and paste from console, but takes away from computer "efficiency". ---- The accuracy of Stonehenge is essentially the delta or divergence between the poles over the line of sight distance. For a simple circle of aligned poles, the line of sight distance is treated as the diameter. Later circles or more complex monuments had added causeways to the original line of sight. So the calculator has a causeway length added, if not zero. While the testcases below are in meters, the units cancel out in the accuracy equation. So the units could entered as inches, feet, cubits, or chinese inches. This is an advantage since the units in the ancient Sumerian, Indian, and Chinese texts are open to question. Two or three angular points are needed at a minimum for the divergence, so doorways, doorposts, postholes, columns, and windows measures are usable. Note that the solar and lunar disks have an apparent diameter of 0.5 degrees, so the Stonehenge resolution or accuracy of 0.5 degrees might be expected. pseudocode: accuracy = delta (divergence) over the line of sight distance pseudocode: accuracy in radians = atan ( delta over the line of sight distance ) pseudocode: accuracy in degrees = (180. degrees / pi radians) * atan(ratio) pseudocode: load results into answer fields For most numerical programs, an important work is assembling the testcases, using hand calculators and results of other computer programs. With the TCL console, it is easy enough to write little test programs or demos of the equations or algorithms used. Testcase 1 Stonehenge phase1, Audrey holes. diameter 114 meters. pole divergence 1 meters answer 0.008 radians answer 0.5 degrees. 2900 and 2600 bc Testcase 2 buried Wooden circle , adjacent and possibly comtempory to Stonehenge 2. diameter 75 meters pole divergence 1 meters answer 0.01 radians answer 0.76 degrees. ---- ***Screenshots Section*** [http://img690.imageshack.us/img690/4333/stonetclwiki.gif] ---- '''Comments Section''' Please place any comments here, Thanks. Note, compare the visual style of this new page you have created to other wiki pages on this wiki. Notice how your pages are not in keeping with the high standards of formatting and presentation on the remainder of this wiki. To be a good community member, you should also strive to maintain the existing high quality standards for formatting and presentation as presented on the remainder of this wiki. To do otherwise makes yourself, and the whole wiki community, look bad. You can read the [Formatting Rules] page for details on how to format your submissions, and you can look at existing page formatting for clues as to how something was done. You can even look at some of your own pages that have been reformatted to see how to make the necessary changes. [gold] With respect, I have pretty printed my TCL code from the ased editor, what is free and available on the PC for a recognized TCL format. If you have got a mechanized css format like google and most editors, I'll be happy to print from that. eg. http://google-code-prettify.googlecode.com/svn/trunk/README.html http://code.google.com/chrome/devtools/docs/elements-styles.html The Ased output is at least referenced on the wiki style page, if not blessed. Ref the discussion on Tcl Style Guide, http://wiki.tcl.tk/708. ---- ***References:*** http://flintknapper.com/Woodhenge.htm http://news.bbc.co.uk/2/hi/science/nature/434821.stm http://cahokiamounds.org/explore/cahokia-mounds/woodhenge http://en.wikipedia.org/wiki/Woodhenge http://wiki.worldflicks.org/woodhenge.html#coords=(51.18945745,-1.785568)&z=18 ****Appendix Code**** ****appendix TCL programs and scripts **** ********************* ****Pretty Print VERSION *** ---- # pretty print from autoindent and ased editor # stonehenge circle equation # written on Windowws XP on eTCL # working under TCL version 8.5.6 and eTCL 1.0.1 # gold on TCL WIKI , 10sep2010 package require Tk frame .frame -relief flat -bg aquamarine4 pack .frame -side top -fill y -anchor center set names {{} {diameter meters:} {pole separation} {causeway length} {not used:} {not used:} {not used} {answer radians:} { answer degrees:} } foreach i {1 2 3 4 5 6 7 8} { label .frame.label$i -text [lindex $names $i] -anchor e entry .frame.entry$i -width 35 -textvariable side$i grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 } proc about {} { set msg "Calculator for Stonehenge Circle Accuracy. from TCL WIKI, written on eTCL " tk_messageBox -title "About" -message $msg } proc pi {} {expr acos(-1)} proc interlinear { xx1 yy1 xx3 yy3 xx2 } { return [expr { ((($xx2-$xx1)*($yy3-$yy1))/($xx3-$xx1))+ $yy1 } ] ;} proc pol { xx1 yy1 xx3 yy3 xx2 } { return [expr { ((($xx2-$xx1)*($yy3-$yy1))/($xx3-$xx1))+ $yy1 } ] ;} proc errorx {aa bb} {expr { $aa > $bb ? (($aa*1.)/$bb -1.)*100. : (($bb*1.)/$aa -1.)*100.}} proc height5 { aa bb cc } { set bb [ expr { $cc*[pi]/180. } ] set cc [ expr { $cc*[pi]/180. } ] set dd [ expr { 1.*$aa*tan($bb)*tan($cc)/( tan($cc)-tan($bb))} ] return $dd } proc circle5 { xx1 } { global side1 side2 side3 global side4 side5 side6 side7 side8 set term1 0 set term2 0 set term3 0 set current 0 set tanratio [expr { $side2/($side1+$side3) }] set acc [ expr { atan($tanratio) +.00000000001 } ] set side7 $acc set acc [ expr { (180./[pi])*$acc} ] set side8 $acc return $side8 } proc calculate { } { global colorwarning global colorback global answer2 answer3 global side1 side2 side3 side4 side5 side6 side7 side8 set answer2 5 set answer2 [ circle5 $side8 ] set side8 $answer2 } proc fillup {aa bb cc dd ee ff gg hh} { .frame.entry1 insert 0 "$aa" .frame.entry2 insert 0 "$bb" .frame.entry3 insert 0 "$cc" .frame.entry4 insert 0 "$dd" .frame.entry5 insert 0 "$ee" .frame.entry6 insert 0 "$ff " .frame.entry7 insert 0 "$gg " .frame.entry8 insert 0 "$hh " } proc clearx {} { foreach i {1 2 3 4 5 6 7 8} { .frame.entry$i delete 0 end } } proc reportx {} { global side1 side2 side3 side4 side5 side6 side7 side8 console show; puts " The interpolation function takes two know points on a line and solves for an intermediate point. The points are xx1,yy1 xx2,yy2 and xx3,?yy3? The input order of the five items is xx1 yy1 xx2 yy2 xx3 and solving for ?yy3?. The interpolation function loaded as proc pol. User should be able to write pol 50. 1000. 200. 1200. 150. and save answer (1133.3) on console." puts " $side1 " puts " $side2 " puts " $side3 " puts " $side4 " puts " $side5 " puts " $side6 " puts " $side7 " puts " $side1 " puts " $side2 " puts " $side3 " puts " $side4 " puts " $side5 " puts " $side6 " puts " $side7 " puts " $side8 " puts "answer $side8 " } frame .buttons -bg aquamarine4 ::ttk::button .calculator -text "Solve" -command { calculate } ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 114. 1. 0. 1. 1. 1. .008 .5 } ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 75. 1. 0. 1. 1. 1. .01 .7 } ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 114. 1. 0. 1. 1. 1. .008 .5 } ::ttk::button .clearallx -text clear -command {clearx } ::ttk::button .about -text about -command about ::ttk::button .cons -text report -command { reportx } ::ttk::button .exit -text exit -command {exit} pack .calculator -in .buttons -side top -padx 10 -pady 5 pack .clearallx .cons .about .exit .test4 .test3 .test2 -side bottom -in .buttons grid .frame .buttons -sticky ns -pady {0 10} . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30 bind . {wm title . 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