**Babylonian Irregular Reciprocal Algorithm and eTCL demo example calculator, numerical analysis** 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 in your comment with the same courtesy that I will give you. Its very hard to reply intelligibly without some background of the correspondent. Thanks,[gold] ---- <> [gold] Here is some eTCL starter code for Babylonian irregular reciprocal algorithm in calculator shell. ---- **Pseudocode Section** ====== # using pseudocode for Babylonian irregular reciprocal algorithm. # possible problem instances include, given irregular n , find 1/n # irregular defined as not in standard B. table of reciprocals target_number= supplied value # decompose target number c = a + b a+b is not unique, test a for prime, even, odd? find a as factorable into 2**x, 3**y, 5**z, or a/<(2**x)*(3**y)*(5**z)>??? take (1/a) table lookup (1/a) take (1/a)*(b) take 1/(1+(1/a)*(b)) take (1/a)* (1/(1+(1/a)*(b))) check_answer new area =? desired goal , n*(1/n) =? 1 , (yes/no logic) set answers and printout with resulting values ====== ***Testcases Section*** 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). **** Testcase 1 **** %|table 1|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 1:|testcase_number | |& &| 10.0 :|target number (c=a+b) meters | |& &| 2.0 :|decomposed a meters | |& &| 8.0 :|decomposed b meters | |& &| 1.0 :|answers: optional| |& &| 1. :|optional | |& &| 1. :|optional | |& &| 1.0 :|check product c*(1/c) =? 1 | |& &| 0.100 :|irregular reciprocal meters | |& **** Testcase 2 **** %|table 2|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 2:|testcase_number | |& &| 20.0 :|target number (c=a+b) meters | |& &| 4.0 :|decomposed a meters | |& &| 16.0 :|decomposed b meters | |& &| 1.0 :|answers: optional| |& &| 1. :|optional | |& &| 1. :|optional | |& &| 1.0 :|check product c*(1/c) =? 1 | |& &| 0.050 :|irregular reciprocal meters | |& **** Testcase 3 **** %|table 3|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 3:|testcase_number | |& &| 5.0 :|target number (c=a+b) meters | |& &| 2.0 :|decomposed a meters | |& &| 3.0 :|decomposed b meters | |& &| 1.0 :|answers: optional| |& &| 1. :|optional | |& &| 1. :|optional | |& &| 1.0 :|check product c*(1/c) =? 1 | |& &| 0.200 :|irregular reciprocal meters | |& ---- ***Screenshots Section*** ****figure 1.**** [Babylonian Irregular Reciprocal Algorithm and eTCL demo example calculator screenshot] ---- ***References:*** * Interpretation of reverse algorithms in several mesopotamian texts, Christine Proust * A Geometric Algorithm with Solutions to Quadratic Equations * in a Sumerian Juridical Document from Ur III Umma * Joran Friberg, Chalmers University of Technology, Gothenburg, Sweden * google search engine * Wikipedia search engine * mathworld.wolfram.com, Trapezoid and right trapezoid * Mathematical Treasure: Old Babylonian Area Calculation, uses ancient method * Frank J. Swetz , Pennsylvania State University * Wikipedia, see temple of Edfu, area method used as late as 200 BC in Egypt. * [Oneliner's Pie in the Sky] * [One Liners] * [Category Algorithm] * [Babylonian Number Series and eTCL demo example calculator] * [Brahmagupta Area of Cyclic Quadrilateral and eTCL demo example calculator] * [Gauss Approximate Number of Primes and eTCL demo example calculator] * Land surveying in ancient Mesopotamia, M. A. R. Cooper * [Sumerian Approximate Area Quadrilateral and eTCL Slot Calculator Demo Example , numerical analysis] * Thomas G. Edwards, Using the Ancient Method of False Position to Find Solutions * Joy B. Easton, rule of double false position * Vera Sanford, rule of false position * www.britannica.com, topic, mathematics trapezoid * [Sumerian Equivalency Values, Ratios, and the Law of Proportions with Demo Example Calculator] * [Babylonian Sexagesimal Notation for Math on Clay Tablets in Console Example] * Babylonians Tracked Jupiter With Advanced Tools: Trapezoids, Michael Greshko, news.nationalgeographic.com * Geometry in Babylonian Astronomy, Cluster of Excellence Topology, Humboldt University of Berlin * Mathieu Ossendrijver: „Ancient Babylonian astronomers calculated Jupiter’s position * from the area under a time-velocity graph“, in: Science, January 29, 2016. * Late Babylonian Field Plans in the British Museum, books.google.com/books * Karen Rhea Nemet-Nejat * Late Babylonian Surface Mensuration Author(s): Marvin A. Powell Source: jstor * translation: trapezoid in two babylonian astronomical cuneiform * texts for jupiter (act 813 & act 817) from the seleucid era , 310 BC -75 AD * Otto Neugebauer, Astronomical Cuneiform Texts, 3 Vols. * Lund Humphreys, London, 1955:405,430-31. * DeSegnac, MS 3908 A RE-CONSTRUCTION, D.A.R. DeSegnac * A draft for an essay * DeSegnac, MENTAL COMPUTING OF THREE ARCHAIC * MESOPOTAMIAN PUZZLES W 20044, 35, W 20044, 20 & W 20214, essay draft * DeSegnac, HARMONY OF NUMBERS I and II, D.A.R. DeSegnac, A draft for an essay ---- **Appendix Code** ***appendix TCL programs and scripts *** ====== # pretty print from autoindent and ased editor # Babylonian Irregular Reciprocal Algorithm calculator # written on Windows XP on eTCL # working under TCL version 8.5.6 and 1.0.1 # gold on TCL WIKI, 25jan2017 package require Tk package require math::numtheory namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory } set tcl_precision 17 frame .frame -relief flat -bg aquamarine4 pack .frame -side top -fill y -anchor center set names {{} { target number (c=a+b) meters :} } lappend names { decomposed a meters :} lappend names { decomposed b meters : } lappend names { answers: optional : } lappend names { optional :} lappend names { optional: } lappend names { check product c*(1/c) =? 1 : } lappend names { irregular reciprocal 1/meters :} 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 Babylonian Irregular Reciprocal Algorithm from TCL WIKI, written on eTCL " tk_messageBox -title "About" -message $msg } proc calculate { } { global answer2 global side1 side2 side3 side4 side5 global side6 side7 side8 global testcase_number incr testcase_number set side1 [* $side1 1. ] set side2 [* $side2 1. ] set side3 [* $side3 1. ] set side4 [* $side4 1. ] set side5 [* $side5 1. ] set side6 [* $side6 1. ] set side7 [* $side7 1. ] set side8 [* $side8 1. ] set target_number $side1 set decom_a $side2 set decom_b $side3 set term1 1 set term2 1 # initialize placeholder answer set reciprocal 1. catch {set term1 [* [/ 1. $decom_a ] $decom_b ]} set term2 [/ 1. [+ 1. $term1 ]] set reciprocal [* [/ 1. $decom_a ] $term2 ] set check_answer_product [* $target_number $reciprocal ] # check for lazy entries of zero, revert to modern way of reciprocals if { $side2 < .00001 } { set reciprocal [/ 1. $target_number ] } if { $side3 < .00001 } { set reciprocal [/ 1. $target_number ] } if { $side2 < .00001 } { set check_answer_product [* $target_number $reciprocal ] } if { $side3 < .00001 } { set check_answer_product [* $target_number $reciprocal ] } set side5 1. set side6 1. set side7 $check_answer_product set side8 $reciprocal } proc fillup {aa bb cc dd ee ff gg hh} { .frame.entry1 insert 0 "$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 global side6 side7 side8 global testcase_number reference_factor flag console show; puts "%|table $testcase_number|printed in| tcl wiki format|% " puts "&| quantity| value| comment, if any|& " puts "&| $testcase_number:|testcase_number | |& " puts "&| $side1 :|target number (c=a+b) meters | |&" puts "&| $side2 :|decomposed a meters | |& " puts "&| $side3 :|decomposed b meters | |& " puts "&| $side4 :|answers: optional| |&" puts "&| $side5 :|optional | |&" puts "&| $side6 :|optional | |&" puts "&| $side7 :|check product c*(1/c) =? 1 | |&" puts "&| $side8 :|irregular reciprocal meters | |&" } frame .buttons -bg aquamarine4 ::ttk::button .calculator -text "Solve" -command { calculate } ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 10. 2. 8.0 1. 1. 1. 1. 0.1} ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 20. 4.0 16. 1. 1. 1. 1. .05 } ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 5. 2.0 3.0 1. 1. 1. 1. .2 } ::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 wm title . "Babylonian Irregular Reciprocal Algorithm Calculator" ====== ---- *** Pushbutton Operation*** 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. 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 ====== puts " %| testcase $testcase_number | value| units |comment |%" puts " &| volume| $volume| cubic meters |based on length $side1 and width $side2 |&" ====== **Console program under test. ** ---- [gold] This page is copyrighted under the TCL/TK license terms, [http://tcl.tk/software/tcltk/license.html%|%this license]. **Comments Section** <> Please place any comments here, Thanks. <> Numerical Analysis | Toys | Calculator | Mathematics| Example| Toys and Games | Games | Application | GUI ---- <> Development | Concept| Algorithm