**Babylonian Cube Root Rule of Eight 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 weight riddle problems in calculator shell. In the cuneiform math problems and coefficient lists on clay tablets, there are coefficient numbers which were used in determining the amount of materials and the daily work rates of the workers. In most cases, the math problem is how the coefficient was used in estimating materials, work rates, and math problems. One difficulty is determining the effective magnitude or power of the number coefficient in the base 60 notation. In cuneiform, numbers in base 60 are written using a relative notation. For example, 20 could represent either 20*3600,20,20/60, 20/3600, or even 1/20. The basic dimensions and final tallies were presented in the cuneiform accounts on clay tablets, but some calculations and some units were left off the tablet. At least one approach for the modern reader and using modern terminology is to develop the implied algebraic equations and decimal equivalents from the cuneiform numbers. Then the eTCL calculator can be run over a number of testcases to validate the algebraic equations. ---- **Pseudocode Section** ====== # using pseudocode for Babylonian cube root rule of eight algorithm # possible problem instances include, given n , # find sqrt(n) from rule of eight and second known sqrt target_number = supplied value # cube root rule of eight algorithm # initilize place holder set target_number 1. B. 7.30 notation = 7/60+30/3600= decimal 0.125, reciprocal of 0.125 = 8 B. 30 notation = 30/60 = 1/2 = decimal 0.5 cube root 0.125 = decimal 0.5 set term2 (8 * (target_number - 0.125)) # assuming integer cube table lookup here set term3 [** $term2 [/ 1. 3. ]] set cube_root_answer .5*term3 issue whether operation is target_number - 0.125 or target_number * 0.125 if target_number * 0.125 is correct, equivalent to (attempt?) removing factor of 8 from target number 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 | |& &| 60.0 :|final weight | |& &| 7.0 :|fraction 1/a | |& &| 11.0 :|fraction 1/b | |& &| 1.0 :|answers: optional| |& &| 1. :|optional | |& &| 1. :|optional | |& &| 1. :|optional | |& &| 48.125 :|initial weight | |& %|table 2|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 2:|testcase_number | |& &| 60.0 :|final weight | |& &| 8.0 :|fraction 1/a | |& &| 12.0 :|fraction 1/b | |& &| 1.0 :|answers: optional| |& &| 1. :|optional | |& &| 1. :|optional | |& &| 1. :|optional | |& &| 49.230769230769234 :|initial weight | |& %|table 3|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 3:|testcase_number | |& &| 120.0 :|final weight | |& &| 12.0 :|fraction 1/a | |& &| 15.0 :|fraction 1/b | |& &| 1.0 :|answers: optional| |& &| 1. :|optional | |& &| 1. :|optional | |& &| 1. :|optional | |& &| 103.84615384615385 :|initial weight | |& (tclprograms) 1 % **** Testcase 2 **** **** Testcase 3 **** ---- ***Screenshots Section*** ****figure 1.**** [Babylonian Cube Root Rule of Eight Algorithm and eTCL demo example calculator screenshoot png] ---- ***References:*** * Extraction of Cube Roots in Babylonian Mathematics, Kazuo Muroi, Centaurus Volume 31, issue 3, 1988 * Babylonian Mathematical Texts II-III Author(s): A. Sachs Source: Journal of Cuneiform Studies, Vol. 6, No. 4 * (1952), pp. 151-156 Published by: The American Schools of Oriental Research * Computing the Cube Root, Ken Turkowski, Apple Computer Technical Report #KT-32 10 February 1998 * Approximating Square Roots and Cube Roots , Ali Ibrahim Hussenom, 2014/11/04 * Aryabhata’s Root Extraction Methods, Abhishek Parakh , Louisiana State University, Aug 31st 2006 * Another Method for Extracting Cube Roots, Brian J. Shelburne, * Dept of Math and Computer, Science Wittenberg University * Jeanette C. Fincke* and Mathieu Ossendrijver* BM 46550 – a Late Babylonian Mathematical Tablet with * Computations of Reciprocal Numbers,Zeitschrift für Assyriologie 2016; 106(2): 185–197 * 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 Weight Riddle Problems 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 {{} { final weight :} } lappend names { fraction 1/a :} lappend names { fraction 1/b : } lappend names { answers: optional : } lappend names { optional :} lappend names { optional : } lappend names { optional : } lappend names { initial weight :} 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 Weight Riddle Problems 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 weight $side1 set fraction1 $side2 set fraction2 $side3 # initialize placeholder answer set result 1. set term1 [+ 1. [/ 1. $fraction1 ]] set term2 [/ 1. $fraction2 ] set term3 [+ $term1 [* $term2 $term1] ] set result [/ $weight $term3 ] set side5 1. set side6 1. set side7 1. set side8 $result } proc fillup {aa bb cc dd ee ff gg hh} { .frame.entry1 insert 0 "$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 console show; puts "%|table $testcase_number|printed in| tcl wiki format|% " puts "&| quantity| value| comment, if any|& " puts "&| $testcase_number:|testcase_number | |& " puts "&| $side1 :|final weight | |&" puts "&| $side2 :|fraction 1/a | |& " puts "&| $side3 :|fraction 1/b | |& " puts "&| $side4 :|answers: optional| |&" puts "&| $side5 :|optional | |&" puts "&| $side6 :|optional | |&" puts "&| $side7 :|optional | |&" puts "&| $side8 :|initial weight | |&" } frame .buttons -bg aquamarine4 ::ttk::button .calculator -text "Solve" -command { calculate } ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 60. 7. 11.0 1. 1. 1. 1. 48.0} ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 60. 8.0 12.0 1. 1. 1. 1. 49.0 } ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 120. 12.0 15.0 1. 1. 1. 1. 104.0 } ::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 Weight Riddle Problems 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 |&" ====== ---- [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