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gold Here is some eTCL starter code for Babylonian cube root rule of eight algorithm in calculator shell.
The Babylonian tablets VAT8587 and YBC6295 with cube root problems have been analysed by Sachs and Muroi. The tablets call for a integer square root solution, but after some manipulation, use a second known integer square root to find the answer. These cube root problems are of historic interest, and there are linguistic and procedural elements in these cube root problems which may aid in understanding other tablets. As best understood, the cube root rule of eight algorithm was loaded into an eTCL calculator shell.
# 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 [** $term2 [/ 1. 3. ]] set cube_root_answer .5*term3 issue whether operation is target_number - 0.125 or target_number * 0.125 if target_number * 0.125 is correct, equivalent to (attempt?) removing factor of 8 from target number set answers and printout with resulting values
In planning any software, it is advisable to gather a number of testcases to check the results of the program. The math for the testcases can be checked by pasting statements in the TCL console. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the capacity functions (subroutines).
# pretty print from autoindent and ased editor # Babylonian Cube Root Algorithm calculator # written on Windows XP on eTCL # working under TCL version 8.5.6 and 1.0.1 # gold on TCL WIKI, 25jan2017 package require Tk package require math::numtheory namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory } set tcl_precision 17 frame .frame -relief flat -bg aquamarine4 pack .frame -side top -fill y -anchor center set names {{} { target number :} } lappend names { optional :} lappend names { optional : } lappend names { answers: optional : } lappend names { optional :} lappend names { optional : } lappend names { optional : } lappend names { cube root :} foreach i {1 2 3 4 5 6 7 8} { label .frame.label$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 Cube Root Algorithm 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 # initialize placeholder answer set cube_root 1. set term1 [- $target_number 0.125 ] set term2 [* $term1 8. ] # assuming table look up here set term3 [** $term2 [/ 1. 3. ]] set cube_root [* $term3 [/ 30. 60.] ] set side5 1. set side6 1. set side7 1. set side8 $cube_root } proc fillup {aa bb cc dd ee ff gg hh} { .frame.entry1 insert 0 "$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 | |&" puts "&| $side2 :|optional | |& " puts "&| $side3 :|optional | |& " puts "&| $side4 :|answers: optional| |&" puts "&| $side5 :|optional | |&" puts "&| $side6 :|optional | |&" puts "&| $side7 :|optional | |&" puts "&| $side8 :|cube root | |&" } frame .buttons -bg aquamarine4 ::ttk::button .calculator -text "Solve" -command { calculate } ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 27. 1. 1.0 1. 1. 1. 1. 3.0} ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 64. 1.0 1.0 1. 1. 1. 1. 4.0 } ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 125. 1.0 1.0 1. 1. 1. 1. 5.0 } ::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 Cube Root Algorithm Algorithm Calculator"
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 |&"
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