**Babylonian Number Series 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 number series. # following statements can be pasted into eTCL console ====== set project 1.0 set sum_of_squares [ expr 1*1+2*2+3*3+4*4+5*5+6*6+7*7+8*8+9*9+10*10 ] # answer 385 set sum_of_squares [ expr 5*5+6*6+7*7+8*8+9*9+10*10 ] # answer 355 ====== For the first testcase, the first term is 1, final term is 100, sum is 385. For the second testcase, the final term is 100.For the third testcase, the final term is 55. ---- ***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 | |& &| 0.0 :|start| |& &| 10.0 :|end | |& &| 1.0 :|optional | |& &| 1.0 :|optional | |& &| 0.0 :|answers: initial term | |& &| 100 :|final term | |& &| 385 :|sum | |& &| 385 :|sum | |& **** Testcase 2 **** %|table 2|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 2:|testcase_number | |& &| 2.0 :|start| |& &| 5.0 :|end | |& &| 1.0 :|optional | |& &| 1.0 :|optional | |& &| 1.0 :|answers: initial term | |& &| 25 :|final term | |& &| 54 :|sum | |& &| 54 :|sum | |& **** Testcase 3 **** %|table 3|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 3:|testcase_number | |& &| 0.0 :|start| |& &| 15.0 :|end | |& &| 1.0 :|optional | |& &| 1.0 :|optional | |& &| 1.0 :|answers: initial term | |& &| 225 :|final term | |& &| 1240 :|sum | |& &| 1240 :|sum | |& ---- ***Screenshots Section*** ****figure 1.**** [Babylonian Number Series and eTCL demo example calculator screenshot] ****figure 1.**** [Old Babylonian Interest Rates and eTCL demo example calculator screenshot] [Babylonian Number Series and eTCL demo example calculator screenshot] ---- ***References:*** * goggle "Babylonian Number cuneiform Series" * [Oneliner's Pie in the Sky] * [One Liners] * google < Babylonian Interest Rates Wikipedia > * Ancient Babylonian Algorithms, Donald E. Knuth, Stanford University * The oldest example of compound interest in Sumer, seventh power of four thirds (4/3)**7 , Kazuo MUROI * Interest, Price, and Profit: An Overview of Mathematical Economics in YBC 46981, * Robert Middeke-Conlin Christine Proust, CNRS and Université Paris Diderot * Compound Interest Doubling Time Rule: Extensions and Examples from Antiquities, * Saad Taha Bakir, ISSN: 2241 - 1968 (print), 2241 – 195X (online) * Two Sumerian Words of Fractions in Babylonian Mathematics: igi-n-gál and igi-te-en , Kazuo MUROI * O. Neugebauer and A. Sachs, Mathematical Cuneiform Texts, American Oriental Society, Series 29. New Haven, 1945. * K. Muroi, Interest Calculation in Babylonian Mathematics: * New Interpretations of VAT 8521 and VAT 8528, Historia Scientiarum, 39, (1990), 29-34 * O. Nuegebauer, The Exact Sciences in Antiquity, Second edition, Dover Publication Inc., New York, 1969 ---- **Appendix Code** ***appendix TCL programs and scripts *** ====== # pretty print from autoindent and ased editor # Babylonian Number Series calculator # written on Windows XP on eTCL # working under TCL version 8.5.6 and eTCL 1.0.1 # gold on TCL WIKI, 15dec2016 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 {{} {start :} } lappend names {end :} lappend names {optional : } lappend names {optional : } lappend names {answers: initial term :} lappend names {final term: } lappend names {sum: } lappend names {sum:} 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 Number Series from TCL WIKI, written on eTCL " tk_messageBox -title "About" -message $msg } proc sum_function { start end } { global side1 side2 side3 side4 side5 global side6 side7 side8 set sum 0 set counter 1 set start [int $start ] set counter [int $start ] set end [int $end ] while { $counter < 1E6 } { set sum [+ $sum [* $counter $counter ]] if { $counter < $start } {set side5 [* $counter $counter ] } set side6 [* $counter $counter ] if { $counter > [- $end 1. ] } { break} incr counter } return $sum } 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 start $side1 set end $side2 set sum_of_squares [sum_function $start $end ] set side7 $sum_of_squares set side8 $sum_of_squares } proc fillup {aa bb cc dd ee ff gg hh} { .frame.entry1 insert 0 "$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 :|start| |&" puts "&| $side2 :|end | |& " puts "&| $side3 :|optional | |& " puts "&| $side4 :|optional | |&" puts "&| $side5 :|answers: initial term | |&" puts "&| $side6 :|final term | |&" puts "&| $side7 :|sum | |&" puts "&| $side8 :|sum | |&" } frame .buttons -bg aquamarine4 ::ttk::button .calculator -text "Solve" -command { calculate } ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 0.0 10. 1.0 1.0 0.0 100. 385 385} ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 2.0 5.0 1.0 1.0 1.0 25. 55. 55. } ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 0.0 15. 1.0 1.0 1.0 225 1240 1240 } ::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 Number Series 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