Version 12 of Babylonian Number Series and eTCL demo example calculator

Updated 2017-01-02 21:38:06 by gold

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 1printed 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 2printed 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 3printed 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, this license .

Comments Section

Please place any comments here, Thanks.