Updated 2017-03-31 14:25:35 by gold

Babylonian Irregular Reciprocal Algorithm and eTCL demo example calculator, numerical analysis edit

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 edit

           # 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 n/<(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 1printed 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 2printed 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 3printed 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.


References:

  • follow-on wiki page Babylonian trailing edge algorithm and reverse sequence algorithm for reciprocals, eTCL demo example calculator, numerical analysis
  • 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 <Trapezoid area bisection>
  • Wikipedia search engine <Trapezoid area >
  • 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 edit

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   |&"  

gold This page is copyrighted under the TCL/TK license terms, this license.

Comments Section edit

Please place any comments here, Thanks.