Babylonian Trapezoid Bisection Algorithm and eTCL demo example calculator, numerical analysis edit

Page contents

 Babylonian Trapezoid Bisection Algorithm and eTCL demo example calculator, numerical analysis

 Introduction

 Pseudocode Section

 Testcases Section

  Testcase 1 

  Testcase 2 

  Testcase 3 

 Screenshots Section

 figure 1.

 figure 2.

 figure 3.

 figure 4.

 References:

 Appendix Code

 appendix TCL programs and scripts 

  Pushbutton Operation

 Comments Section

Introduction edit

Pseudocode Section edit

    # using  pseudocode for Babylonian  trapezoid bisection algorithm. 
    # possible problem instances include trapezoid split in 2 to 7 sections
     long_front = supplied value
     short_front  =  supplied value
     height = supplied value
     solve for bisection length, trapezoid full area, feed (~~ slant info ) 
    # bisection rule  d**2 = (a**2+b**2) /2, d = sqrt ((a**2+b**2) /2)
     set trapezoid_area  h*((a+b)/2)
     set feed ($long_front - $short_front)/$height , negative feed?, need abs
     set bisection  [* [+ [* $long_front $long_front ] [* $short_front $short_front] ] .5 ]
     set bisection [sqrt $bisection ]
     half area =  trapezoid_area  * .5
     quarter area =  trapezoid_area  * .25
     check_answer   trapezoid area =? true_area , second formula   (yes/no)
     set answers and printout with resulting values

Testcases Section

Testcase 1

Testcase 2

Testcase 3

Screenshots Section

figure 1.

figure 2.

figure 3.

figure 4.

References:

• 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 Trapezoid Bisection Algorithm calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI, 15jan2017
        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 {{} { trapezoid long front meters  :} }
        lappend names { trapezoid short front meters :}
        lappend names { height meters : }
        lappend names { answers: feed (~ slant info )  meters : }
        lappend names { quarter area square meters :}
        lappend names { half area square meters : }
        lappend names { area square meters : }
        lappend names { bisection length 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 Trapezoid 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 long_front $side1
            set short_front $side2
            set height $side3
            set feed [abs [/ [- $long_front $short_front ] $height ] ]
            set area [* [* [+ $long_front $short_front] .5 ] $height ]
            # bisection rule  d**2 = (a**2+b**2) /2, d = sqrt ((a**2+b**2) /2)
            set bisection  [* [+ [* $long_front $long_front ] [* $short_front $short_front] ] .5 ]
            set bisection [sqrt $bisection ]
            set side4  $feed
            set side5 [* $area 0.25 ]
            set side6 [* $area 0.5 ]
            set side7 $area 
            set side8 $bisection 
                    }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$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 :|trapezoid long front meters |   |&"
            puts "&| $side2 :|trapezoid short front meters| |& "  
            puts "&| $side3 :|height meters| |& "
            puts "&| $side4 :|answers: feed (~ slant info )  meters| |&"
            puts "&| $side5 :|quarter area square meters  | |&"
            puts "&| $side6 :|half area square meters |  |&"
            puts "&| $side7 :|full area square meters  |  |&"
            puts "&| $side8 :|bisection length meters |  |&" 
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 20.0  10.  14.0 .71  52.5  105. 210. 15.8}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 120. 60. 80. .75  1800.0  3600. 7200. 95. }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 360.0  120.  20.0 12.66  1200.0  2400.  4800. 268.0 }
        ::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 Trapezoid Bisection Algorithm Calculator"      

Pushbutton Operation

  puts " %| testcase $testcase_number | value| units |comment |%"
  puts " &| volume| $volume| cubic meters |based on length $side1 and width $side2   |&"  

this license

Comments Section edit

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