Babylonian False Position Algorithm and eTCL demo example calculator, numerical analysis edit

Page contents

 Babylonian False Position Algorithm and eTCL demo example calculator, numerical analysis

 Pseudocode Section

 Testcases Section

  Testcase 1 

  Testcase 2 

  Testcase 3 

 Screenshots Section

 figure 1.

 References:

 Appendix Code

 appendix TCL programs and scripts 

  Pushbutton Operation

 Comments Section

Pseudocode Section edit

    # using  pseudocode for Babylonian false position algorithm
    # possible problem instances include separate tables for  cubes n*n*n and quasi_cubes
     true_area = supplied value
     false_long_side = initial guess
     false_short_side  =  2/3 length, supplied ratio
     set false_area [expr  $false_long_side*$false_short_side   ]
     initialise correction = 0.25
     correction  = sqrt (true_area / false_area)
     long_side = false_long_side * correction
     short_side  =  false_short_side  * correction
     check_answer   long_side * short_side  =? true_area    (yes/no)
     set answers and printout with resulting values

Testcases Section

Testcase 1

Testcase 2

Testcase 3

Screenshots Section

figure 1.

References:

• Wikipedia <False position method>
• Galdino, Sérgio (2011). "A family of regula falsi root-finding methods".
• Proceedings of 2011 World Congress on Engineering
• 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 false position
• [Sumerian Equivalency Values, Ratios, and the Law of Proportions with Demo Example Calculator]
• Babylonian Sexagesimal Notation for Math on Clay Tablets in Console Example

Appendix Code edit

appendix TCL programs and scripts

        # pretty print from autoindent and ased editor
        # Babylonian False Position 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 {{} { true area meters squared :} }
        lappend names { short side is x of long (ratio) :}
        lappend names { initial guess of long side meters : }
        lappend names { answers: false short side meters : }
        lappend names { false area meters squared :}
        lappend names { correction factor (ratio) : }
        lappend names { short side meters : }
        lappend names { long side 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 False Position 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 true_area $side1
            set false_long $side3
            set false_short [* $false_long $side2 ]
            set false_area [* $false_long  $false_short  ]
            set correction_ratio .25
            set correction_ratio [/  $true_area $false_area]
            set correction_ratio [sqrt $correction_ratio ]
            set side4 $false_short
            set side5 $false_area
            set side6 $correction_ratio
            set side7 [* $false_short $correction_ratio ]
            set side8 [* $side3 $correction_ratio ]  
                    }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$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 :|true area meters squared |   |&"
            puts "&| $side2 :|short side is x of long (ratio)| |& "  
            puts "&| $side3 :|initial guess of long side meters| |& "
            puts "&| $side4 :|answers: false short side meters| |&"
            puts "&| $side5 :|false area meters squared  | |&"
            puts "&| $side6 :|correction factor (ratio) |  |&"
            puts "&| $side7 :|short side meters  |  |&"
            puts "&| $side8 :|long side meters |  |&" 
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1000.0 .666  100.0 66.0  6660.0  0.38 26. 38.}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 1200. .666 120. 79.  9590.0  0.35 28. 42. }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 60.0  .666  10.0 6.66  66.0  0.5  3.33 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 False Position 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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