Updated 2017-03-07 22:57:48 by gold

Sumerian Approximate Area of Quadrilateral and eTCL demo example calculator, numerical analysis  edit

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Introduction edit

gold Here is some eTCL starter code for Sumerian approximate area of quadrilateral.

This approximate method for quadrilateral area was multipling the averages of opposite sides, area =~ ((s1+s3)*.5)*((s2+s4)*.5). This method or formula was apparently used in some math problems, brother inheritance problems, and court inheritance problems. This formula is not exact and inaccurate for areas other than squares or rectangles, but the issue here is to obtain the equivalent numbers in the ancient texts. Some of the brother inheritance problems called for equal inheritance for some number of brothers, area / N1. Other brother inheritance problems called for proportional schemes.

In the eTCL calculator, a reference factor is calculated and the area calculations are nulled, if the reference_factor does not equal unity. The reference factor is (s1**2+s2**2)/(s3**2+s4**2) which is unity, if the diagonals are perpendicular.

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
1.0 :side a meters
1.0 :side b meters
1.0 :side c meters
1.0 :side d meters
1.0 :answers: inheritance section number
2.0 :quad semiperimeter meters
4.0 :quad perimeter meters
1.0 :inheritance section meters squared
1.0 :approx_quad_area meters squared

Testcase 2

table 2printed in tcl wiki format
quantity value comment, if any
2:testcase_number
2.0 :side a meters
2.0 :side b meters
2.0 :side c meters
2.0 :side d meters
1.0 :answers: inheritance section number
4.0 :quad semiperimeter meters
8.0 :quad perimeter meters
4.0 :inheritance section meters squared
4.0 :approx_quad_area meters squared

Testcase 3

table 3printed in tcl wiki format
quantity value comment, if any
3:testcase_number
3.0 :side a meters
3.0 :side b meters
3.0 :side c meters
3.0 :side d meters
1.0 :answers: inheritance section number
6.0 :quad semiperimeter meters
12.0 :quad perimeter meters
9.0 :inheritance section meters squared
9.0 :approx_quad_area meters squared


Screenshots Section

figure 1.


References:


Appendix Code edit

appendix TCL programs and scripts

        # pretty print from autoindent and ased editor
        # Approximate Area Quadrilateral 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 {{} {side a meters :} }
        lappend names {side b meters:}
        lappend names {side c meters: }
        lappend names {side d meters: }
        lappend names {inheritance sections:}
        lappend names {answers: quad semiperimeter meters : }
        lappend names {quad perimeter meters : }
        lappend names {approx_quad_area meters squared:} 
        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 Approximate Area Quadrilateral 
            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 reference_factor flag
            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 flag 0.
            set inheritance_sections $side5
            set perimeter [+ $side1 $side2 $side3 $side4 ]
            set reference_factor [/ [+ [* $side1 $side1 ] [* $side2 $side2 ]] [+ [* $side3 $side3 ] [* $side4 $side4 ]]]
            if  { $reference_factor > 1.1} { set flag 1. }
            if  { $reference_factor < 0.9} { set flag 1. }
            set semip [* $perimeter .5 ]
            set cyclic_quad_area [sqrt [* [- $semip $side1 ] [- $semip $side2 ] [- $semip $side3 ] [- $semip $side4 ]]]
            set approx_quad_area [* [* .5 [+ $side1 $side3 ]] [* .5 [+ $side2 $side4 ] ] ]
            # calculation nulled if reference_factor offset from unity 
            if { $flag > 0 } { set approx_quad_area 0 }
            set side7 $perimeter
            set side8 $approx_quad_area    
                    }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$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 :|side a meters|   |&"
            puts "&| $side2 :|side b meters   | |& "  
            puts "&| $side3 :|side c meters | |& "
            puts "&| $side4 :|side d meters | |&"
            puts "&| $side5 :|answers: inheritance section number  | |&"
            puts "&| $side6 :|quad semiperimeter  meters |  |&"
            puts "&| $side7 :|quad perimeter meters  |  |&"
            puts "&| $reference_factor :|reference factor  |  |&"
            puts "&| $flag :| flag = 1 and calc nulled, if reference_factor |= 1  |  |&"
            puts "&| [/ $side8 $side5 ] :|inheritance section meters squared |  |&"
            puts "&| $side8 :|approx_quad_area meters squared |  |&" 
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1.0 1.  1.0 1.0  1.0  2. 4. 1.}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 2.0 2.0 2.0 2.0  1.0  4. 8. 4. }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 3.0 3.  3.0 3.0  1.0  6. 12. 9. }
        ::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 . "Approximate Area Quadrilateral 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.