# 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

        # 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"      

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