# using  pseudocode for Babylonian  field expansion procedure algorithm. 
    # possible problem instances include add 1/60 to sides until area goal reached
     long_side = supplied value
     short_side  =  supplied value
     desired_goal  =  supplied value 
    # desired_goal usually 100 square units in some early math problems
     set old_field_area = a*b ,  old field_area = long_side * short_side  
     set new_side_a = long_side + 1/60
     set new_side_b = short_side + 1/60
     set new_field_area = (long_side + 1/60) * ( short_side + 1/60 )
     is  new_field_area =? desired_area within +/- (1/60) , yes = finished loop
     check error , abs (desired_goal -  new_field_area) <= [/ 1. 60.] 
     half area =  area  * .5
     quarter area = area * .25
     check_answer   new area =? desired goal , desired goal reached (yes/no)
     set answers and printout with resulting values

        # pretty print from autoindent and ased editor
        # Babylonian Field Expansion Procedure 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 {{} { long side meters :} }
        lappend names { short side meters :}
        lappend names { desired area (usually 1 iku, 100 square units) : }
        lappend names { answers: old area meters squared : }
        lappend names { area lacking meters squared :}
        lappend names { area from new sides  meters squared: }
        lappend names { long side meters : }
        lappend names { short 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 Field Expansion Procedure 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 $side2 ]
            set desired_area $side3
            # initialize ancient correction fraction
            set correction_fraction [/  1. 60. ]
            set correction_fraction [* [/ [- $desired_area $true_area] $desired_area ] 5. ]
             set counter 1
             while { $counter < 50.  } {
             if { [* [+ $side1 [/ $counter 60. ]] [+ $side2 [/ $counter 60. ]]  ]  > $desired_area } {; break}           
             incr counter   
             }  
            set correction_fraction [/  $counter 60. ]
            set side4 $true_area
            set side5 $correction_fraction
            set side6 [* [+ $side1 $correction_fraction ] [+ $side2 $correction_fraction ]   ]
            set side7 [+ $side1 $correction_fraction ]
            set side8 [+ $side2 $correction_fraction ]  
                    }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$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 :|long side meters |   |&"
            puts "&| $side2 :|short side meters | |& "  
            puts "&| $side3 :|desired area (usually 1 iku, 100 square units)| |& "
            puts "&| $side4 :|answers: old area meters squared| |&"
            puts "&| $side5 :|area lacking meters squared  | |&"
            puts "&| $side6 :|area from new sides  meters squared |  |&"
            puts "&| $side7 :|long side meters  |  |&"
            puts "&| $side8 :|short side meters |  |&" 
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 10.2  9.5  100.0 96.9  0.0166  100.2 10.2 9.51}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 9.6  9.06 100. 86.9  .68  100.2 10.2 9.74 }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 9.5  9.0  100.0 85.5  0.76  100.3  10.26 9.7 }
        ::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 Field Expansion Procedure Algorithm Calculator"  

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

                  # autoindent from ased editor
                  # console program for babylonian field_expansion_procedure.
                  # troubles updating variables below and above solution  
                  # written on Windows XP on eTCL
                  # working under TCL version 8.5.6 and eTCL 1.0.1
                  # TCL WIKI , 28jan2017
             console show
             package require math::numtheory
             namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
             set tcl_precision 17
             proc field_expansion_procedure_function2 { side1 side2 side3 side4 epsilon } { 
             set counter 1
             set token1 $side1
             set token2 $side2
             set epsilon [/ 1. $side4]
             while { $counter < 50.  } {
             if { [abs [- $side3 [* $token1 $token2  1. ] ] ]  < $epsilon } {break;} 
             if { [- $side3 [* $token1 $token2  1. ] ]   > 0 } {set correction_fraction [* 1. [/ 1. $side4]  ]} 
             if { [- $side3 [* $token1 $token2  1. ] ]   < 0 } {set correction_fraction [* -1. [/ 1. $side4]  ]}        
             set correction_fraction [- $side3 [* $token1 $token2  1. ] ]
             set token1 [+ $token1 $correction_fraction ]
             set token2 [+ $token2 $correction_fraction ]  
             incr counter  
             puts "token $token1 token $token2 product [* $token1 $token2 ] correction $correction_fraction"
             }   }
             set side8 [ field_expansion_procedure_function2   5. 4. 100. 60. .15   ]