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

## 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 :inheritance section 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
4.0 :inheritance section 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
9.0 :inheritance section meters squared

## Appendix Code edit

### appendix TCL programs and scripts

```        # pretty print from autoindent and ased editor
# 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 {quad perimeter 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
set msg "Calculator for Approximate Area Quadrilateral
from TCL WIKI,
written on eTCL "
tk_messageBox -title "About" -message \$msg }
proc calculate {     } {
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
}
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 .cons -text report -command { reportx }
::ttk::button .exit -text exit -command {exit}
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   |&"  ```