## Brahmagupta Area of Cyclic Quadrilateral and eTCL demo example calculator, numerical analysis

This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Aside from your courtesy, your wiki MONIKER and date as a signature and minimal good faith of any internet post are the rules of this TCL-WIKI. Its very hard to reply reasonably without some background of the correspondent on his WIKI bio page. Thanks,gold,12DEC2018

## Introduction

gold Here is some eTCL starter code for Brahmagupta Area of Cyclic Quadrilateral.

### 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 :optional
2.0 :answers: semiperimeter meters
4.0 :cyclic quad perimeter meters
1.0 :cyclic_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 :optional
4.0 :answers: semiperimeter meters
8.0 :cyclic quad perimeter meters
4.0 :cyclic_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 :optional
6.0 :answers: semiperimeter meters
12.0 :cyclic quad perimeter meters
9.0 :cyclic_quad_area meters squared

### References:

• Brahmagupta’s derivation of the area of a cyclic quadrilateral
• Satyanad Kichenassamy
• Brahmagupta formula,mathworld.wolfram.com/
• Heron's Formula and Brahmagupta's Generalization, mathpages.com
• Brahmagupta on wikipedia
• goggle "Brahmagupta cyclic quadrilateral "
• Oneliner's Pie in the Sky
• One Liners
• A little slide-rule
• What if you do not have exp()?
• Category Algorithm
• Asger Aaboe, Episodes from the Early History of Mathematics
• G.Emch, M.D.Srinivas, R.Sridharan editors, Contributions to the History of Indian Mathematics
• Victor J. Katz, A History of Mathematics
• Steven G. Krantz, An Episodic History of Mathematics Mathematical Culture through Problem Solving

## Appendix Code

### appendix TCL programs and scripts

```        # pretty print from autoindent and ased editor
# Brahmagupta Area of Cyclic Quadrilateral calculator
# written on Windows XP on eTCL
# working under TCL version 8.6
# gold on TCL, 15dec2016
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 {optional:}
lappend names {answers: quad semiperimeter meters : }
lappend names {quad perimeter meters : }
lappend names {cyclic_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 Brahmagupta Area of Cyclic Quadrilateral V2
from TCL,
# gold on TCL WIKI, 15dec2016 "
tk_messageBox -title "About" -message \$msg }
proc self_help {} {
set msg "Brahmagupta Area of Cyclic Quadrilateral V2
from TCL ,
# self help listing
# problem, Brahmagupta Area of Cyclic Quadrilateral V2
# 4 givens follow.
1) side a meters :
2) side b meters :
3) side c meters :
4) side d meters :
# 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 to conventional texteditor. For testcases
# testcase number is internal to the calculator and
# will not be printed until the report button is pushed
# for the current result numbers.
# >>> copyright notice <<<
# This posting, screenshots, and TCL source code is
# copyrighted under the TCL/TK license terms.
# Editorial rights and disclaimers
# retained under the TCL/TK license terms
# and will be defended as necessary in court.
Conventional text editor formulas or  grabbed from internet
screens can be pasted into green console.
# gold on  TCL Club, 2Dec2018 "
tk_messageBox -title "Self_Help" -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 perimeter [+ \$side1 \$side2 \$side3 \$side4 ]
set semip [* \$perimeter .5 ]
set cyclic_quad_area [sqrt [* [- \$semip \$side1 ] [- \$semip \$side2 ] [- \$semip \$side3 ] [- \$semip \$side4 ]]]
set side7 \$perimeter
set side8 \$cyclic_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
console show;
console eval {.console config -bg palegreen}
console eval {.console config -font {fixed 20 bold}}
console eval {wm geometry . 40x20}
console eval {wm title . " Brahmagupta Area of Cyclic Quadrilateral  Report   , screen grab and paste from console 2 to texteditor"}
console eval {. configure -background orange -highlightcolor brown -relief raised -border 30}
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 :|optional | |&"
puts "&| \$side6 :|answers: semiperimeter  meters |  |&"
puts "&| \$side7 :|cyclic quad perimeter meters  |  |&"
puts "&| \$side8 :|cyclic_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 .self_help -text self_help -command { self_help }
::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 .self_help .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 . "Brahmagupta Area of Cyclic Quadrilateral Calculator V2"  ```

### 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   |&"  ```

## Comments Section

Please place any comments here with your wiki MONIKER and date, Thanks.gold 12DEC2018

gold 9/27/2021. Switched some comment signs ;# to #. This a big file. Check earlier editions, if not compatible. Maybe obvious, but this page was written on Windows10 Tcl ports including ActiveTCL. I assume that the reader can cut and paste on screen, what the reader needs, and tootle on to his own project and own contribution pages to the TCL Wiki.

 Category Numerical Analysis Category Toys Category Calculator Category Mathematics Category Example Toys and Games Category Games Category Application Category GUI