Updated 2017-01-25 13:28:54 by gold

Babylonian False Position Algorithm and eTCL demo example calculator, numerical analysis edit

gold Here is some eTCL starter code for Babylonian false position algorithm.

The Babylonian false position algorithm was loaded into an eTCL calculator. The Babylonians did not use algebra notation, so the reader will have to bear some anachronisms in the eTCL pseudocode. The field is assumed to be a square or right rectangle. The area of the field and the short side constraint ratio are given values. The tablet has a set of line by line calculations which effectively guess the two sides of a field and compute a scale factor from the sqrt ratio of true area to the product of the guessed or false position sides. The short and long false position sides are constrained, multiplied, and rescaled to calculate the short and long sides of the field. The answer was checked to see if product of the corrected short and long sides equal the given initial area. For restating the problem in a computer algorithm, the sides and field area will be in meters and square meters, respectively.

Pseudocode Section edit

```    # using  pseudocode for Babylonian false position algorithm
# possible problem instances include separate tables for  cubes n*n*n and quasi_cubes
true_area = supplied value
false_long_side = initial guess
false_short_side  =  2/3 length, supplied ratio
set false_area [expr  \$false_long_side*\$false_short_side   ]
initialise correction = 0.25
correction  = sqrt (true_area / false_area)
long_side = false_long_side * correction
short_side  =  false_short_side  * correction
check_answer   long_side * short_side  =? true_area    (yes/no)
set answers and printout with resulting values```

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
1000.0 :true area meters squared
0.6660 :short side is x of long (ratio)
100.0 :initial guess of long side meters
66.600 :answers: false short side meters
6660.000 :false area meters squared
0.387 :correction factor (ratio)
25.806 :short side meters
38.7492 :long side meters

Testcase 2

table 2printed in tcl wiki format
quantity value comment, if any
2:testcase_number
1200.0 :true area meters squared
0.666 :short side is x of long (ratio)
120.0 :initial guess of long side meters
79.920 :answers: false short side meters
9590.399 :false area meters squared
0.353 :correction factor (ratio)
28.270 :short side meters
42.447 :long side meters

Testcase 3

table 3printed in tcl wiki format
quantity value comment, if any
3:testcase_number
60.0 :true area meters squared
0.666 :short side is x of long (ratio)
10.0 :initial guess of long side meters
6.660 :answers: false short side meters
66.599 :false area meters squared
0.949 :correction factor (ratio)
6.321 :short side meters
9.491 :long side meters

Appendix Code edit

appendix TCL programs and scripts

```        # pretty print from autoindent and ased editor
# Babylonian False Position 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 {{} { true area meters squared :} }
lappend names { short side is x of long (ratio) :}
lappend names { initial guess of long side meters : }
lappend names { answers: false short side meters : }
lappend names { false area meters squared :}
lappend names { correction factor (ratio) : }
lappend names { short side meters : }
lappend names { long 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
set msg "Calculator for Babylonian False Position Algorithm
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
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
set false_long \$side3
set false_short [* \$false_long \$side2 ]
set false_area [* \$false_long  \$false_short  ]
set correction_ratio .25
set correction_ratio [/  \$true_area \$false_area]
set correction_ratio [sqrt \$correction_ratio ]
set side4 \$false_short
set side5 \$false_area
set side6 \$correction_ratio
set side7 [* \$false_short \$correction_ratio ]
set side8 [* \$side3 \$correction_ratio ]
}
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 :|true area meters squared |   |&"
puts "&| \$side2 :|short side is x of long (ratio)| |& "
puts "&| \$side3 :|initial guess of long side meters| |& "
puts "&| \$side4 :|answers: false short side meters| |&"
puts "&| \$side5 :|false area meters squared  | |&"
puts "&| \$side6 :|correction factor (ratio) |  |&"
puts "&| \$side7 :|short side meters  |  |&"
puts "&| \$side8 :|long side meters |  |&"
}
frame .buttons -bg aquamarine4
::ttk::button .calculator -text "Solve" -command { calculate   }
::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1000.0 .666  100.0 66.0  6660.0  0.38 26. 38.}
::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 1200. .666 120. 79.  9590.0  0.35 28. 42. }
::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 60.0  .666  10.0 6.66  66.0  0.5  3.33 5.0 }
::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 . "Babylonian False Position Algorithm 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   |&"  ```