Updated 2017-03-15 16:04:58 by gold

## Babylonian Combined Market Rates and eTCL demo example calculator, numerical analysis  edit

gold Here is some eTCL starter code for Babylonian Combined Market Rates.

### 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 :aa quantity per silver piece
2.0 :bb quantity per silver piece
3.0 :cc quantity per silver piece
4.0 :dd quantity per silver piece
1.0 :optional:
2.083 :sum_of_fractions
0.480 :combined_market_price
0.480 :combined_market_price

#### Testcase 2

table 2printed in tcl wiki format
quantity value comment, if any
2:testcase_number
3.0 :aa quantity per silver piece
5.0 :bb quantity per silver piece
7.0 :cc quantity per silver piece
9.0 :dd quantity per silver piece
1.0 :optional:
0.787 :sum_of_fractions
1.270 :combined_market_price
1.270 :combined_market_price

#### Testcase 3

table 3printed in tcl wiki format
quantity value comment, if any
3:testcase_number
3.0 :aa quantity per silver piece
4.0 :bb quantity per silver piece
5.0 :cc quantity per silver piece
7.0 :dd quantity per silver piece
1.0 :optional:
0.926 :sum_of_fractions
1.0796 :combined_market_price
1.0796 :combined_market_price

#### Testcase 4

from prices on pump printed in tcl wiki format
1 / (fuel price) fuel price comment, if any
market rate dollars per gallon
0.5524 1.81 regular gas
0.4807 2.08 midgrade gas
0.42918 2.33 premium gas
0.47846 2.09 diesel fuel
dollar was originally a silver piece of one once

table 4printed in tcl wiki format
quantity value comment, if any
4:testcase_number
0.5524 :aa quantity per silver piece
0.48070000000000002 :bb quantity per silver piece
0.42918000000000001 :cc quantity per silver piece
0.47846 :dd quantity per silver piece
1.0 :optional:
8.3106455401769956 :sum_of_fractions
0.1203275961133944 :combined_market_price
0.1203275961133944 :combined_market_price

### References:

• Mathematical Treasure: Old Babylonian Area Calculation, uses ancient method
• Frank J. Swetz , Pennsylvania State University
• Wikipedia, see temple of Edfu, area method used as late as 200 BC in Egypt.
• Oneliner's Pie in the Sky
• One Liners
• Category Algorithm
• Brahmagupta Area of Cyclic Quadrilateral and eTCL demo example calculator
• Gauss Approximate Number of Primes and eTCL demo example calculator
• goggle "Babylonian Number cuneiform Series"
• Oneliner's Pie in the Sky
• One Liners
• google < Babylonian Interest Rates Wikipedia >
• Ancient Babylonian Algorithms, Donald E. Knuth, Stanford University
• The oldest example of compound interest in Sumer, seventh power of four thirds (4/3)**7 , Kazuo MUROI
• Interest, Price, and Proﬁt: An Overview of Mathematical Economics in YBC 46981,
• Robert Middeke-Conlin Christine Proust, CNRS and Université Paris Diderot
• Compound Interest Doubling Time Rule: Extensions and Examples from Antiquities,
• Saad Taha Bakir, ISSN: 2241 - 1968 (print), 2241 – 195X (online)
• Two Sumerian Words of Fractions in Babylonian Mathematics: igi-n-gál and igi-te-en , Kazuo MUROI
• O. Neugebauer and A. Sachs, Mathematical Cuneiform Texts, American Oriental Society, Series 29. New Haven, 1945.
• K. Muroi, Interest Calculation in Babylonian Mathematics:
• New Interpretations of VAT 8521 and VAT 8528, Historia Scientiarum, 39, (1990), 29-34
• O. Nuegebauer, The Exact Sciences in Antiquity, Second edition, Dover Publication Inc., New York, 1969
• Square Root , Keith Vetter
• A little slide-rule
• What if you do not have exp()?
• Category Algorithm
• A Remarkable Collection of Babylonian Mathematical Texts, Joran Friberg, 2007
• Chalmers University of Technology Gothenburg, Sweden
• Weighted means and means as weighted sums
• Morningstar Methodology Paper, Average Price Ratios
• using weighted harmonic mean, August 31, 2005

## Appendix Code edit

### appendix TCL programs and scripts

```        # pretty print from autoindent and ased editor
# Babylonian Combined Market Rate 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 {{} {aa quantity per silver piece :} }
lappend names {bb quantity per silver piece:}
lappend names {cc quantity per silver piece: }
lappend names {dd quantity per silver piece: }
lappend names {optional:}
lappend names {answers: sum_of_fractions  : }
lappend names {combined market rate: }
lappend names {combined market rate:}
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 Combined Market Rate
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 sum_of_fractions [+ [/ 1. \$side1 ] [/ 1. \$side2 ] [/ 1. \$side3 ] [/ 1. \$side4 ] ]
set combined_market_price [/ 1. \$sum_of_fractions ]
set side6 \$sum_of_fractions
set side7 \$combined_market_price
set side8 \$combined_market_price
}
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;
puts "%|table \$testcase_number|printed in| tcl wiki format|% "
puts "&| quantity| value| comment, if any|& "
puts "&| \$testcase_number:|testcase_number | |&"
puts "&| \$side1 :|aa quantity per silver piece|   |&"
puts "&| \$side2 :|bb quantity per silver piece   | |& "
puts "&| \$side3 :|cc quantity per silver piece | |& "
puts "&| \$side4 :|dd quantity per silver piece| |&"
puts "&| \$side5 :|optional:  | |&"
puts "&| \$side6 :|sum_of_fractions |  |&"
puts "&| \$side7 :|combined_market_price |  |&"
puts "&| \$side8 :|combined_market_price |  |&"
}
frame .buttons -bg aquamarine4
::ttk::button .calculator -text "Solve" -command { calculate   }
::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1. 2.  3.0 4.  1.0  2.083 .48 .48}
::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 3.0 5.0 7.0 9.0  1.0  .787 1.27 1.27 }
::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 3.0 4.  5.0 7.0  1.0  0.986 1.07 1.07 }
::ttk::button .clearallx -text clear -command {clearx }
::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 Combined Market Rate 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   |&"  ```