Babylonian Weight Riddle Problems and eTCL demo example calculator, numerical analysis edit
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gold Here is some eTCL starter code for Babylonian weight riddle problems in calculator shell.The Babylonians did not use algebra notation. The answer was given without worked solution, so problem was solved with algebra, ref Neugebauer and Sachs. User should be able to add and subtract terms of linear equation by 60/+7/+11 or 60/-7/-11 in entry fields. .
# using pseudocode for Babylonian weight riddle problems
# possible problem instances
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 1
printed in
tcl wiki format
quantity
value
comment, if any
1:
testcase_number
60.0 :
final weight
7.0 :
fraction 1/a
11.0 :
fraction 1/b
1.0 :
answers: optional
1. :
optional
1. :
optional
1. :
optional
48.125 :
initial weight
Testcase 2
table 2
printed in
tcl wiki format
quantity
value
comment, if any
2:
testcase_number
60.0 :
final weight
8.0 :
fraction 1/a
12.0 :
fraction 1/b
1.0 :
answers: optional
1. :
optional
1. :
optional
1. :
optional
49.230 :
initial weight
Testcase 3
table 3
printed in
tcl wiki format
quantity
value
comment, if any
3:
testcase_number
120.0 :
final weight
12.0 :
fraction 1/a
15.0 :
fraction 1/b
1.0 :
answers: optional
1. :
optional
1. :
optional
1. :
optional
103.846 :
initial weight
Screenshots Section
figure 1.
References:
Mathematical Cuneiform Texts, Neugebauer and Sachs
Extraction of Cube Roots in Babylonian Mathematics, Kazuo Muroi, Centaurus Volume 31, issue 3, 1988
Babylonian Mathematical Texts II-III Author(s): A. Sachs Source: Journal of Cuneiform Studies, Vol. 6, No. 4
(1952), pp. 151-156 Published by: The American Schools of Oriental Research
Computing the Cube Root, Ken Turkowski, Apple Computer Technical Report #KT-32 10 February 1998
Approximating Square Roots and Cube Roots , Ali Ibrahim Hussenom, 2014/11/04
Aryabhata’s Root Extraction Methods, Abhishek Parakh , Louisiana State University, Aug 31st 2006
Another Method for Extracting Cube Roots, Brian J. Shelburne,
Dept of Math and Computer, Science Wittenberg University
Jeanette C. Fincke* and Mathieu Ossendrijver* BM 46550 – a Late Babylonian Mathematical Tablet with
Computations of Reciprocal Numbers,Zeitschrift für Assyriologie 2016; 106(2): 185–197
Interpretation of reverse algorithms in several mesopotamian texts, Christine Proust
A Geometric Algorithm with Solutions to Quadratic Equations
in a Sumerian Juridical Document from Ur III Umma
Joran Friberg, Chalmers University of Technology, Gothenburg, Sweden
google search engine <Trapezoid area bisection>
Wikipedia search engine <Trapezoid area >
mathworld.wolfram.com, Trapezoid and right trapezoid
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.
# pretty print from autoindent and ased editor
# Babylonian Weight Riddle Problems calculator
# written on Windows XP on eTCL
# working under TCL version 8.5.6 and 1.0.1
# gold on TCL WIKI, 25jan2017
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 {{} { final weight :} }
lappend names { fraction 1/a :}
lappend names { fraction 1/b : }
lappend names { answers: optional : }
lappend names { optional :}
lappend names { optional : }
lappend names { optional : }
lappend names { initial weight :}
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 Weight Riddle Problems
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 weight $side1
set fraction1 $side2
set fraction2 $side3
# initialize placeholder answer
set result 1.
set term1 [+ 1. [/ 1. $fraction1 ]]
set term2 [/ 1. $fraction2 ]
set term3 [+ $term1 [* $term2 $term1] ]
set result [/ $weight $term3 ]
set side5 1.
set side6 1.
set side7 1.
set side8 $result
}
proc fillup {aa bb cc dd ee ff gg hh} {
.frame.entry1 insert 0 "$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 :|final weight | |&"
puts "&| $side2 :|fraction 1/a | |& "
puts "&| $side3 :|fraction 1/b | |& "
puts "&| $side4 :|answers: optional| |&"
puts "&| $side5 :|optional | |&"
puts "&| $side6 :|optional | |&"
puts "&| $side7 :|optional | |&"
puts "&| $side8 :|initial weight | |&"
}
frame .buttons -bg aquamarine4
::ttk::button .calculator -text "Solve" -command { calculate }
::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 60. 7. 11.0 1. 1. 1. 1. 48.0}
::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 60. 8.0 12.0 1. 1. 1. 1. 49.0 }
::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 120. 12.0 15.0 1. 1. 1. 1. 104.0 }
::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 Weight Riddle Problems 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 |&"
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