Babylonian Weight Riddle Problems and eTCL demo example calculator, numerical analysis
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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. .
Pseudocode Section
# 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.
Babylonians Tracked Jupiter With Advanced Tools: Trapezoids, Michael Greshko, news.nationalgeographic.com
Geometry in Babylonian Astronomy, Cluster of Excellence Topology, Humboldt University of Berlin
Mathieu Ossendrijver: „Ancient Babylonian astronomers calculated Jupiter’s position
from the area under a time-velocity graph“, in: Science, January 29, 2016.
Late Babylonian Field Plans in the British Museum, books.google.com/books
Karen Rhea Nemet-Nejat
Late Babylonian Surface Mensuration Author(s): Marvin A. Powell Source: jstor
translation: trapezoid in two babylonian astronomical cuneiform
texts for jupiter (act 813 & act 817) from the seleucid era , 310 BC -75 AD
Otto Neugebauer, Astronomical Cuneiform Texts, 3 Vols.
Lund Humphreys, London, 1955:405,430-31.
DeSegnac, MS 3908 A RE-CONSTRUCTION, D.A.R. DeSegnac
A draft for an essay
DeSegnac, MENTAL COMPUTING OF THREE ARCHAIC
MESOPOTAMIAN PUZZLES W 20044, 35, W 20044, 20 & W 20214, essay draft
DeSegnac, HARMONY OF NUMBERS I and II, D.A.R. DeSegnac, A draft for an essay
Appendix Code
appendix TCL programs and scripts
# pretty print from autoindent and ased editor
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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