Version 2 of Sanskrit Number Words Handling in Formulas and Demo Calculator Example

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Sanskrit Number Words Handling in Formulas Demo Calculator Example

This page is under development. Comments are welcome, but please load any comments in the comments section at the middle of the page. Please include your wiki MONIKER in your comment with the same courtesy that I will give you. Its very hard to reply intelligibly without some background of the correspondent. Thanks,gold

# gold Here is an eTCL script on ----

Testcases Section

Testcase 1. 120 degree sector: .5 .25 0.866 120. 0.153 0.3

Testcase 2. 90 degree sector: .5 .353553391 .707 90. 0.071 0.14

Testcase 3. 168 degree sector 10. 1. 19.89 168.52 137.11301 274.2

Coefficients for cuneiform math from clay tablets

english	sumerian	akkadian	area	coefficient	coefficient	ref length	ref length	comment
			square units	decimal	base sixty	decimal	base sixty
circle	ka-kes	kippatum	0.75	0.0833	0;05	3	3;00	circle area = 45/60
square	ib-si	mithartum	1	1	1;00	1	1;00	perimeter = 4 * side,sym. la-gad
semicircle	gan u-sakar	uskarum	0.375	0.1666	0;10	1.5	1;30	semicircumference is 1.5 ,diameter is 1.0
triangle	gan sag-du,sag-kak	santakkum	0.4375	0.5	0;30:00	1	1;00	modern area= 0.5LB,sides are 1.0 and 0.5
rectangle	us-u-sag?	siliptum	0.75	1	1;00	1	1;00	sumerian area= 1.LW,sides are 1.0 and (45/60)
trapezoid	gan sag-ki-gud	mithartum?	0.375	0.5	0;30	1	1;00	modern area= ((B1B2)/2)H,
grain field	gan se?	pannakum	0.1199	0.1094	0;06:33:45	1.0471	0;52:30	120 deg sector
bent stick	illar	tilpanum	0.2397	0.2187	0;13:07:30	1.0471	0;52:30	120 deg sector
oxeye	igi-gu?	in alpim	0.2436	0.2222	0;13:20	1.0471	0;52:30	120 deg sector
barge	ma-gur	makurrum?	0.1369	0.2222	0;13:20	0.875	0;52:30	90 deg sector
wood bow	gan ges-pan	qastum	0.1595	0.2083	0;12:30	0.875	0;52:30	90 deg sector, ~ one seed figure
two seed	2-se	2-uttatum?	0.3194	0.4171	0;25:02	0.875	0;52:30	90 deg sector, ~ two seed
three seed	3-se	3-uttatum?	0.5106	0.6666	0;40	0.875	0;52:30	90 deg sector, ~ three seed
concave square	ab-za-mi?	apsamikkum	0.3402	0.4444	0;26:40	0.875	0;52:30	90 deg sector, ~ four seed
throug?	sa-ka-na-ka-tim?	sakkatum?	0.902	0.902	0;54:07	1	1;	estimated from unlabeled sketch
bullseye	igi-gud	in alpim?	0.2153	0.2182	0;16:52:20	0.875	0;52:30	several tablets involved, maybe inconsistent
poss. lyre?	gan gis-za-mi	sammum?	0.3507	0.4444	0;26:40	0.8888	0;53:19	estimated from unlabeled sketch
bucket?	a-bal	pisannum?	0.75	0.75	0;45	1	1;00	cylinder volume is 0.75 c*c, height is 1 cubit, diameter is 1 cubit

# Notes: These coefficients are partly from the coefficient list and partly from estimates from figures graphed on clay tablets. There was definitely more that one kind of ship type and more than one kind of lyre type. Question mark means uncertain, label not found on tablet, or term rarely found on tablets. Tilde sign (~) means estimated from other numbers. Units refer to unit square of side 1.0 and unit circle with diameter of 1.0. The coefficients of 1 for rectangle and square may seem trivial, but were used as essential unit conversions to Sumerian metrological standards tables ).

Screenshots Section

figure 1.

figure 2.

figure 3.

figure 4.

figure 5. figure 3c.

figure 6.

figure 7.

figure 8a. figure 8b.

figure 10. figure 11. figure 12.

figure 13.

figure 14. figure 15.

figure 16.

figure 17.

figure 18.

a d

e f g.

Comments Section

Please place any comments here, Thanks.

References:

Robson, Eleanor, Mesopotamian Mathematics, 2100-1600BCE,Oxford 1999
Horowitz, Wayne, Late Babylonian Tablet CBS1766, Hebrew University
Steele, J.M. Celestial Measurement in Bablylonian Astronomy,Annals of Science,2007
Mathematical Cuneiform Texts, Neugebauer and A. Sachs, American Oriental Society, 1945
Gregory Zaro and Jon C. Lohse, Maya Solar Observation
Latin American Antiquity, Vol. 16, No. 1 (Mar., 2005), pp. 81-98
Friberg 1987-90:555,Firberg on tablet BM15285
Eclipse Prediction and the Length of the Saros in
Babylonian Astronomy LIS BRACK-BERNSEN∗AND JOHN M. STEELE
Celestial Measurement in Babylonian Astronomy, J. M. STEELE, University of Durham
Amazing Traces of a Babylonian Origin in Greek Mathematics, Jöran Friberg and Joachim Marzahn
The area and the side i added: some old babylonian geometry, duncan j. melville
Mathematics hidden behind the two coefficients of babylonian geometry, kazuo muroi
Especially oven/kiln problem in YBC7997, area of ring annulus complements bullseye figure.

Appendix Code

appendix TCL programs and scripts

Pretty Print Version

        # pretty print from autoindent and ased editor
        # circular segment area
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI , 14may2013
        package require Tk
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center        
        set names {{} {radius meters:} }
        lappend names {distance to chord meters:}
        lappend names {transverse bar meters: }
        lappend names {answer angle degrees:}
        lappend names {answer segment (bow area):}
        lappend names {double segment (seed area):}
        foreach i {1 2 3 4 5 6} {
            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 Circular Segment Area
            from TCL WIKI,
            written on eTCL "            
            tk_messageBox -title "About" -message $msg
        }
        proc pi {} {expr acos(-1)}                
        proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6
            set term1 0
            set term2 0
            set term3 0
            set arcsin .2
            set r $side1
            set x $side2
            set arcsin [ expr {  $x/$r } ]
            set arcsin [ expr { asin($arcsin) } ]
            set sumsquares [ expr {($r*$r-$x*$x) }]
            set area  [ expr {(([pi]/2.)*$r*$r) }]
            set area  [ expr { $area-$x*sqrt($sumsquares) } ]
            set area  [ expr { $area-$r*$r*$arcsin } ]
            set side3 [ expr { 2.*sqrt($sumsquares)} ]
            set side4 [ expr { 2.*(180./[pi])*acos($x/$r)} ]
            set side5 [ expr { (1.* $area)} ]
            set side6 [ expr { (2.* $area)} ]
            return $side5            
        }
        proc fillup {aa bb cc dd ee ff} {            
            .frame.entry1 insert 0 "$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 "$ff"
        }        
        proc clearx {} {
            foreach i {1 2 3 4 5 6 } {
                .frame.entry$i delete 0 end
            }
        }        
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6
            console show;
            puts "radius meters: $side1 "
            puts "distance to chord meters: $side2 "
            puts "transverse bar meters: $side3    "
            puts "answer angle degrees: $side4    "
            puts "answer segment (bow area): $side5    "
            puts "double segment (seed area): $side6    "
        }        
        frame .buttons -bg aquamarine4        
        ::ttk::button .calculator -text "Solve" -command { calculate   }

        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup .5 .25 0.866 120. 0.153 0.3}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup .5 .353553391 .707 90. 0.071 0.14}
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 10. 1. 19.89 168.52 137.11301 274.2}
        ::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 . "Circular Segment Area Calculator "

# 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, but takes away from computer "efficiency". While the testcases are in meters, the units cancel out in the calculator equations. So the units could be entered as inches, Indian yojanams, Sumerian cubits, or Chinese inches. This is an advantage since the units in the ancient Sumerian, Indian, and Chinese texts are open to question.

tcl8.5 code scraps

Category Numerical Analysis

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