This is an empty page. ***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= 0.5*L*B,sides are 1.0 and 0.5 |& &| rectangle | us-u-sag? | siliptum | 0.75 | 1 | 1;00 | 1 | 1;00 | sumerian area= 1.*L*W,sides are 1.0 and (45/60) |& &| trapezoid | gan sag-ki-gud | mithartum? | 0.375 | 0.5 | 0;30 | 1 | 1;00 | modern area= ((B1*B2)/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. [http://imageshack.us/a/img24/835/kez.gif] figure 2. [http://imageshack.us/a/img27/3169/nh7.gif] figure 3. [http://imageshack.us/a/img819/7111/5ia.gif] figure 4. [http://imageshack.us/a/img20/8317/kq7.gif] figure 5. [http://imageshack.us/a/img845/1261/88h2.gif] figure 3c. [http://imageshack.us/a/img823/4968/fh1.gif] figure 6. [http://imageshack.us/a/img59/3401/92x.gif] figure 7. [http://imageshack.us/a/img189/4246/8n5.gif] figure 8a. [http://imageshack.us/a/img543/1718/9zp.gif] figure 8b. [http://imageshack.us/a/img694/1907/61c.gif] figure 10. [http://imageshack.us/a/img13/9292/q0h.gif] figure 11. [http://imageshack.us/a/img856/1884/ccf.gif] figure 12. [http://imageshack.us/a/img571/2417/ove.gif] figure 13. [http://imageshack.us/a/img35/7269/n8v.gif] figure 14. [http://imageshack.us/a/img109/5233/mxj.gif] figure 15. [http://imageshack.us/a/img546/9673/6nu.gif] figure 16. [http://imageshack.us/a/img706/6907/vnj.gif] figure 17. [http://imageshack.us/a/img266/8347/6x8.gif] figure 18. a [http://imageshack.us/a/img43/8881/hkau.gif] d [http://imageshack.us/a/img203/9099/jp8.gif] [http://imageshack.us/a/img14/6794/eyv.gif] [http://imageshack.us/a/img38/1646/4zc.gif] e [http://imageshack.us/a/img46/1204/abb.gif] f [http://imageshack.us/a/img17/7665/hxd.gif] g. [http://imageshack.us/a/img850/3287/dqf.gif] ---- '''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 *** <> Numerical Analysis | Toys | Calculator | Example | Package Enter page contents here, upload content using the button above, or click cancel to leave it empty. <>Enter Category Here