**Babylonian Irregular Reciprocal Algorithm and eTCL demo example calculator, numerical analysis** This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom 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 some eTCL starter code for Babylonian irregular reciprocal algorithm in calculator shell. Additional console program below is used to check or improve subroutine. ---- **Pseudocode Section** ====== # using pseudocode for Babylonian field expansion procedure algorithm. # possible problem instances include add 1/60 to sides until area goal reached long_side = supplied value short_side = supplied value desired_goal = supplied value # desired_goal usually 100 square units in some early math problems set old_field_area = a*b , old field_area = long_side * short_side set new_side_a = long_side + 1/60 set new_side_b = short_side + 1/60 set new_field_area = (long_side + 1/60) * ( short_side + 1/60 ) is new_field_area =? desired_area within +/- (1/60) , yes = finished loop check error , abs (desired_goal - new_field_area) <= [/ 1. 60.] half area = area * .5 quarter area = area * .25 check_answer new area =? desired goal , desired goal reached (yes/no) 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 **** **** Testcase 2 **** **** Testcase 3 **** ---- ***Screenshots Section*** ****figure 1.**** [Babylonian Field Expansion Procedure Algorithm and eTCL demo example calculator screenshot] ---- ***References:*** September 2009 * 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 * Wikipedia search engine * 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. * [Oneliner's Pie in the Sky] * [One Liners] * [Category Algorithm] * [Babylonian Number Series and eTCL demo example calculator] * [Brahmagupta Area of Cyclic Quadrilateral and eTCL demo example calculator] * [Gauss Approximate Number of Primes and eTCL demo example calculator] * Land surveying in ancient Mesopotamia, M. A. R. Cooper * [Sumerian Approximate Area Quadrilateral and eTCL Slot Calculator Demo Example , numerical analysis] * Thomas G. Edwards, Using the Ancient Method of False Position to Find Solutions * Joy B. Easton, rule of double false position * Vera Sanford, rule of false position * www.britannica.com, topic, mathematics trapezoid * [Sumerian Equivalency Values, Ratios, and the Law of Proportions with Demo Example Calculator] * [Babylonian Sexagesimal Notation for Math on Clay Tablets in Console Example] * 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 |&" ====== **Console program under test. ** ---- [gold] This page is copyrighted under the TCL/TK license terms, [http://tcl.tk/software/tcltk/license.html%|%this license]. **Comments Section** <> Please place any comments here, Thanks. <> Numerical Analysis | Toys | Calculator | Mathematics| Example| Toys and Games | Games | Application | GUI <> Mathematics | Concept| Algorithm