21. String And M Theory Duality X Re The Rare and the Nonfactorizable geometryMetric with Gravity - OsherDoctorow5/17 pascals triangle is Pelastrians Domain?) - sol 5/12/03 (7) Re pascals http://www.superstringtheory.com/forum/dualboard/index10.html

String Theory Discussion Forum String Theory Home Forum Index This board has been archived. Please post on the new board String and M Theory Duality X Search For: Reload page to see your post McInnes' et al's Phantom Spacetime and Rare Events - OsherDoctorow The Sphere and M theory - sol Re: The Sphere and M theory Re: The Sphere and M theory - DocN Re: The Sphere and M theory - sol M Physics 21: Average Cosmic Speed ~ c.... Speed of Light Never Changes - sol M Physics 21: The Probability of varying c is more than Zero Rare Convolutional Codes and Holes - OsherDoctorow Re: Rare Convolutional Codes and Holes - sol Re: Rare Convolutional Codes and Holes - OsherDoctorow Revision of Rare and Complex Thread - OsherDoctorow Rare and Complex More Closely Related - OsherDoctorow The Rare and the Nonfactorizable Geometry-Metric with Gravity - OsherDoctorow Re: The Rare and the Nonfactorizable Geometry-Metric with Gravity - OsherDoctorow Re: The Rare and the Nonfactorizable Geometry-Metric with Gravity - OsherDoctorow Re: The Rare and the Nonfactorizable Geometry-Metric with Gravity - OsherDoctorow Re: The Rare and the Nonfactorizable Geometry-Metric with Gravity - cspace Re: The Rare and the Nonfactorizable Geometry-Metric with Gravity - OsherDoctorow BECAUSE THE BRANE IS GRAVITY - pelastration Re: BECAUSE THE BRANE IS GRAVITY - cspace Re: BECAUSE THE BRANE IS GRAVITY - pelastration Re: BECAUSE THE BRANE IS GRAVITY - sol Interesting to note.

22. Encyclopedia: Blaise-Pascal This article is about angles in geometry. A triangle is one of the six rows of pascals triangle In mathematics, pascals triangle is a geometric http://www.nationmaster.com/encyclopedia/Blaise_Pascal

Supporter Benefits Signup Login Sources ... Pies What's new? Our next offering Latest newsletter Student area Lesson plans Recent Updates Santiago Segura Samuel Sewall Sampling (statistics) Samos ... More Recent Articles Top Graphs Richest Most Murderous Most Taxed Most Populous ... More Stats Encyclopedia: Blaise-Pascal Updated 3 days 44 minutes ago. Other descriptions of Blaise-Pascal Blaise Pascal Blaise Pascal Born June 19 Clermont France Died August 19 Paris France Blaise Pascal June 19 August 19 ) was a French mathematician physicist , and religious philosopher . Pascal was a child prodigy , who was educated by his father. Pascal's earliest work was in the natural and applied sciences , where he made important contributions to the construction of mechanical calculators and the study of fluids , and clarified the concepts of pressure and vacuum by expanding the work of Evangelista Torricelli . Pascal also wrote powerfully in defence of the scientific method Image File history File links Blaise Pascal source : http://www. ... June 19 is the 170th day of the year (171st in leap years) in the Gregorian Calendar, with 195 days remaining. ... Events August 6 - Pope Urban VIII is elected to the Papacy. ...

23. Encyclopedia: 400 (number) In Euclidean geometry, a circle is the set of all points in a plane at a the fifth cell of any row of pascals triangle starting with the 5term row 1 4 http://www.nationmaster.com/encyclopedia/400-(number)

Supporter Benefits Signup Login Sources ... Pies Related Articles People who viewed "400 (number)" also viewed: 200 (number) 151 (number) 79 (number) Leo constellation ... Howard Hughes What's new? Our next offering Latest newsletter Student area Lesson plans Recent Updates Santiago Segura Samuel Sewall Sampling (statistics) Samos ... More Recent Articles Top Graphs Richest Most Murderous Most Taxed Most Populous ... More Stats Encyclopedia: 400 (number) Updated 14 days 1 hour 50 minutes ago. Other descriptions of 400 (number) Four hundred is the natural number following three hundred ninety-nine and preceding four hundred one. Natural number can mean either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). Natural numbers have two main purposes: they can be used for counting (there are 3 apples on the table), or they can be used for ordering (this is... List of numbers Integers This is a list of articles about numbers. ... (zero) or nought is both a number and a numeral. ... 100 (the Roman numeral is C for centum) is the natural number following 99 and preceding 101. ... 200 is the natural number following 199 and preceding 201. ...

24. Pascal Lines: Steiner And Kirkman Theorems II Projective geometry lied abandoned for about two hundred years; and Pascal s result Next, have a look at the following triangle formed by three pascals http://www.cut-the-knot.com/Curriculum/Geometry/MorePascal.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Pascal Lines: Steiner and Kirkman Theorems II At the age of sixteen B. Pascal proved a remarkable theorem The three intersections of the pairs of opposite sides of a hexagon inscribed in a conic are collinear. It is said [ Bell , p. 78] that from that result (and two other lemmas) Pascal derived all Apollonius' theorems on conics and more, no fewer than 400 propositions in all. Little wonder he called it the Mystic Hexagram Hexagrammum Mysticum ). The original manuscript (that was lost) was examined and praised by Leibniz. Descartes was been stunned to learn that the work had been performed by a sixteen years old. A shorter version written a year later has survived, see [ Source , p. 326-330], but contains no derivation. The theorem is clearly of projective nature, and in the surviving manuscript Pascal leaves no doubt of his intention to imitate the methods of Projective Geometry that Desargues introduced a short time beforehand. In the 17 th century, identification with Desargues' work was certainly detrimental to any discovery. The ridicule with which his concepts and notations were met caused Desargues to give up on mathematical research. Projective Geometry lied abandoned for about two hundred years; and Pascal's result had shared its fate. However, in the 19

25. Do You Speak Mathematics? Projective geometry lay abandoned for about two hundred years; and Pascal s result Next, have a look at the following triangle formed by three pascals http://www.cut-the-knot.com/ctk/Mathematics.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Cut The Knot! An interactive column using Java applets by Alex Bogomolny Do You Speak Mathematics? November 2002 Mr Thomas Hobbes told me, that this Mr Cavendish told him, that the Greeks doe sing their Greeke. John Aubrey Brief Lives , Penguin Books, 2000, p. 74 I call on him to explain everything as clearly as if it were in Latin. Epictetus Discourses and Enchiridion , Classics Club, 1944, p. 47 Do you speak mathematics? is a very valid question assuming mathematics is a language. Many think it is. Josiah Willard Gibbs gave a speech on that account. Galileo and R. Feynman thought so. Mathematics is even judged to be a universal language, the only one suitable to initiate extraterrestrial communication [ Jacobs , p. 1]. Some object. For example, Jean-Pierre Bourguignon argues [ Basis , p. 173] that For some people, mathematics is just the language of the quantitative . This opinion is shared by some of our fellow scientists. ... We mathematicians know how wrong this opinion is, and how much effort goes into building concepts, making new links, establishing facts, and following avenues we once thought plausible but turned out to be dead ends. I generally accept the above sentiment with reservations concerning mathematics being just the language of quantitative The potency of the bond between mathematics and its language is such that many mathematicians do indeed identify the two [ Spectrum , p. 112]:

26. Voyage 200 BASIC Math Programs - Ticalc.org geometry Assistant The program analyses a lot of analytic geometry problems with 0603, Pascal s triangle Matrix This stores many rows of pascals triangle to a http://www.ticalc.org/pub/v200/basic/math/date.html

Basics Archives Community Services ... File Archives Voyage 200 BASIC Math Programs File Archives VOYAGE 200 BASIC MATH PROGRAMS Click a filename to download that file. Click a folder name to view files in that folder. Click for file information. indicates files with screen shots. indicates files with animated screen shots. indicates files with reviews. indicates featured programs. Archive Statistics Number of files Last updated Tuesday, 13 September 2005 Total downloads Most popular file Laplace and Z transform with 10,736 downloads. Name Size Date Rating Description (Parent Dir) folder Up to Voyage 200 BASIC Files modfib.zip Modular Generalized Fibonacci Functions v1.0 Collection of functions that will very quickly calculate the values of the Fibonacci, Lucas, Generalized Fibonacci, and Perrin Sequences to any modulus. Speed improved by using modular exponentiation with the Q-Matrix method, performing 32-digit calculations in about 15sec and 64-digit calculations in one minute. unitcircle.zip Graphical Unit Circle Displays a graphical unit circle with the degree and radian angle measure when a degree or radian measure angle is given lineal.zip

27. Voyage 200 BASIC Math Programs - Ticalc.org This stores many rows of pascals triangle to a matrix for easy viewing. The program analyses a lot of analytic geometry problems with points and lines http://www.ticalc.org/pub/v200/basic/math/

Basics Archives Community Services ... File Archives Voyage 200 BASIC Math Programs File Archives VOYAGE 200 BASIC MATH PROGRAMS Click a filename to download that file. Click a folder name to view files in that folder. Click for file information. indicates files with screen shots. indicates files with animated screen shots. indicates files with reviews. indicates featured programs. Archive Statistics Number of files Last updated Tuesday, 13 September 2005 Total downloads Most popular file Laplace and Z transform with 10,736 downloads. Name Size Date Rating Description (Parent Dir) folder Up to Voyage 200 BASIC Files antirand68k.zip Central Tendancies Graphics These programs, for the TI-89 V200, graphically show how TI's random routine isn't truly random. asi_v200.zip Advanced Symbolic Integration - version 2.0.0b ASI: Advanced Symbolic Integration is a fast program that can integrate by use of special-functions and integrate expressions containing special-functions. ASI is equipped with a library of highly flexible special-functions, and it is easy to use all of it. bezout.zip

28. Patterns Sites are available for patterns in algebra, geometry, calculus, statistics,fractals, fractions, Also has some work with pascals triangle. http://www.svsu.edu/mathsci-center/mpatterns.htm

I. Patterns, Relationships, and Functions Patterns Variability and Change Pattern Middle School Benchmark 1. "Describe, analyze and generalize patterns arising in a variety of contexts and express them in general terms." Easier Fibonacci Puzzles - Patterns (I.1.MS.1) Easier Fibonacci Number puzzles appropriate for Middle School level students offers a variety of exercises, all simply related to the Fibonacci numbers. Uses many other types of patterning. Goes beyond, using pictures and diagrams to completely cover the patterning. Students have to find the missing number in a pattern of numbers. It correctly keeps track of percentage. Good for introduction to patterns or a review of patterns. Number Cracker - Patterns (I.1.MS.1)

29. Classroom Procedures g. Circle Graphs. h. Slope. V. Beginning Plane geometry. a. Points, Lines, Planes, Angles. c. pascals triangle. d. Theoretical Probability. e. Dependent vs. http://www.fallcreek.k12.wi.us/FCMIDDLE/Dept/Math/Mlsna/Course outline 7th.html

Math 7 Course Outline Home Mr. Mlsna I. Data a. i. Surveys b. Mean, Median, Mode and Range c. ii. Circle Graphs iii. Scattergrams iv Line Plots II. a. Integers b. Operations with Integers c. Order of Operations e. Coordinate Graphing f. Inequalities g. Graphing Inequalities on a Number Line b. Operations with Fractions c. Mixed numbers and their Operations g. Decimals, Place Value, + Rounding h. Operations with Decimals k. Negative and Zero Exponents a. Ratios and Rates b. Solving Proportions c. Cross Products d. e. Similar Figures f. Solving Equations with Percents g. Circle Graphs h. Slope V. Beginning Plane Geometry a. b. c. d. Polygons and Special Angles e. Perimeter of Polygons f. g. Circumference of Circles h. Area of Circles i. Area of Irregular Shapes j. Constructions k. Pythagorean Triples VI. Probability a. Terminology with Probability b.

30. PASCALS TRIANGLE, Essay Express, Term Papers, 050924 Pascal s study of mathematics and geometry helped lead The author concludes thatPascal s growing religious convictions the Japanese novel s love triangle as a http://www.termpapers.essayexpress.com/lib/essay?A=www.qualityessays.comwhite&KE

31. World Crossing - Missing Template 1.1dde3fdf as a Field • 4 messages + Discussion geometry of Consciousness Discussion Pascaland Pelastrian • 10 messages + Discussion pascals triangle and the http://worldcrossing.com/WebX?1.1dde3fdf

32. MathsNet: ICME 9 visually and links between dynamic geometry and the structure of proteins . pascals triangle, probability distributions tesselation polyhedra http://www.mathsnet.net/courses/icme9acc/

Courses/ Conferences Monday, July 31st to Sunday August 6th, 2000 Makuhari, Tokyo, Japan International Conference on Mathematics Education A brief account of some of the lectures, presentations and events at the conference, with photographs. Bryan Dye, Head of Maths, Hewett School, Norwich The conference took place in Makuhari, which is to the east of Toyko, in a new conference centre. At the Opening ceremony in Makuhari Event Hall a sequence of welcoming messages were delivered (with simultaneous Japanese/English translation) from key figures in Japanese education and organisers of ICME. Messages were quoted from the Japanese Prime Minister and the US President. At the International Round Table , video conferencing was used to link Japan with Singapore and USA. Mr Wee Heng Tin, Director General of Education, Singapore, talked about the possibilities of the Internet, with users customising content. 40% on Singapore households are on-line. But what about the "digital divide" - those with on-line access and those without? The US speaker Bruce Alberts talked about hands-on learning and learning how to learn. Akito Akihira discussed issues caused by students downloading without understanding. Gilah Leder from Australia was ambivalent about technology, mentioning again the digital divide in less developed countries compared to affluent homes. Teachers have inadequate training in new technologies; in fact their students are more proficient. Other issues included: reduced teaching time for maths;

33. A Few Swedish Math Words Introduction Word List Phrases Notational pascals triangel Pascal s triangle. periodiska - periodic rymdgeometri -solid geometry (However, a course which studied equations of planes, spheres, http://www.augustana.edu/users/Mabengtson/Swmath.htm

A Few Swedish Math Words Introduction Word List Phrases Notational Quirks ... Bibliography Introduction Augustana College is home of the largest undergraduate program in Swedish outside of Sweden. Every year Augustana has several students from Sweden, and this year one of them, Krister Boëthius (Han kommer från Göteborg.) was kind enough to loan me one of his math books in Swedish. The book is Studium matematik NT3 by Nyman, Emanuelsson, Bergman, and Bergström. His book provided the impetus I needed to construct the following little list of Swedish math words. I have only indicated forms I have actually found in Swedish. Hence there are many forms which I have not included. My intention was to include, for nouns, indefinite singular (with article), definite singular, and (indefinite) plural; for verbs, infinitive and present tense; and for adjectives whichever forms I ran across. (We hadn't talked about adjectives in my Swedish class when I wrote this, so I didn't really know what the forms were.) In English I only wrote the singular form of a noun, without an article. I did not look any of these words up in a dictionary, and my indication of their meaning must therefore be taken as an amateur opinion. The English meaning is one which works in the mathematical context in which I found the word. I almost always understood the mathematical intention, and hence I am moderately confident about my proposed equivalent expressions in English. I often consulted my colleagues in the math department for help in determining customary English usage, especially with words in geometry and probability and statistics. When a single English word seemed inadequate or ambiguous, I have tried to include a short phrase. Occasionally a word seemed to be a close cognate and I indicated an English equivalent on what would otherwise have been rather skimpy evidence.

34. Ntermath | CPTM Summer Institute | Geometry Syllabus, Summer 2003 | Day 1 Mathography. WriteUps. Insert links and text about InterMath write-ups here..Lesson Plans. pascals triangle. Journals. Journal March 2nd. Email E-mail me. http://www.intermath-uga.gatech.edu/tweb/augusta-alg/tmitchem/webpage.htm

InterMath Augusta , Number Sense, Spring 2004 Portfolio Name Teresa Mitchem Class Information [Add to the description as you wish] About me 2 facts Some Links I Like InterMath National Council of Teachers of Mathematics Saint Andrews University History of Mathematics Site Jim Wilson's Web Site ... Math is Fun [add your own favorite links] Mathography Write-Ups [Insert links and text about InterMath write-ups here.] Lesson Plans Pascals Triangle Journals Journal March 2nd Email E-mail me ClassTemplate.htm Failed! Click Here To Go Back! template.htm Failed! Click Here To Go Back! webpage.htm Failed! Click Here To Go Back! webpage.htm Failed! Click Here To Go Back!

35. Ntermath | CPTM Summer Institute | Geometry Syllabus, Summer 2003 | Day 1 Writeup 2. Write-up 3. Write-up 4. Lesson Plans. pascals triangle. McNugget Numbers.Consecutive Odds and Evens. Summing Multiples. Journals. Journal March 2nd http://www.intermath-uga.gatech.edu/tweb/augusta-alg/awiliams/webpage.htm

InterMath Augusta , Number Sense, Spring 2004 Portfolio Name Ava Williams Class Information [Add to the description as you wish] About me 2 facts Some Links I Like InterMath National Council of Teachers of Mathematics Saint Andrews University History of Mathematics Site Jim Wilson's Web Site ... Math is Fun [add your own favorite links] Mathography Article Summary Middle-School Algebra: Ready or Not? Write-Ups Write-up 1 Write-up 2 Write-up 3 Write-up 4 Lesson Plans Pascals Triangle McNugget Numbers Consecutive Odds and Evens Summing Multiples Journals Journal March 2nd Electronic Journal Email E-mail me ClassTemplate.htm Failed! Click Here To Go Back! template.htm Failed! Click Here To Go Back! webpage.htm Failed! Click Here To Go Back! webpage.htm Failed! Click Here To Go Back!

36. Python And Mathematics (PyCon 2004) def pascal() Generate rows of pascals triangle row = 1 while True yield In a second pass through coordinate geometry, we ll swap out tuples and http://www.python.org/pycon/dc2004/papers/15/

Python in the Mathematics Curriculum a talk prepared by Kirby Urner for Pycon '04 March 24-26, 2004 Preamble I thought it would be useful, at least in the written version of this talk, to attempt more overview and context. I've already posted a lot of example code and curriculum , in conjunction with others, to the web. Rather than include too much of that here, I'd like to take this opportunity to provide a snap shot of my current thinking, something to look back on later, partly to gauge how accurately I was reading the signs or how misled. Those mostly interested in reading source code should follow the links or run some searches. Setting the Stage Computer science used to be an exclusively university-based discipline, as universities were the only institutions, outside the government and big business, who could afford big iron. Then came the PC revolution, spearheaded by Apple and IBM, the latter in partnership with Microsoft. A generation of IT workers trained up on this equipment, while a separate and still university- based cadre continued in the Unix tradition. These last two trajectories converged thanks largely to the GNU and Linux projects, which brought a Unix-like operating system to the desktop. Apple has followed suit, basing OS X on FreeBSD. The pre-college curriculum was somewhat indirectly impacted by the universities-only phase of the computer revolution in the 1960s, with the advent of the new mathematics in the United States. This included a hefty helping of boolean algebra, so-called truth tables, which have remained in most curricula to this day. "Computer programmer" entered the lexicon of school kids, as a new career possibility. Computers invaded science fiction and popularizations. The dream of a chess playing computer, first triggered by

37. MAA Florida Section Newsletter - February 2001 In particular, no prior knowledge of spectral geometry or diffusions is assumed . Room 244, A Variant of pascals triangle http://www.spcollege.edu/central/maa/archives/Feb01.htm

Florida Section Newsletter The Mathematical Association of America February 2001 Volume 22, Issue 2 In conjunction with FTYCMA, the 34th Annual Meeting of the Florida Section of the Mathematical Association of America, March 2 and 3, 2001, Florida Gulf Coast University, Ft. Myers, Florida Friday, March 2 A workshop on using TI Calculators in the Mathematics Curriculum by Doug Child - Rollins College A workshop on Successful Grant Writing by Bill Bauldry - Appalachian State University Presidential Welcomes Pleanary Address from Barry Cipra, Freelance Writer, Northfield, MN Room 101 Adventures in Number Theory via Mathematical Data Scott Hochwald - UNF Abstract: The harmonic series is usually thought of as a creature from Analysis. However, when we look at partial sums of the harmonic series, we enter a world full of number theoretic possibilities. I will present some partial sums and let you look for patterns. We will discuss the patterns. Room 265 My Erdos Number is Sqrt [-1] Li Zhou - Polk CC Abstract: Ill discuss some useful problem solving strategies, such as collecting data, using calculators and computers, working backwards, and so on. In particular, Ill illustrate these concepts using my solutions to Problem 667 (College Mathematics Journal, Jan. 2000), Problem 1597 (Mathematics Magazine, Apr 2000), and Problems 10771, 10798, and 10814 (American Mathematical Monthly, Dec. 1999, Apr. and Jun. 2000).

38. Math2020 Fall2005 geometry junk yard links to pages about mathematics related to Eschers art. There was a handout with some more questions on pascals triangle. http://www.math.lsu.edu/~verrill/teaching/discrete2020/

Solving Discrete Problems. Math 2020, Fall 2005. H. A. Verrill Course text book: The art and craft of Problem solving, by Paul Zeitz. Additional text: "The art of problem posing" by Stephen Brown and Marion Walter. Handouts for the first class (will be added here soon). Included are grading scheme, class meeting time and place, office hours, etc. Useful web pages: The art of problem solving web site. The Spring 2005 version of this course. Week 1, Class 1 Handouts: Handout with details about the course Second side Handout with questionaire Handout with homework due this Wednesday Class outline 1) Discussed outline of the course (see first handout) 2) Completed questionaire (second handout) 3) Hand shake problem: For a group of 5 or so students, what's the fastest way everyone can shake hands? Regarding this problem, we discussed: Using a graph to find a solution Using symmetry to find a solution How to prove the solution found is the best possible solution e.g., for 8 people, there must be at least 7 handshake times. For 5 people, at least 4 - though it turns out you need at least 5 times people have to shake hands, since one person it always left out. Other questions we could ask about this situation.

39. Python And Mathematics (PyCon 2004) The analytic geometry we already teach will be transposed to the screen, def pascal() Generate rows of pascals triangle row = 1 while True yield http://python.fyxm.net/pycon/dc2004/papers/15/

Python in the Mathematics Curriculum a talk prepared by Kirby Urner for Pycon '04 March 24-26, 2004 Preamble I thought it would be useful, at least in the written version of this talk, to attempt more overview and context. I've already posted a lot of example code and curriculum , in conjunction with others, to the web. Rather than include too much of that here, I'd like to take this opportunity to provide a snap shot of my current thinking, something to look back on later, partly to gauge how accurately I was reading the signs or how misled. Those mostly interested in reading source code should follow the links or run some searches. Setting the Stage Computer science used to be an exclusively university-based discipline, as universities were the only institutions, outside the government and big business, who could afford big iron. Then came the PC revolution, spearheaded by Apple and IBM, the latter in partnership with Microsoft. A generation of IT workers trained up on this equipment, while a separate and still university- based cadre continued in the Unix tradition. These last two trajectories converged thanks largely to the GNU and Linux projects, which brought a Unix-like operating system to the desktop. Apple has followed suit, basing OS X on FreeBSD. The pre-college curriculum was somewhat indirectly impacted by the universities-only phase of the computer revolution in the 1960s, with the advent of the new mathematics in the United States. This included a hefty helping of boolean algebra, so-called truth tables, which have remained in most curricula to this day. "Computer programmer" entered the lexicon of school kids, as a new career possibility. Computers invaded science fiction and popularizations. The dream of a chess playing computer, first triggered by

40. History Of Math Notes - Simon Fraser University pascals triangle. Known to Chinese in 11th Century. They used it to extract roots Mainly interested in geometry, and nonpractical math. http://www.math.sfu.ca/histmath/math380notes/math380.html

History of Math Notes These are my notes from Math-380 lectures in Spring 1998. Also available in Microsoft Word 97 format: math380.zip Babylon Oldest civilization: Mesopotamia (Babylonia) The superiority of Babylonian mathematics is based on the place-value notation of its number system. 3500 BC Clay tablets with numbers 1800 BC King Hamorabi wrote laws on clay tablets Flourishing period of Babylonian math. 700’s BC King Nabonasssar Eclipse records 530 BC Triangular inscriptions of Bisistun (Iran) Cuneiform (script language of Babylon) deciphered by Rawlonson in 1800s Number System Base 60 Positional Had a special symbol for empty places (zero) Algebra Uses algorithms , but doesn’t explain them No symbols Only one solution in quadratic equation , not the usual two. No negative numbers No apparent practical value (always produced nice round numbers) Study of solutions of Pythagorean triangles Babylonians were the only ancient people to solve quadratic equations as we do today. Right Triangles st to state Pythagorean theorem They knew how to solve a + b = c Plimpton 322 Root Extraction Approximated roots by method of "completing the square"

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