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History of Mathematics




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History

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A Brief History of Quaternions Complex numbers were a hot subject for research in the early eighteen hundreds. An obvious question was that if a rule for multiplying two numbers together was known, what about multiplying three numbers? For over a decade, this simple question had bothered Hamilton, the big mathematician of his day. The pressure to find a solution was not merely from within. Hamilton wrote to his son: Every morning in the early part of the above-cited month [Oct. 1843] on my coming down to breakfast, your brother William Edwin and yourself used to ask me, 'Well, Papa, can you multiply triplets?' Whereto I was always obliged to reply, with a sad shake of the head, 'No, I can only add and subtract them.' We can guess how Hollywood would handle the Brougham Bridge scene in Dubl Read More
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Chaitin, Conversations with a Mathematician

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Chaitin, Conversations with a Mathematician Lecture — A Century of Controversy over the Foundations of Mathematics [Originally published in C. S. Calude and G. Paun, Finite versus Infinite , Springer-Verlag, 2000, pp. 75-100.] This 1999 talk at UMass-Lowell was my last major lecture of the previous century, and it summarizes that century's work on the foundations of mathematics, discusses connections with physics, and proposes a program of research for the next century. Not to be confused with another talk with the same title, my Distinguished Lecture given at Carnegie-Mellon University in 2000. Prof. Ray Gumb We're happy to have Gregory Chaitin from IBM's Thomas J. Watson Research Lab to speak with us today. He's a world-renowned figure, and the developer as a teenager of the theory Read More
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Who was Fibonacci?

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A brief biographical sketch of Fibonacci, his life, times and mathematicalachievements. Contents of this Page Who was Fibonacci? His names Fibonacci's Mathematical Contributions Introducing the Decimal Number system into Europe Roman Numerals Arithmetic with Roman Numerals The Decimal Positional System "Algorithm" The Fibonacci Numbers Did Fibonacci invent this Series? Naming the Series Fibonacci memorials to see in Pisa Fibonacci's mathematical books References to Fibonacci's Life and Times Who was Fibonacci? The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in Italiansince he was born in Pisa (Italy), the city with the famous Leaning Tower, about 1175 AD. Pisa was an important commercial town in its day and had links with m Read More
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Chaos Theory: A Brief Introduction

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Chaos Theory: A Brief Introduction What exactly is chaos? The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data. When was chaos first discovered? The first true experimenter in chaos was a meteorologist, named Edward Lorenz. In 1960, he was working on the problem of weather prediction. He had a computer set up, with a set of twelve equations to model the weather. It didn't predict the weather itself. However this computer program did theoretically predict what the weather might be. One day in 1961, he wanted to see a particular sequence again. To save time, he started in the middle of the sequence, instead of the beginning. He entered the numbe Read More
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History of Statistics - Timeline

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History of Statistics - Timeline Time Contributor Contribution Ancient Greece Philosophers Ideas - no quantitative analyses 17th Century Graunt, Petty Pascal, Bernoulli studied affairs of state, vital statistics of populations studied probability through games of chance, gambling 18th Century Laplace, Gauss normal curve, regression through study of astronomy 19th Century Quetelet Galton astronomer who first applied statistical analyses to human biology studied genetic variation in humans(used regression and correlation) 20th Century (early) Pearson Gossett (Student) Fisher studied natural selection using correlation, formed first academic department of statistics, Biometrika journal, helped develop the Chi Square analysis studied process of brewing, alerted the statistics community about p Read More
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List by Discipline

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Listing by Discipline Note that some women are listed in here more than once because their work encompassed more than one field. Agronomist Scientist File Last Updated Ramsey, Martha Laurens (1718 - 1811) November 27, 2005 Anthropologist Scientist File Last Updated Benedict, Ruth (1887 - 1948) November 19, 2005 Fletcher, Alice (1838 - 1923) November 21, 2005 Astronomer Scientist File Last Updated Brahe, Sophia (16th century) November 20, 2005 Burbidge, Margaret (1919 - ) November 20, 2005 Cannon, Annie Jump (1863 - 1941) November 20, 2005 Crocker, Deborah (1957 - ) October 08, 1999 Cunitz, Marie (1610-1664) November 20, 2005 Dumee, Jeanne (18th century) November 21, 2005 En Hedu'Anna (circa 2354 BCE) November 21, 2005 Fleming, Williamina (1857 - 1911) November 21, 2005 Payne-Gaposchkin, Ce Read More
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The origin of the decimal system

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The origin of the decimal system A common claim from the Muslim side is Should I remind you that the numbers you use (1,2,3, ... ) are Arabic? Algebra, Algorithm, and many other mathematical words are also Arabic. If you like Math and Science, you should thank the Qur'an for bringing them to you, because there is no other scripture that has given to science more than the Qur'an did. Let us investigate these claims. The Arabic numerals are more properly called Hindu-Arabic numerals because they did not originate in Arabia but originated with the Hindus as early as 200 B.C. The system was adopted by the Arabs by about A.D. 800 at the very earliest. They brought it to Spain about 900. It was brought to the rest of Europe about 1100... Very few Arabs at the time of Mohammad could read or write Read More
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?@

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?@ This site "SANGAKU" has removed to the following address. http://www.wasan.jp/english/ Read More
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A Brief History of the Metric System Nugget

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A Brief History Nugget of the Metric System The metric system was developed during the French Revolution in the late 1700's. It was first promoted in the United States by Thomas Jefferson and in 1866 the US Congress offically recognized the metric system as a legal system of units. In 1893, the Office of Weights and Measures (now the National Bureau of Standards), fixed the value of the U.S. "yard" in terms of themeter as follows: 1 yard = 3600/3937 meter or 1 yard = 0.914 401 8288 meter this relation is equivalent to: 1 foot = 12/39.37 meter or 1 foot = 0.304 800 609 6012 meter Unfortunately, other nations used a slightly different conversion factor. To solve this deviation, a refinement was made in the definition of the yard to bring the US yard and the yard used in other count Read More
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A Brief History of the Notation of Boole's Algebra

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Next: 1 Introduction Up: Contents A Brief History of the Notation of Boole's Algebra Michael Schroeder Institut für Rechnergestützte Wissensverarbeitung Universität Hannover, Germany Abstract: In this article we investigate the development of Boolean Algebra, the notation that allowed a first glance at contemporary computational logic. We trace the history of algebraic notation and the idea of logic and computation. Furthermore, we describe the on-goings in British mathematics of the first half of the 19th century. With this background we focus on De Morgan's and Boole's work on logic. We compare the work and especially the notation used by thes two colleagues and friends and pinpoint why Boole's notation was so successful. 1 Introduction 2 Algebraic Notation 3 Logic and Com Read More
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A Common Book of Pi

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A Common Book of 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679... The mysterious and wonderful is reduced to a gargle that helps computing machines clear their throats. -- Philip J. Davis In recent years, the computation of the expansion of has assumed the role of a standard test of computer integrity. -- David H. Bailey It requires a mere 39 digits of in order to compute the circumference of a circle of radius (an upper bound on the distance travelled by a particle moving at the speed of light for 20 billion years, and as such an upper bound for the radius of the universe) with an error of less than meters (a lower bound for the radius of a hydrogen atom). -- Jonathan and Peter Borwein The number has been the subject of a great deal Read More
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A Modern History of Blacks in Mathematics

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A Modern History of Blacks in Mathematics On this web page we consider a contemporary history of Blacks in Mathematics , not Who are the greatest Black Mathematicians? (for that click the question). Here you can learn about (and even before ) the first African Americans in the Mathematical Sciences , (for the First African American Women click) The First Africans , and Other Important Events in the past 300 years . For earlier periods in history see the web pages of Mathematics in Ancient Africa . For a history of African Americans in science read Kenneth Manning's article Can History Predict the Future? Benjamin Banneker (1731-1806) is often recognized as the first African American mathematician; however, ex-slave Thomas Fuller 's (1710-1790) and the Nigerian Muhammad ibn Muhammad 's (16? Read More
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A Short History of Probability

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A Short History of Probability From Calculus, Volume II by Tom M. Apostol (2 nd edition, John Wiley &amp Sons, 1969 ): "A gambler's dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Antoine Gombaud, Chevalier de M&#233r&#233, a French nobleman with an interest in gaming and gambling questions, called Pascal's attention to an apparent contradiction concerning a popular dice game. The game consisted in throwing a pair of dice 24 times; the problem was to decide whether or not to bet even money on the occurrence of at least one "double six" during the 24 throws. A seemingly well-established gambling rule led de M&#233r&#233 to believe that betting on a double six in 24 throws would be profitable Read More
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A.D. Bell: Math History Quiz

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A brief, but not easy, quiz on the history of mathematics Please tell me your name (don't worry, your results won't go on your permanent record): The creator of calculus as we know it now was Euclid Gottfried Leibniz Albert Einstein Isaac Newton The word "Algebra" comes from the title of a book in what language? Arabic Babylonian French Greek Who proved that it is impossible to give an explicit system of axioms for all the properties of whole numbers? Georg Cantor Kurt GÖdel Gottlob Frege Bertrand Russell When and where was the sign = introduced? Ancient Greece Renaissance Italy Early Arabia Renaissance England Carl Friedrich Gauss published Disquisitiones Arithmeticae in 1701 1801 1901 2001 Who was the first person to prove that pi is not a rational number (that is, not a fraction)? L Read More
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An overview of the history of mathematics

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An overview of the history of mathematics Mathematics starts with counting. It is not reasonable, however, to suggest that early counting was mathematics. Only when some record of the counting was kept and, therefore, some representation of numbers occurred can mathematics be said to have started. In Babylonia mathematics developed from 2000 BC. Earlier a place value notation number system had evolved over a lengthy period with a number base of 60. It allowed arbitrarily large numbers and fractions to be represented and so proved to be the foundation of more high powered mathematical development. Number problems such as that of the Pythagorean triples (a,b,c) with a +b = c were studied from at least 1700 BC. Systems of linear equations were studied in the context of solving number problems Read More
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Archimedes' Approximation of Pi

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Archimedes' Approximation of Pi One of the major contributions Archimedes made to mathematics was his method for approximating the value of pi. It had long been recognized that the ratio of the circumference of a circle to its diameter was constant, and a number of approximations had been given up to that point in time by the Babylonians, Egyptians, and even the Chinese. There are some authors who claim that a biblical passage 1 also implies an approximate value of 3 (and in fact there is an interesting story 2 associated with that). At any rate, the method used by Archimedes differs from earlier approximations in a fundamental way. Earlier schemes for approximating pi simply gave an approximate value, usually based on comparing the area or perimeter of a certain polygon with that of a cir Read More
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Art of Algebra No Longer Available

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The contents of this folder have been removed and are no longer available. May 6, 2005 Read More
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Art of Algebra No Longer Available

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The contents of this folder have been removed and are no longer available. May 6, 2005 Read More
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Blaise Pascal (1623 - 1662)

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Blaise Pascal (1623 - 1662) From `A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball. Among the contemporaries of Descartes none displayed greater natural genius than Pascal, but his mathematical reputation rests more on what he might have done than on what he actually effected, as during a considerable part of his life he deemed it his duty to devote his whole time to religious exercises. Blaise Pascal was born at Clermont on June 19, 1623, and died at Paris on Aug. 19, 1662. His father, a local judge at Clermont, and himself of some scientific reputation, moved to Paris in 1631, partly to prosecute his own scientific studies, partly to carry on the education of his only son, who had already displayed exceptional ability. Pascal was kept at home in orde Read More
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Brief History of Fractal Geometry

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Brief History of Fractal Geometry Brief History Historically, the revolution ws forced by the discovery of mathematical structures that did not fit the patterns of Euclid and Newton. Many of the fractals go back to classical mathematics and mathematicians of the past like Georg Cantor, Guisseppi Peano, Helge Von Koch, Waclaw Sierpinski and many others. However, reputable scientists and mathematicians called these structures a "gallery of monsters." Jules Henri PoincarÉ deemed many of Cantor's creations "pathological." Cantor's Dust, for example, constructed in 1877, seemed to jump dimensions. It is constructed by chopping up one dimensional line segments - but in the end it contains only zero dimensional points without length or width. Peano's curve is a space filling curve These monster c Read More
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British Society for the History of Mathematics

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The British Society for the History of Mathematics Society · Events · Bulletin · Resources The British Society for the History of Mathematics exists to promote research into the history of mathematics and its use at all levels of mathematics education. The Society's Bulletin is published by Taylor and Francis, and carries a wide range of articles and reviews of interest to the history of mathematics community. This link provides information about how to join the Society ; this site also contains information about the Society and its history , its current activities , and various resources on the history of mathematics. Next meeting: Musical instruments and mathematical instruments Saturday 15 December 2007, 10.00 am to 5.00 pm, The Museum of the History of Science, Oxford Introduced by Rob Read More
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Calculating Machines

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Calculating Machines If you are unable to see anything else other than this line Press here to continue (Your browser is somewhat old and does not support frames, time to upgrade (;-) Read More
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Chinese Mathematics : Rebecca And Tommy

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Time Line of Ancient Chinese Mathematics 2000 B.C. Magic squares discovered by Yu the Great 1000 - 500 B.C. Rod numerals Pythagoras theorem 300 - 0 B.C. Square and cube roots Systems of linear equations Measurement of a circle Volume of a pyramid Chiu chang suah shu , most famous Chinese mathematical book Chou-pei, oldest of Chinese mathematical classics (300 B.C. ??) 213 B.C. burning of related books and burial of protesting scholars 200 - 400 Liu Hui - (263 - ?) mathematics of surveying Sun Zi - chinese remainder problem 400 - 800 Zhang Quijian - hundred fowl problem Yi Xing - (683-727) first tangent table 1000 - 1200 Jian Xian - pascal triangle Li Ye - (1192 - 1279) algebraic equations for geometry 1200 - 1400 Qin Jiushao - (1202 - 1261) chinese remainder theorem (Ta-Yen) Yang Hui - (12 Read More
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Cynthia Lanius' Lessons: The History of Geometry

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Cynthia Lanius Thanks to PBS for permission to use the Pyramid photo. History of Geometry Egyptians c. 2000 - 500 B.C. Ancient Egyptians demonstrated a practical knowledge of geometry through surveying and construction projects. The Nile River overflowed its banks every year, and the river banks would have to be re-surveyed. See a PBS Nova unit on those big pointy buildings. In the Rhind Papyrus, pi is approximated. Babylonians c. 2000 - 500 B.C. Ancient clay tablets reveal that the Babylonians knew the Pythagorean relationships. One clay tablet reads 4 is the length and 5 the diagonal. What is the breadth? Its size is not known. 4 times 4 is 16. 5 times 5 is 25. You take 16 from 25 and there remains 9. What times what shall I take in order to get 9? 3 times 3 is 9. 3 is the breadth. Greek Read More
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Earliest Known Uses of Some of the Words of Mathematics

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Earliest Known Uses of Some of the Words of Mathematics LEFT TO RIGHT: James Joseph Sylvester, who introduced the words matrix, discriminant, invariant, totient, and Jacobian; Gottfried Wilhelm Leibniz, who introduced the words variable, constant, function, abscissa, parameter, coordinate and perhaps derivative; RenÉ Descartes, who introduced the terms real number and imaginary number; Sir William Rowan Hamilton, who introduced the terms vector, scalar, tensor, associative, and quaternion; and John Wallis, who introduced the terms induction, interpolation, continued fraction, mantissa, and hypergeometric series. A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z - Sources These pages attempt to show the first uses of various words used in Read More
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Earliest Uses of Various Mathematical Symbols

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Earliest Uses of Various Mathematical Symbols These pages show the names of the individuals who first used various common mathematical symbols, and the dates the symbols first appeared. The most important written source is the definitive A History of Mathematical Notations by Florian Cajori . Symbols of operation , including +, -, X , division, exponents, radical symbol, dot and vector product Grouping symbols, including (), [], {}, vinculum Symbols of relation , including =, >, < Fractions , including decimals Symbols for various constants , such as π, i, e, 0 Symbols for variables Symbols to represent various functions , such as log, ln, γ, absolute value; also the f(x) notation Symbols used in geometry Symbols used in trigonometry ; also symbols for hyperbolic functions S Read More
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EARTH MYSTERIES: Notes on Pi (&#188 )

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written and produced by Chris Witcombe - Sweet Briar College - witcombe@sbc.edu Notes on Pi ( ) Pi, which is denoted by the Greek letter , is the most famous ratio in mathematics, and is one of the most ancient numbers known to humanity. Pi is approximately 3.14 - the number of times that a circle's diameter will fit around the circle. Pi goes on forever, and can't be calculated to perfect precision: 3.1415926535897932384626433832795028841971693993751.... This is known as the decimal expansion of pi. No apparent pattern emerges in the succession of digits - a predestined yet unfathomable code. They do not repeat periodically, seemingly to pop up by blind chance, lacking any perceivable order, rule, reason, or design - "random" integers, ad infinitum. In 1991, the Chudnovsky brothers in New Read More
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Egyptian Fractions

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Egyptian Fractions Nowadays, we usually write non-integer numbers either as fractions (2/7) or decimals (0.285714). The floating point representation used in computers is another representation very similar to decimals. But the ancient Egyptians (as far as we can tell from the documents now surviving) used a number system based on unit fractions : fractions with one in the numerator. This idea let them represent numbers like 1/7 easily enough; other numbers such as 2/7 were represented as sums of unit fractions (e.g. 2/7 = 1/4 +1/28). Further, the same fraction could not be used twice (so 2/7 = 1/7 + 1/7 is not allowed). We call a formula representing a sum of distinct unit fractions an Egyptian fraction . This notation is cumbersome and difficult to compute with, so the Egyptian scribes m Read More
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Egyptian mathematics

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Egypt, pyramids, the pharaohs and temple reconstructions. Free screen savers and hieroglyphics - you can write your name in the ancient script. 1 2 3 4 5 6 7 8 9 10 100 1,000 10,000 100,000 1,000,000 Discovering Egypt Newsletter *Click Here* to find out what you get. Egyptian Math Numbers The ancient Egyptians were possibly the first civilisation to practice the scientific arts. Indeed, the word chemistry is derived from the word Alchemy which is the ancient name for Egypt. Where the Egyptians really excelled was in medicine and applied mathematics. But although there is a large body of papyrus literature describing their achievements in medicine, there are no records of how they reached their mathematical conclusions. Of course they must have had an advanced understanding of the subject b Read More
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Einstein-Image and Impact. AIP History Center exhibit.

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Text version Download this Einstein Web site in PDF format (3.5 MB) Sign up to find out when we put more exhibits online Einstein en EspaÑol Albert Einstein: Read about Einstein's astounding theory of relativity and his discovery of the quantum, his thoughtful philosophy, and his rise above a turbulent life including marriages and exile. This Einstein exhibit contains many pictures, cartoons, voice clips, and essays on Einstein's work on special relativity, Brownian motion, and more. Brought to you by The Center for History of Physics Copyright ? 1996 - American Institute of Physics Site created Nov. 1996, revised November 2004 Read More
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Euclid's Elements, Introduction

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Introduction Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences. The Elements have been studied 24 centuries in many languages starting, of course, in the original Greek, then in Arabic, Latin, and many modern languages. I'm creating this version of Euclid's Elements for a couple of reasons. The main one is to rekindle an interest in the Elements, and the web is a great way to do that. Another reason is to show how Java applets can be used to illustrate geometry. That also helps to bring the Elements alive. The text of all 13 Books is complete, an Read More
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Fermat's Last Theorem -- from Wolfram MathWorld

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Search Site Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index Interactive Entries Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute an Entry --> Send a Message to the Team Order book from Amazon 12,720 entries Tue Oct 23 2007 Number Theory > Diophantine Equations Foundations of Mathematics > Mathematical Problems > Solved Problems Foundations of Mathematics > Mathematical Problems > Prize Problems Recreational Mathematics > Mathematics in the Arts > Mathematics in Television > The Simpsons Recreational Mathematics > Mathematics in the Arts > Mathematics in Theat Read More
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Foundations of Greek Geometry

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Please note: These papers were prepared for the Greek Science course taught at Tufts University by Prof. Gregory Crane in the spring of 1995. The Perseus Project does not and has not edited these student papers. We assume no responsibility over the content of these papers: we present them as is as a part of the course, not as documents in the Perseus Digital Library . We do not have contact information for the authors. Please keep that in mind while reading these papers. Foundations of Greek Geometry Michael Tirabassi Look at the comments on this paper. Introduction The birth of Greek astronomy has been attributed to Thales of Miletus. Thales brought from Egypt a number of fundamental geometric principles. He was able to take what he learned, develop upon it, and put it to practical use fo Read More
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Frame page for History of Computers

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This page uses frames, but your browser doesn't support them. Read More
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Greek Demonstration: The Return of Odysseus and the Elements of Euclid

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Greek Demonstration: The Return of Odysseus and the Elements of Euclid The Return of Odysseus and the Elements of Euclid This paper was written by Andrew Wiesner and submitted to the classics department of the Colorado College in May of 1994. Introduction It is the overall aim of this paper to obtain a new perspective on the often-treated question of the origins of Greek mathematics. For a number of reasons, an inquiry into these origins must take its start from a consideration of the Elements of Euclid. To begin with, the Elements, in actuality a late achievement of Greek mathematics, is the earliest text of its kind to survive to the present day. Secondly, Euclid himself has come to be viewed less as an original mathematician, and more as the author of a systematic compilation of a tradi Read More
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Greek Mathematics and its Modern Heirs

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Greek Mathematics and its Modern Heirs Greek Mathematics and its Modern Heirs Classical Roots of the Scientific Revolution For over a thousand years--from the fifth century B.C. to the fifth century A.D.--Greek mathematicians maintained a splendid tradition of work in the exact sciences: mathematics, astronomy, and related fields. Though the early synthesis of Euclid and some of the supremely brilliant works of Archimedes were known in the medieval west, this tradition really survived elsewhere. In Byzantium, the capital of the Greek-speaking Eastern empire, the original Greek texts were copied and preserved. In the Islamic world, in locales that ranged from Spain to Persia, the texts were studied in Arabic translations and fundamental new work was done. The Vatican Library has one of the Read More
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HISTORIA MATEMATICA - Julio Gonzalez Cabillon

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HISTORIA MATEMATICA - Julio Gonzalez Cabillon The purpose of this site is to provide a virtual environment for scholarly discussion of the History of Mathematics. If you are using a browser without frames capability click here Read More
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History

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Main Page Equations and Figures PI to 157,500 Digits Definitions Recommendation History of PI Pi has always been known to be the ratio of a circle's circumference to its diameter. It was first used by the Babylonians in about 2000 B.C. They said PI= 3 1/8, which was amazingly accurate. The Egyptians, Chinese, Indians, Europeans, Persians, and many other ancient civilizations also calculated pi with amazing accuracy for their time. Whether they knew it or not, ancient civilizations used PI. For example, the ratio of one side to the of a pyramid on Geae was PI:2. Around 420 B.C., two mathematicians, Antiphon and Byrson of Herclea, came up with a brilliant new way to calculate PI. They knew that to calculate PI, they would need a full circle. They figured that if you start with a hexagon and Read More
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History

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Mathematics started with counting. In about the 2000 BC’s, the Babylonians developed some mathematical ideas. Number problems like the Pythagorean triples (discovered by Pythagoras and the Pythagoreans, his students) were studied from 1700 BC. Linear equations were studied to solve problems, as well as quadratic equations. These led to a kind of numerical algebra. The Greeks studied similar figures, volume and area (geometry problems). Values were also determined for p . The Babylonian’s mathematics passed on to the Greeks. From 450 BC on the Greeks studied and improved many kinds of mathematics. The ancient Greeks discovered conic sections (circular shapes formed when cutting a cone at different angles). They also made many discoveries in astronomy and trigonometry. While the Gr Read More
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History

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A Brief History of Linear Algebra There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants. Arthur Cayley, 1855 Determinants Used Before Matrices 1693 Leibniz 1750 Cramer solving systems of equations Implicit Use of Matrices Late 18th century Lagrange bilinear forms for the optimization of a real valued function of 2 or more variables Gaussian Elimination 1800 Gauss Method known by Chinese for 3x3 in 3rd century BC Vector Algebra 1844 Grassmann Matrix Algebra 1848 J. J. Sylvester introduced the term matrix which is the Latin word for womb (determinants emanate from a matrix) define the nullity of a matrix in 1884 1855 Arthur Cayley definition of matrix multiplication motivated by composite transformations, also introdu Read More
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History of Mathematics

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Lectures on the History of Mathematics by G. Donald Allen Texas A&M University Introduction Web resources Print References The Origins of Mathematics Mathematics of the Indians North of Mexico. Egyptian and Babylonian Mathematics The Mathematics of Ancient Greece Islamic Mathematics The Medieval Period Mathematics of the Renaissance The Transition Period Calculus The Riemann Integral and beyond Algebra and Number Theory This History of Infinity (and other delights) © 1999-2003 G. Donald Allen Read More
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History of Mathematics - Table of Contents

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And Insights into the History of Mathematics Table of Contents Prologue The First Mathematicians The Most Famous Teacher Al'Khwarizmi & Al Jabr Pi: It Will Blow Your Mind Beginnings of Trigonometry Of Amusement and Recreation The Newer Mathematics Bookstore Bibliography Java Based Chat About Mathematics Comments and Notices "If your computer is having problems, you can send it to certified nerds Check out the site by clicking this Ohio Computer repair link" Read More
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History of Mathematics Home Page

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Every culture on earth has developed some mathematics. In some cases, this mathematics has spread from one culture to another. Now there is one predominant international mathematics, and this mathematics has quite a history. It has roots in ancient Egypt and Babylonia, then grew rapidly in ancient Greece. Mathematics written in ancient Greek was translated into Arabic. About the same time some mathematics of India was translated into Arabic. Later some of this mathematics was translated into Latin and became the mathematics of Western Europe. Over a period of several hundred years, it became the mathematics of the world. There are other places in the world that developed significant mathematics, such as China, southern India, and Japan, and they are interesting to study, but the mathematic Read More
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History of Mathematics Home Page

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Every culture on earth has developed some mathematics. In some cases, this mathematics has spread from one culture to another. Now there is one predominant international mathematics, and this mathematics has quite a history. It has roots in ancient Egypt and Babylonia, then grew rapidly in ancient Greece. Mathematics written in ancient Greek was translated into Arabic. About the same time some mathematics of India was translated into Arabic. Later some of this mathematics was translated into Latin and became the mathematics of Western Europe. Over a period of several hundred years, it became the mathematics of the world. There are other places in the world that developed significant mathematics, such as China, southern India, and Japan, and they are interesting to study, but the mathematic Read More
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History of Mathematics: China

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Mathematics in China Table of Contents A brief outline of the history of Chinese mathematics Chronology of Mathematicians and Mathematical Works On-line References Bibliography Menubar access to other pages A brief outline of the history of Chinese mathematics Primary sources are Mikami's The Development of Mathematics in China and Japan and Li Yan and Du Shiran's Chinese Mathematics, a Concise History . See the bibliography below. Numerical notation, arithmetical computations, counting rods Traditional decimal notation -- one symbol for each of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 1000, and 10000. Ex. 2034 would be written with symbols for 2,1000,3,10,4, meaning 2 times 1000 plus 3 times 10 plus 4. Goes back to origins of Chinese writing. Calculations performed using small bamboo counting Read More
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History of Pi

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History of PI The value of Pi has a great value in our scientific life, the importance of that value was gained through the ages. The fact that the ratio of the circumference to the diameter of a circle is constant has been known for so long that it is quite umtraceable. The first value of Pi, including the Biblical value of 3, were almost certainly found by measurement. It was also found that the Egyptians took to be a value for Pi. The first theoretical calculation have been carried out by Archimedes (287-212 BC), he obtained the approximation: 223/71< Pi <22/7. Various people also computed Pi including: Ptolemy (150 AD) => 3.1416 Tsu Chung Chi (430-501 AD) => 355/113 Al Khawarizmi (800) => 3.1416 Al Kashi (1430) => computed Pi to 14 places ViÈte (1540- 1603) => 9 pl Read More
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History overview

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History Page

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History Page NOTE: The following paragraphs give an extremely detailed and organized account of the development of Calculus. Instead of diluting this information by retelling the history of Calculus in my own words, I chose to copy it directly from Microsoft Encarta 97. Please forgive my apparent laziness. Thank you. The English and German mathematicians, respectively, Isaac Newton and Gottfried Wilhelm Leibniz invented calculus in the 17th century, but isolated results about its fundamental problems had been known for thousands of years. For example, the Egyptians discovered the rule for the volume of a pyramid as well as an approximation of the area of a circle. In ancient Greece, Archimedes proved that if c is the circumference and d the diameter of a circle, then 3 (1/7) d During the l Read More
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History Timeline

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Math 490: History Timeline The goal is to create an interactive history of mathematics timeline. By clicking on the line, a surfer should get information about which mathematicians are alive and the important work being done at that time. You are responsible for submitting an entry every Friday by midnight for inclusion on the timeline. Your submission should consider the mathematicians themselves and the type of mathematics being produced. Use several references and be sure to document your sources. Math 490 Home Class Tasks Class Mailing List History Links Progress Check Professor Quinn: Email - Home Office Hours Last updated December 1998 Read More
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History Topics

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History Topics Index This index has been moved. You should be automatically forwarded to the correct page. If your browser leaves you on this page, then press HERE . JOC/EFR November 2000 The URL of this page is: School_of_Mathematics_and_Statistics University_of_St_Andrews,_Scotland http://www-history.mcs.st-andrews.ac.uk/history/HistoryTopics.html Read More
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Hypatia of Alexandria

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Hypatia of Alexandria Mathematician, Astronomer, and Philosopher (d. 415 C.E.) Hypatia was a mathematician, astronomer, and Platonic philosopher. According to the Byzantine encyclopedia The Suda , her father Theon was the last head of the Museum at Alexandria. Hypatia's prominence was accentuated by the fact that she was both female and pagan in an increasingly Christian environment. Shortly before her death, Cyril was made the Christian bishop of Alexandria, and a conflict arose between Cyril and the prefect Orestes. Orestes was disliked by some Christians and was a friend of Hypatia, and rumors started that Hypatia was to blame for the conflict. In the spring of 415 C.E., the situation reached a tragic conclusion when a band of Christian monks seized Hypatia on the street, beat her, and Read More
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Introduction to the works of Euclid

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An Introduction to the Works of Euclid with an Emphasis on the Elements (first posted to the web in 1995) jump to: outline of paper | text of paper | suggestions for further study | bibliography | bottom of page [ anchor here ] Outline of paper Introduction I. The Life of Euclid II. The Works of Euclid Other than the Elements Extant Works Lost Works Questionable Works III. The Structure of the Elements Definitions, Postulates, and Axioms Propositions Parts of a Proposition Sample Proposition from Book I Porisms and Lemmas Overview of the Thirteen Books of the Elements Dependencies Among the Books of the Elements IV. The Contents of the Elements Book I Definitions of Book I Postulates and Axioms of Book I Propositions of Book I Book II Book III Book IV Book V Book VI Book VII Book VIII Book Read More
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Islamic History in Arabia and Middle East

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Islam and Islamic History and The Middle East Arabic Numerals The Message | The Hijrah | The Rightly Guided Caliphs | The Umayyads | Islam In Spain | The 'Abbasids | The Golden Age | The Fatimids | The Seljuk Turks | The Crusaders | The Mongol and The Mamluks | The Legacy | The Ottomans | The Coming of The West | Revival in The Arab East | Related Topics The Holy Quran | The Faith of Islam | Arabic Writing | Science and Scholarship in Al-Andalus | Arabic Literature | ARABIC NUMERALS: Photo: From top - Modern Arabic (western); Early Arabic (western); Arabic Letters (used as numerals); Modern Arabic (eastern); Early Arabic (eastern); Early Devanagari (Indian); Later Devanagari The system of numeration employed throughout the greater part of the world today was probably developed in India, bu Read More
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Ivar's Peterson's Math Trek Archives

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Ivars Peterson's MathTrek Archives Sculpting with a Twist December 22, 2003 Tricky Crossings December 15, 2003 Megaprime Champion December 8, 2003 The Cow in the Classroom December 1, 2003 Pentomino Battleships November 24, 2003 Cool Rationals November 17, 2003 Geometreks November 10, 2003 Strolling Down MÖbius Lane November 3, 2003 Seven-Game World Series October 27, 2003 Election Reversals October 20, 2003 Goldbach Computations October 13, 2003 A Magic Knight's Tour October 6, 2003 The Bias of Random-Number Generators September 29, 2003 Rolling with Reuleaux September 22, 2003 Trimathlon Palindromes September 15, 2003 Pennant Races and Magic Numbers September 8, 2003 Hyperbolic Five September 1, 2003 SET Math August 25, 2003 Golf Clubs and Driving Distance August 18, 2003 Running Lanes a Read More
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MacTutor History of Mathematics

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The MacTutor History of Mathematics archive Biographies Index History Topics Index Additional material index Famous curves index Mathematicians of the day Search the archive Help FAQ Contact us Recent changes to the archive (Up to SEPTEMBER 2007 ) There are 36 new biographies and 1 updated biography. There are 2 new History Topics and 2 new entries in the Honours, medals, etc. category There are 106 new entries in the Additional Material category Other indexes . . . Birthplace Maps index Anniversaries for the year Chronology index Time lines index Quotations index Mathematical Societies index Medals, honours, etc. index Glossary index Poster index St Andrews Colloquium index Index of female mathematicians Mathematical Education index Student projects index Index of Famous Curves with a Jav Read More
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Math Forum - Ask Dr. Math Archives: Elementary History/Biography

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Ask Dr. Math Elementary Archive Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ TOPICS This page: history/biography Search Dr. Math See also the Dr. Math FAQ : Roman numerals Internet Library : history/biography ELEMENTARY Arithmetic addition subtraction multiplication division fractions/decimals Definitions Geometry 2-dimensional circles triangles/polygons 3D and higher polyhedra Golden Ratio/ Fibonacci Sequence History/Biography Measurement calendars/ dates/time temperature terms/units Number Sense/ About Numbers infinity large numbers place value prime numbers square roots Projects Puzzles Word Problems Browse Elementary History/Biography Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common qu Read More
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Mathematical games

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Mathematical Problems of David Hilbert

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The Mathematical Problems of David Hilbert About Hilbert's address and his 23 mathematical problems Hilbert's address of 1900 to the International Congress of Mathematicians in Paris is perhaps the most influential speech ever given to mathematicians, given by a mathematician, or given about mathematics. In it, Hilbert outlined 23 major mathematical problems to be studied in the coming century. Some are broad, such as the axiomatization of physics (problem 6) and might never be considered completed. Others, such as problem 3, were much more specific and solved quickly. Some were resolved contrary to Hilbert's expectations, as the continuum hypothesis (problem 1). Hilbert's address was more than a collection of problems. It outlined his philosophy of mathematics and proposed problems import Read More
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Mathematical Quotation Server

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"Life is good for only two things, discovering mathematics and teaching mathematics"--Sim?on Poisson Quick links : ---- Search --- Browse --- Download --- Random A Random Quotation: Veblen, Thorstein (1857-1929) Invention is the mother of necessity. J. Gross, The Oxford Book of Aphorisms, Oxford: Oxford University Press, 1983. The Collection This page points to a collection of mathematical quotations culled from many sources. You may conduct a keyword search through the quotation database by clicking here. Now, By popular demand, you may download the whole collection at once. (It's about 243k...83 printed pages or so.) Follow this link to download the entire collection. Of course, you may also access the quotations "page by page". They are organized in alphabetic order Read More
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Mathematicians of the Seventeenth and Eighteenth Centuries

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Mathematicians of the Seventeenth and Eighteenth Centuries Available here are accounts of the lives and works of seventeenth and eighteenth century mathematicians (and some other scientists), adapted from A Short Account of the History of Mathematics by W. W. Rouse Ball (4th Edition, 1908). The ordering of the mathematicians and scientists below is approximately chronological. A separate index is provided which lists these people in alphabetical order . RenÉ Descartes (1596 - 1650) Bonaventura Cavalieri (1598 - 1647) Pierre de Fermat (1601 - 1665) John Wallis (1616 - 1703) William, Viscount Brouncker (1620 - 1684) Blaise Pascal (1623 - 1662) Christian Huygens (1629 - 1695) Isaac Barrow (1630 - 1677) James Gregory (1638 - 1675) Some Contemporaries of Descartes, Fermat, Pascal and Huygens: C Read More
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Mathematics

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Mathematics Mathematics Ancient Science and Its Modern Fates Until recently, historians of the Scientific Revolution of the 16th and 17th centuries treated it as a kind of rebellion against the authority of ancient books and humanist scholarship. In fact, however, it began with the revival of several tremendously important and formidably difficult works of Greek science. The mathematics and astronomy of the Greeks had been known in medieval western Europe only through often imperfect translations, some of them made from Arabic intermediary texts rather than the Greek originals. The papal curia became a center for the recovery of the original Greek manuscripts, often very old and remarkably elegant, and the production of new translations of these works. Ptolemy's "Geography" -- the book whi Read More
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Mathematics

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Mathematics Mathematics Ancient Science and Its Modern Fates Until recently, historians of the Scientific Revolution of the 16th and 17th centuries treated it as a kind of rebellion against the authority of ancient books and humanist scholarship. In fact, however, it began with the revival of several tremendously important and formidably difficult works of Greek science. The mathematics and astronomy of the Greeks had been known in medieval western Europe only through often imperfect translations, some of them made from Arabic intermediary texts rather than the Greek originals. The papal curia became a center for the recovery of the original Greek manuscripts, often very old and remarkably elegant, and the production of new translations of these works. Ptolemy's "Geography" -- the book whi Read More
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Mathematics

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Mechanisation Philosophy Logic General Threads in the Web of Mathematics Re-use and Abstraction Real Numbers Real Numbers - a logical development Real Numbers - some history Computing with reals History A Short History of Rigour in Mathematics Classical Greek Mathematics Mathematics and the Scientific Revolution The Formalisation of Mathematics Formality and Rigour in 20 th Century Mathematics © created 1995/10/29 modified 1998/11/3 Read More
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Mathematics (Rome Reborn: The Vatican Library & Renaissance Culture)

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The Library of Congress >> Exhibitions Rome Reborn: The Vatican Library & Renaissance Culture HOME | Exhibition Sections: Introduction | The Vatican Library | Archaeology Humanism | Mathematics | Music | Medicine | Nature | Orient to Rome | Rome to China Exhibition Companion Volume | Credits MATHEMATICS Until recently, historians of the Scientific Revolution of the 16th and 17th centuries treated it as a kind of rebellion against the authority of ancient books and humanist scholarship. In fact, however, it began with the revival of several tremendously important and formidably difficult works of Greek science. The mathematics and astronomy of the Greeks had been known in medieval western Europe only through often imperfect translations, some of them made from Arabic intermediary text Read More
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Mayan math and culture

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pictures of Cancun Condos you can rent click here for capsule overview of our properties and services Mayan Math The history and civilization of the Mayans has always intrigued tourists to Cancun. The math of the Mayans was sophisticated, logical, and ahead of it's time. THE MAYAN NUMBERS The Mayan' s number system is in some respects very similar to ours. They used only 3 symbols as opposed to our 10 and at the time hundreds of symbols used in Roman Numerals. These symbols are shown below. The bar symbol represents 5, and the dots are 1's. The numbers can be written with the dots on top of horizontal lines . They may also be combined with shells for zero. The top left represents the number 6 . Under this is 8 . Under this is 14 . Then the bottom left is 7 . The top middle is 16 . Can you Read More
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Mersenne Primes: History, Theorems and Lists

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Mersenne Primes: History, Theorems and Lists A forty fourth Mersenne found September 2006: 2 32582657 -1 Contents: Early History Perfect Numbers and a Few Theorems Table of Known Mersenne Primes The Lucas-Lehmer Test and Recent History Conjectures and Unsolved Problems See also Where is the next larger Mersenne prime? and Mersenne heuristics For remote pages on Mersennes see the Prime Links' Mersenne directory Primes: [ Home || Largest | Proving | How Many? | Mersenne | Glossary | Mailing List ] 1. Early History Many early writers felt that the numbers of the form 2 n -1 were prime for all primes n , but in 1536 Hudalricus Regius showed that 2 11 -1 = 2047 was not prime (it is 23 . 89). By 1603 Pietro Cataldi had correctly verified that 2 17 -1 and 2 19 -1 were both prime, but then incorre Read More
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Mesopotamian Mathematics

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Mesopotamian Mathematics The purpose of this page is to provide a source of information on all aspects of Mesopotamian mathematics. We explain the origins of mathematics in Mesopotamia from the earliest tokens, through the development of Sumerian mathematics to the grand flowering in the Old Babylonian period, and on into the later periods of Mesopotamian history. We include some general surveys to get you oriented in each period, and some more detailed resources for those interested in specific aspects of this fascinating episode in history. Like most other Web pages it is under slow construction as time permits. Some of these resources are of general interest, others are intended mainly for use by students in my History of Mathematics class. Background History A very brief and biased sum Read More
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MONTE CARLO METHOD

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HISTORY OF MONTE CARLO METHOD by Sabri Pllana | Home | History | Buffon | Links | E-mail | Read More
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Non-Euclidean Geometries, Discovery

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. --> G o o g l e Web CTK Sites for teachers Sites for parents Terms of use Awards Interactive Activities CTK Exchange Games & Puzzles What Is What Arithmetic/Algebra Geometry Probability Outline Mathematics Make an Identity Book Reviews Eye Opener Analog Gadgets Inventor's Paradox Did you know?... Proofs Math as Language Things Impossible Visual Illusions My Logo Math Poll Cut The Knot! MSET99 Talk Other Math sites Front Page Movie shortcuts Personal info Reciprocal links Privacy Policy Guest book News sites Recommend this site --> Sites for teachers Sites for parents Education & Parenting --> --> Non-Euclidean Geometries Drama of the Discovery Four names - C. F. Gauss (1777-1855), N. Lobachevsky (1792-1856), J. Bolyai (1802-1860), and B. Riemann (1826-1866) - are traditionally associated Read More
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Pagina nueva 1

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Esta p?gina usa marcos, pero su explorador no los admite. Read More
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Pi History

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History of Pi Pi was known by the Egyptians, who calculated it to be approximately (4/3)^4 which equals 3.1604. The earliest known reference to pi occurs in a Middle Kingdom papyrus scroll, written around 1650 BC by a scribe named Ahmes. He began the scroll with the words: "The Entrance Into the Knowledge of All Existing Things" and remarked in passing that he composed the scroll "in likeness to writings made of old." Towards the end of the scroll, which is composed of various mathematical problems and their solutions, the area of a circle is found using a rough sort of pi. Around 200 BC, Archimedes of Syracuse found that pi is somewhere about 3.14 (in fractions; Greeks did not have decimals). Pi (which is a letter in the Greek alphabet) was discovered by a Greek mathematician named Archim Read More
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Proofs of the Quadratic Reciprocity Law

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Proofs of the Quadratic Reciprocity Law These things are best done with Frames Author Year Method 1. Legendre 1788 Quadratic forms; incomplete 2. Gauß 1 1801 Induction; April 8, 1796 3. Gauß 2 1801 Quadratic forms; June 27, 1796 4. Gauß 3 1808 Gauß's Lemma; May 6, 1807 5. Gauß 4 1811 Cyclotomy; May 1801 6. Gauß 5 1818 Gauß's Lemma; 1807/08 7. Gauß 6 1818 Gauß sums; 1807/08 8. Cauchy 1829 Gauß 6 9. Jacobi 1830 Gauß 6 10. Dirichlet 1 1835 Gauß 4 11. Lebesgue 1 1838 N(x 1 2 + ... + x q 2 = 1 mod p) 12. SchÖnemann 1839 quadratic period equation 13. Cauchy 1840 Gauss 4 14. Eisenstein 1 1844 generalized Jacobi sums 15. Eisenstein 2 1844 Gauß 6 16. Eisenstein 3 1844 Gauß's Lemma 17. Eisenstein 4 1845 Sine 18. Eisenstein 5 1845 infinite products 19. Kummer 1 1846 period equation 20. Liouville 1847 Read More
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Roger A. McCain

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Welcome to Roger A. McCain's Personal Web Pages About these pages These pages will continue to offer many of the pages formerly served from Dr. McCain's "William King" server, including "Essential Principles of Economics. Caution -- the version of Essential Principles of Economics offered here has only partly been updated to the 2000's, and contains some inconsistencies and outdated material as a result. There is no timetable for the update as of now. The relatively political pages from the William King server will not be served here. See http://home.comcast.net/~romccain/intro.html for those pages. In any case, all opinions and assertions of fact found here are attributable to Roger A. McCain and are not positions of Drexel University, the Department of Economics and International Busines Read More
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Sacred Geometry

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Home Visit The Dome Directions History Science Rejuvenation Sacred Geometry Membership Photo Gallery Contact Sacred Geometry The Virtue of Domes The Integratron and the Tabernacle of Moses The Virtue of Domes St. Peter's Basilica in Rome, the Church of the Transfiguration on Mt. Taber in Israel, and the Capitol rotunda in Washington, DC are three well-known domed buildings. The concave lenses in telescopes focus light from distant stars. Dish antennas are used to focus sound and electromagnetic waves. Mechanically speaking, domes are power-enhancers or power-focusers. A whisper on one side of a parabolic domed building can easily be heard on the other because the sound is focused toward the center by its spherical shape. This energy-focusing ability was considered when the Integratron was Read More
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Sacred geometry -- What Is It?

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A {TEXT-DECORATION: none}A:visited {TEXT-DECORATION: none}A:hover {TEXT-DECORATION: none}A:active {TEXT-DECORATION: none} SACRED GEOMETRY -- WHAT IS IT? The term "sacred geometry" is used by archaeologists,anthropologists, and geometricians to encompass the religious,philosohical, and spiritual beliefs that have sprung up aroundgeometry in various cultures during the course of human history.It is a catch-all term covering Pythagoreangeometry and neo-Platonic gometry, as well as the perceived relationshipsbetween organic curves and logarithmic curves. Here are a few examples of how the "sacred" has entered into geometry in different eras and cultures: 1) The ancient Greeks assigned various attributes to the Platonicsolids and to certain geometrically-derived ratios, investingthem Read More
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Social and Historical Aspects of Mathematics

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SOCIAL AND HISTORICAL ASPECTS OF MATHEMATICS MODULE MM2217 ONLINE Module Guide Module Content: The development of counting systems and notations. The development of notation and concepts in algebra. Changing systems of geometry from Euclid to Klein's programme. The development of calculus. The development of the foundations of mathematics. Group Presentation Modern applications of mathematics in science,technology and business. The development and influence of computers on mathematics. The social implications of mathematics. Other Topics. Links to other History of Mathematics sites For more information about the module please contact: D Thompson (Module Leader) cm1938@mail.wlv.ac.uk , Room MU509, tel 321861 D Wilkinson cm1985@mail.wlv.ac.uk , Room MU517, tel 321452. Maths Home Page Univers Read More
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Social and Historical Aspects of Mathematics

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SOCIAL AND HISTORICAL ASPECTS OF MATHEMATICS MODULE MM2217 ONLINE Module Guide Module Content: The development of counting systems and notations. The development of notation and concepts in algebra. Changing systems of geometry from Euclid to Klein's programme. The development of calculus. The development of the foundations of mathematics. Group Presentation Modern applications of mathematics in science,technology and business. The development and influence of computers on mathematics. The social implications of mathematics. Other Topics. Links to other History of Mathematics sites For more information about the module please contact: D Thompson (Module Leader) cm1938@mail.wlv.ac.uk , Room MU509, tel 321861 D Wilkinson cm1985@mail.wlv.ac.uk , Room MU517, tel 321452. Maths Home Page Univers Read More
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Some Fractal History

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Some Fractal History Before Mandelbrot Like new forms of life, new branches of mathematics and science don't appear from nowhere. The ideas of fractal geometry can be traced to the late nineteenth century, when mathematicians created shapes -- sets of points -- that seemed to have no counterpart in nature. By a wonderful irony, the "abstract" mathematics descended from that work has now turned out to be MORE appropriate than any other for describing many natural shapes and processes. Perhaps we shouldn't be surprised. The Greek geometers worked out the mathematics of the conic sections for its formal beauty; it was two thousand years before Copernicus and Brahe, Kepler and Newton overcame the preconception that all heavenly motions must be circular, and found the ellipse, parabola, and hyp Read More
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Stable algebraic topology 1945-1966, by J.P. May

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Stable algebraic topology 1945-1966, by J.P. May This is a reasonably comprehensive treatment of the history of stable algebraic topology during the cited period. The table of contents gives an idea of the scope and limitations of the study. The emphasis is on the evolution of ideas, but some mathematical exposition of most of the main results is given. This paper will appear in a volume on the history of topology that is being edited by Ioan James. Contents: Setting up the foundations The Eilenberg-Steenrod axioms Stable and unstable homotopy groups Spectral sequences and calculations in homology and homotopy Steenrod operations, K(\pi ,n)'s, and characteristic classes The introduction of cobordism The route from cobordism towards K-theory Bott periodicity and K-theory The Adams spectral Read More
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The Abacus: Index

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Selected by Scientific American as a winner of the 2003 Sci/Tech Web Awards. Contents Introduction Construction · Basics · Java Applet · Technique · The Abacus Today History Timeline · Salamis Tablet · Counting Board · Roman Hand Abacus · Suan Pan · Soroban · Schoty · Nepohualtzitzin · Khipu · Lee Abacus Interactive Abacus Tutor Sarat Chandran and David A. Bagley's incredible Java abacus with a built-in tutor for counting, addition and subtraction. Calculations Addition · Subtraction · Multiplication & Division · Square Roots · Cube Roots The Lee Abacus The manual for the Lee Abacus, c. 1958 is available as Text · Images The Abacus as Art Michael Mode builds exotic abaci as art objects. Abacus: Mystery of the Bead Abacus Techniques by Totton Heffelfinger & Gary Flom. Articles, Excerpts and Read More
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The Euler Society

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Click here to go to the home page of CSHPM . Read More
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The Geometry of War

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Introduction Summaries Essay Catalogue Figures Bibliography Index Acknowledgements Museum Home Page Read More
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The History of Combinatorics

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Combinatorics Combinatorics is the study of permutations and combinations of groups of elements in sets. Combinatorial problems, such as magic squares, have been studied for many hundreds of years. Xenocrates (396-314 BC) is said to have determined that a total of 1 002 000 000 000 syllables could be formed from the letters of the Greek alphabet. Pascal's triangle, named after Blaise Pascal, is a useful tool for determining combinations and although it was named after Blaise Pascal (1623-1662), who discovered it in the 17 th century, it was known to the Arabs in the 13 th century and the Chinese in the 14 th . It looks somewhat like: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 The first and last numbers in each row are both 1, and every other number is the sum of the two a Read More
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Topology enters mathematics

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Topology enters mathematics Listing had examined connectivity in three dimensional Euclidean space but Betti extended his ideas to n dimensions. This is not as straightforward as it might appear since even in three dimensions it is possible to have a surface that cannot be reduced to a point yet closed curves on the surface can be reduced to a point. Betti 's definition of connectivity left something to be desired and criticisms were made by Heegaard. The idea of connectivity was eventually put on a completely rigorous basis by PoincarÉ in a series of papers Analysis situs in 1895. PoincarÉ introduced the concept of homology and gave a more precise definition of the Betti numbers associated with a space than had Betti himself. Euler 's convex polyhedra formula had been generalised to not n Read More
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Web search

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Click here to proceed. Read More
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Welcome to the Wonderful World of Fractals

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Welcome to the Wonderful World of Fractals This web page was designed for North Andover High School, MA math project. This page will discuss the following topics: The history of fractals, the basic concept of fractals, frequently asked questions about fractals, and examples of some famous fractals. There will also be a list of links to some fractal web pages. "I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means 'to break' to create irregular fragments. It is therefore sensible - and how appropriate for our need ! - that, in addition to "fragmented" (as in fraction or refraction), fractus should also mean "irregular", both meanings being preserved in fragment." B. Mandelbrot , Fractals: The Story How long is the easter Read More
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Why study calculus? a brief history of math

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Why Do We Study Calculus? or, a brief look at some of the history of mathematics an essay by Eric Schechter version of August 23, 2006 The question I am asked most often is, "why do we study this?" (or its variant, "will this be on the exam?"). Indeed, it's not immediately obvious how some of the stuff we're studying will be of any use to the students. Though some of them will eventually use calculus in their work in physics, chemistry, or economics, almost none of those people will ever need prove anything about calculus. They're willing to trust the pure mathematicians whose job it is to certify the reliability of the theorems. Why, then, do we study epsilons and deltas, and all these other abstract concepts of proofs? Well, calculus is not a just vocational training course. In part, stu Read More
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Women Mathematicians

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Biographies of W omen Mathematicians Home | Alphabetical Index | Chronological Index | Resources | Credits | Search Welcome to the web site for biographies of women in mathematics. These pages are part of an on-going project at Agnes Scott College in Atlanta, Georgia, to illustrate the numerous achievements of women in the field of mathematics. Here you can find biographical essays or comments on the women mathematicians profiled on this site, as well as additional resources about women in mathematics. Each time this page is reloaded, a randomly selected photo is displayed to the left (if Javascript is enabled). Click on the image to go to the profile of that woman. We also welcome contributions of biographical information or essays from those outside Agnes Scott College. If you are intere Read More
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