Pascal's arithmetical triangle: the story of a mathematical idea
Imagine having some marbles, pebbles, or other objects that you want to lay out in a neat triangular pattern. How many do you need to end up with a complete triangle? Three will do; so will 6, 10, 15, and... These numbers are called triangular numbers. Ask the same question for a triangular pyramid. Four will do; so will 10, 20, 35, and... the so-called pyramidal numbers. This book looks at the discovery of the multiplicity of properties and uses triangular numbers and their many extensions possess.
Although often displayed in a triangular array named after the seventeenth-century French philosopher Blaise Pascal, triangular numbers were known many centuries earlier. In this book A.W.F. Edwards traces the Arithmetical Triangle back to its roots in Pythagorean arithmetic, Hindu combinatorics, and Arabic algebra, and gives an account of the progressive solution of combinatorial problems from the earliest recorded examples to the work of Renaissance and later mathematicians. He shows how Pascal's work -- so modern in style -- in establishing the properties of the numbers and their application in various fields led to Newton's discovery of the binomial theorem for fractional and negative indices and to Leibniz's discovery of calculus.
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Pascal's Arithmetical Triangle: The Story of a Mathematical Idea
A. W. F. Edwards
Limited preview - 2002
Johns Hopkins University Press | Books | Pascal's Arithmetical ...
Pascal's Arithmetical Triangle The Story of a Mathematical Idea. awf Edwards $22.95 paperback 978-0-8018-6946-4 (52 ctn qty) 2002 224 pp. ...
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JSTOR: Pascal's Arithmetical Triangle
<7n, l A- I :l~t R Pascal's arithmetical triangle an individual's use of the triangle, with no sense of historical framework. Amazingly, this anachronistic ...
Pascal's Triangle - Identities from The Treatise
From the cover of the paperback edition of Edwards' Pascal's Arithmetical Triangle This image reproduced by the kind permission of Johns Hopkins University ...
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Book Review. Pascal's Arithmetical Triangle awf Edwards. Isis. Sponsored by the History of Science Society. Search Journal ...
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Earliest Known Uses of Some of the Words of Mathematics (P)
The story of the triangle(s) is told in awf Edwards's Pascal's Arithmetical Triangle. Because the Traité "brought together all the different aspects of the ...
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2003 Royal Statistical Society. 0039–0526/03/52403. The Statistician (2003). 52. ,. Part 3. ,. pp. 403–422. Book reviews. Books for review ...
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Pascal, Blaise. Born: June 19, 1623, in Clermont, France. Died: August 19, 1662, in Paris, France. Blaise Pascal was one of the most influential figures ...
doi.wiley.com/ 10.1002/ 0470011815.b2a17111
Traité du triangle arithmétique , 1654 In 1654 Blaise Pascal ...
Traité du triangle arithmétique, 1654. In 1654 Blaise Pascal entered into correspondence with Pierre de Fermat of Toulouse ...
www.lib.cam.ac.uk/ deptserv/ rarebooks/ PascalTraite/ pascalintro.pdf
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Pascal's Arithmetical Triangle: The Story of a Mathematical Idea · Pascal's Arithmetical Triangle: The Story of a Mathematical Idea ...