Pascal's Arithmetical Triangle: The Story of a Mathematical Idea (Johns Hopkins Paperback)

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9780801869464: Pascal's Arithmetical Triangle: The Story of a Mathematical Idea (Johns Hopkins Paperback)
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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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From the Publisher:

"An impressive culmination of meticulous research into original sources, this definitive study constitutes the first full-length history of the Arithmetic Triangle."—Mathematics of Computation

"A fascinating book . . . giving new insights into the early history of probability theory and combinatorics, and incidentally providing much stimulating material for teachers of mathematics."—G.A. Barnard, International Statistical Institute Review

"Scrupulously researched . . . Carries the reader along in a rewarding manner. It is a scientific who-dun-it, and one must admire the author for the scholarly yet unpedantic manner in which he disperses some of the mists of antiquity."—A.W. Kemp, Biometrics

"Recommended not only to historians and mathematicians, but also to students seeking to put some life into the dry treatment of these topics to which they have doubtless been subjected."—Ivor Grattan-Guinness, Annals of Science

About the Author:

A.W.F. Edwards is a professor of biometry at the University of Cambridge and a fellow of Gonville and Caius College, University of Cambridge, England. He is the coauthor of Annotated Readings in the History of Statistics and author of Foundations of Mathematical Genetics and Likelihood, the last is available from Johns Hopkins.

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