Pascal's arithmetical triangle

A.W.F. Edwards

220 pages, parution le 30/10/2002

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Résumé

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.

Contents

The figurate numbers
Three combinatorial rules
The combinatorial numbers in India
The combinatorial numbers in the West
The binomial numbers
Pascal's Treatise on the Arithmetical Triangle, Part I
Pascal's Treatise, Part II, and associated tracts
The Arithmetical Triangle in analysis
The binomial and multinominal distributions
Bernoulli's Ars conjectandi

Epilogue
Pascal and the Problem of Points
Pascal's Problem: The "Gambler's Ruin"
Commentary on Ars conjectandi
Table of binomial coefficients

Caractéristiques techniques

	PAPIER
Éditeur(s)	Johns Hopkins
Auteur(s)	A.W.F. Edwards
Parution	30/10/2002
Nb. de pages	220
Format	15,2 x 23,5
Couverture	Broché
Poids	327g
Intérieur	Noir et Blanc
EAN13	9780801869464
ISBN13	978-0-8018-6946-4