Pascal's Arithmetical Triangle: Pascal's Arithmetical Triangle: The Story of a Mathematical Idea (Dover Books on Mathematics)

"""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 Pascal's Arithmetical Triangle was named for the seventeenth-century French philosopher/mathematician Blaise Pascal, though he did not invent it. A never-ending equilateral triangle of numbers that follow the rule of adding the two numbers above to get the number below, it appears much earlier in the literature of Hindu and Arabic mathematics and continues to fascinate Western mathematicians. Two sides are comprised of ""all 1s"" and because the triangle is infinite, there is no ""bottom side."" This book by A. W. F. Edwards, Professor of Biometry at the University of Cambridge, explores Pascal's Arithmetical Triangle and the way it has been studied, enjoyed, and used by mathematicians throughout history. ""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. Bernard, 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" Cover Title Page Copyright Page Dedication Contents Note Preface to the Johns Hopkins edition Preface to the original edition 1. The figurate numbers 2. Three combinatorial rules 3. The combinatorial numbers in India 4. The combinatorial numbers in the West 5. The binomial numbers 6. Pascal's Treatise on the Arithmetical Triangle, Part I 7. Pascal's Treatise, Part II, and associated tracts 8. The Arithmetical Triangle in analysis 9. The binomial and multinomial distributions 10. Bernoulli's Ars conjectandi Epilogue Appendix I: Pascal and the Problem of Points Appendix II: Pascal's Problem: The "Gambler's Ruin" Appendix III: Commentary on Ars conjectandi Appendix IV: Table of binomial coefficients References General index Index of names This survey explores the history of the arithmetical triangle, from its roots in Pythagorean arithmetic, Hindu combinatorics, and Arabic algebra to its influence on Newton and Leibniz as well as modern-day mathematicians.