Pascal's arithmetical triangle
The Arithmetical Triangle, one of the most important number patterns in the history of mathematics, has greatly influenced the development of probability theory and the history of analysis. This book is the first to explore its roots in Pythagorean arithmetic, Hindu combinatorics, and Arabic algebra, also describing the progressive solution of combinatorial problems from the earliest recorded examples to the Renaissance and later. Meticulously researched, the work provides a complete account of Pascal's fundamental work on probability and makes a distinctive contribution to the history of mathematics.
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Bernoullis Ars conjectandi
Pascal and the Problem of Points
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addition rule argument Arithmetical Triangle Bernoulli 1713 Bhaskara binomial coefficients binomial distribution binomial expansion binomial numbers binomial theorem Binomial Triangle Boyer Briggs Cardano Chapter column combinatorial numbers Combinatorial Triangle conjectandi correspondence dati David dice edition enumeration equation event-tree Faulhaber figurate numbers Figurate Triangle formula fumma Gambler's Ruin gave given Herigone Hindu Huygens imaginary game integers interpolation Jakob Bernoulli James Bernoulli John Bernoulli Knobloch Leibniz letter Maistrov mathematical induction Mersenne Mesnard method of expectations Moivre Montmort multinomial multinomial coefficient natural numbers Newton Nicholas Bernoulli notation number of arrangements number of combinations obtained Oughtred Pascal and Fermat Pascal's method Pascal's Treatise Pascal's Triangle permutations Problem of Points proof Proposition ratiociniis refers Reprinted result Smith solution solved stake Stifel Tartaglia tetrahedral numbers things taken three players throws Todhunter 1865 tosses Traite du triangle translation triangle arithmetique triangular numbers Vieta Wallis Wallis's whilst Whiteside