Pascal's Triangle from Top to Bottom
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|Matthew Hubbard and Tom Roby|
|A comprehensive resource for the study of Pascal's Triangle. The section "Applications" addresses questions such as "What types of questions are answered by the binomial coefficients?" and "What number greater than 1 shows up most often in Pascal's Triangle?" and draws on Java applets to address "What does Pascal's Triangle look like mod n?" and "What is the Problem of Points?" The section "Identities" organizes identities and proofs into the categories sums, products, sums of products, products of sums, factorization identities, identities by name, and identities involving famous numbers (e.g., Euler numbers, Fibonacci numbers, and Stirling numbers). "Algorithms" includes the hypergeometric series, Sister Celine's Method, Gosper's Algorithm, Zeilberger's Algorithm, and the WZ (Herb Wilf and Doron Zeilberger) Proof. With histories on the study of binomial coefficients in China, India, the Middle East, and Europe.|
|Levels:||High School (9-12), College, Research|
|Resource Types:||Reference Sources, Web Interactive/Java|
|Math Topics:||Polynomials, Number Sense/About Numbers, Patterns/Relationships, History and Biography, Number Theory|
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