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Historical Projects in Discrete Mathematics and Computer Science
"... A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itse ..."
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A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itself, with the notion of counting a discrete operation, usually cited as the first mathematical development
Introduction Counting Triangulations of a Convex Polygon
"... problem of counting the number of triangulations of a convex polygon. Euler, one of the most ..."
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problem of counting the number of triangulations of a convex polygon. Euler, one of the most
Gabriel Lam'e's Counting of Triangulations
"... studied earlier by the prolific Leonhard Euler (17071783), can be stated as follows. Given a convex nsided polygon, divide it into triangles by drawing nonintersecting diagonals connecting some of the vertices of the polygon. Euler calculated the number, Pn, of distinct triangulations of a convex ..."
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studied earlier by the prolific Leonhard Euler (17071783), can be stated as follows. Given a convex nsided polygon, divide it into triangles by drawing nonintersecting diagonals connecting some of the vertices of the polygon. Euler calculated the number, Pn, of distinct triangulations of a convex ngon for the first few values of n, and conjectured a formula for Pn based on an empirical study of the ratios Pn+1/Pn [1, p. 339 350] [2]. Lam'e was one of the first to provide the details for a combinatorial proof of Euler's conjectured result for Pn+1/Pn, a proof which the reader will study in its original (translated) version in this project.