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

problem of counting the number of triangulations of a convex polygon. Euler, one of the most

studied earlier by the prolific Leonhard Euler (1707-1783), can be stated as follows. Given a convex n-sided polygon, divide it into triangles by drawing non-intersecting diagonals connecting some of the vertices of the polygon. Euler calculated the number, Pn, of distinct triangulations of a convex n-gon 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.