The Pascal's triangle and its geometric interpretations

• Main Authors: Semeon, Pearly, Balintec, Gladys
• Format: text
• Language: English
• Published: Animo Repository 1992
• Subjects: Pascal's triangle; Geometry > Problems, exercises, etc.
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/15980
• Institution: De La Salle University

This paper gives a relationship between geometry and Pascal's Triangle. It present three geometric interpretations of Pascal's Triangle. These are fully explained with illustrations provided for easier understanding.The researchers are able to make the following generalizations:1. Given n points in real (n-1)- space, the entry in row n and diagonal m of the Pascal's Triangle gives the number of (m -1) spaces determined by n points taken m at a time.2. Given n points in the plane forming the vertices of a convex polygon, the entry in row n and diagonal m of the Pascal's Triangle gives the number of m-gons determined by those points and the segments joining them.3. In the real plane, if n points are given, the entry in the diagonal m and row n of the Pascal's Triangle gives the number of algebraic polynomial functions in one variable of m - 1 degree which are determined by the point n taken m at a time.