In almost all books on College Algebra, the Pascal Triangle is placed in such a position as to show the binomial coefficients in a horizontal line. This position is appropriate when the only use of the triangle is to help students remember these coefficients; but Pascal had a wider purpose in mind. Pascal's Construction. Pascal first sets up a lattice-work consisting of equal squares, assigning to each square a definite positive integer which he determines as follows. 1. The number in each square of the 1st (top) row, and also in each square of the 1st (left-hand) column is to be unity. 2. To each other square is assigned an integer determined by the recurrence relation which he states thus: "The number in any other square is equal to the sum of the two numbers immediately to the left, and immediately above it."
Proceedings of the Iowa Academy of Science
©1956 Iowa Academy of Science, Inc.
McClenon, R. B.
"Pascal's Arithmetical Triangle,"
Proceedings of the Iowa Academy of Science, 63(1), 534-537.
Available at: https://scholarworks.uni.edu/pias/vol63/iss1/54