What is Pascals Triangle?
In the twelfth century, both Persian and Chinese mathematicians were working on a so-called arithmetic triangle that is relatively easily constructed and that gives the coefficients of the expansion of the algebraic expression (a + b)n for different integer values of n (Boyer, 1991, pp. 204 and 242). Here’s how it works: • Start with a row with just one entry, a 1. • Begin and end each subsequent row with a 1. • Each row should have one more entry than the row above it. Determine each interior entry by adding the number directly above the space for the new entry to the number diagonally above and to the left, so you get 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1 1 11 55 165 330 462 462 330 165 55 11 1 1 12 66 220 495 792 924 792 495 220 66 12 1 1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1 1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1 1 15 105
