Pascal’s Triangle

Pascal’s triangle is an isosceles triangle that is generated from the top down.  The top of the triangle is row zero and has one element, which is 1.  Row one is directly below row zero and has two elements, which are 1 and 1.  Row two contains the numbers 1 3 3 1, where each element is generated from the sum of the two numbers directly above it.  The outer left and right side of the triangle consists of all 1’s.  This pattern of adding the two numbers above to get the number below is continued throughout the triangle.  When you dissect the triangle row by row you start to see that the row is symmetrical can creates a palindrome.  For instance, row 5 is: 1, 5, 10, 10, 5, 1 and can be read forwards and backwards.  A line of horizontal symmetry can be see on the triangle.  Each row of the triangle, as you move down, has exactly one more number in it.  The zeroth and last element of every row is always a 1.

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