Pascal's Triangle

The Fibonacci Series is found in Pascal's Triangle

Pascal's Triangle, developed by the French Mathematician Blaise Pascal, is formed by starting with an apex of 1.  Every number below in the triangle is the sum of the two numbers diagonally above it to the left and the right, with positions outside the triangle counting as zero.

The numbers on diagonals of the triangle add to the Fibonacci series, as shown below.

Pascal's triangle has many unusual properties and a variety of uses:

• Horizontal rows add to powers of 2 (i.e., 1, 2, 4, 8, 16, etc.)

• The horizontal rows represent powers of 11 (1, 11, 121, 1331, etc.)

• Adding any two successive numbers in the diagonal 1-3-6-10-15-21-28... results in a perfect square (1, 4, 9, 16, etc.)

• It can be used to find combinations in probability problems (if, for instance, you pick any two of five items, the number of possible combinations is 10, found by looking in the second place of the fifth row.  Do not count the 1's.)

• When the first number to the right of the 1 in any row is a prime number, all numbers in that row are divisible by that prime number