If you take the sum of the shallow diagonal, you will get the Fibonacci numbers.Ĭatalan numbers are found by taking polygons, and finding how many ways they can be partitianed into triangles. *Note that these are represented in 2 figures to make it easy to see the 2 numbers that are being summed. You can find them by summing 2 numbers together. If you start with row 2 and start with 1, the diagonal contains the triangular numbers.ĭown the diagonal, as pictured to the right, are the square numbers. That last number is the sum of every other number in the diagonal. Then change the direction in the diagonal for the last number. Start with any number in Pascal's Triangle and proceed down the diagonal. Since 10 has two digits, you have to carry over, so you would get 161,051 which is equal to 11^5. The numbers in row 5 are 1, 5, 10, 10, 5, and 1. For example, the numbers in row 4 are 1, 4, 6, 4, and 1 and 11^4 is equal to 14,641.

In fact, if Pascal's triangle was expanded further past Row 15, you would see that the sum of the numbers of any nth row would equal to 2^nĮach row represent the numbers in the powers of 11 (carrying over the digit if it is not a single number). If you will look at each row down to row 15, you will see that this is true. Similiarly, in Row 1, the sum of the numbers is 1+1 = 2 = 2^1. If you notice, the sum of the numbers is Row 0 is 1 or 2^0. That prime number is a divisor of every number in that row. When you look at Pascal's Triangle, find the prime numbers that are the first number in the row. History of Pascal's Triangle Properties of Pascal's Triangle Primes Kate make sure your browser is maxiumized to view this write up Pascal's Triangle Essay Pascal's Triangle

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