Forty-five, the number’s square root, is also a triangular number, and that means we can write it as a sum of consecutive numbers. Like this: 45 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9. That means that ...

To make your own Pascal’s triangle, all you need is a pen and paper and one very simple rule – each number in the triangle is the sum of the two numbers directly above it.

Proof without Words: Every Fourth Power Greater than One Is the Sum of Two Nonconsecutive Triangular Numbers Roger B. Nelsen Mathematics Magazine , p. 44 (1 page) ...