Patterns Within the Triangle

		Diagonals The first diagonal is, of course, just "1"s, and the next diagonal has the Counting Numbers (1,2,3, etc). The third diagonal has the triangular numbers (The fourth diagonal, not highlighted, has the tetrahedral numbers.)
Odds and Evens If you color the Odd and Even numbers, you end up with a pattern the same as the Sierpinski Triangle
		Horizontal Sums What do you notice about the horizontal sums? Is there a pattern? Isn't it amazing! It doubles each time (powers of 2).
Exponents of 11 ⇒ Pascal's Triangle But what happens with 115 ? Simple! The digits just overlap, like this: The same thing happens with 116 and so on.

Fibonacci Sequence Try this: make a pattern by going up and then along, then add up the squares (as illustrated) ... you will get the Fibonacci Sequence. (The Fibonacci Sequence starts "1, 1" and then continues by adding the two previous numbers, for example 3+5=8, then 5+8=13, etc)

Symmetrical And the triangle is also symmetrical. The numbers on the left side have identical matching numbers on the right side, like a mirror image.