more about Pascal's Triangle

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.)


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Odds and Evens
If you color the Odd and Even numbers, you end up with a pattern the same as the Sierpinski Triangle



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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 is made by adding the two previous numbers, for example 3+5=8, then 5+8=13, etc)



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