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Triangle of Pascal
The structure within Pascal's triangle can be found in the tetractys, a pythagoric figure that shows the number 10.
Explanation
The number 10 was the symbol of the completion for the ancient Greeks. With points you can draw this number as a triangle.
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1 + 2 + 3 + 4 = 10
If you begin with 1 point and add more and more rows you get the tetractys, but of course you can continue even further.
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11 + 2 = 3 1 + 2 + 3 = 6 1 + 2 + 3 + 4 = 10 1 + 2 + 3 +4 + 5 = 15