
Pascal's Triangle - peter_d_sherman
https://en.wikipedia.org/wiki/Pascal%27s_triangle
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peter_d_sherman
>"The pattern obtained by coloring only the odd numbers in Pascal's triangle
closely resembles the fractal called the Sierpinski triangle. This resemblance
becomes more and more accurate as more rows are considered;

 _in the limit, as the number of rows approaches infinity, the resulting
pattern is the Sierpinski triangle_

, assuming a fixed perimeter.[22]"

[https://www.goldennumber.net/pascals-
triangle/](https://www.goldennumber.net/pascals-triangle/)

>"The Fibonacci Series is found in Pascal’s Triangle.

Pascal’s Triangle, developed by the French Mathematician Blaise Pascal, is
formed by starting with an apex of 1. Every number below in the triangle is
the sum of the two numbers diagonally above it to the left and the right, with
positions outside the triangle counting as zero.

 _The numbers on diagonals of the triangle add to the Fibonacci series_ , as
shown below."

[see link above, for image]

So, here's a potential identity between Pascal's Triangle, The Sierpinski
Triangle, and Phi.

Recursion too, if we think about the Sierpinski Triangle as being drawn via a
recursive algorithm, and, at least one type of fractal / space-filling curve
(another way of looking at Sierpinski Triangles)...

Pascal's Triangle -- might be some form of Rosetta Stone of Mathematics...

I wonder if there is a relationship between Pascal's Triangle and pi, e, and
the square root of -1...

