➕ Pascal's Triangle ➕

37 7 5
                                        

You know, the-
Oh.
You probably don't know.

Well, that's why I'm here!

Pascal's Triangle is a little thing where the two numbers above calculate the next number. Here's the first nine lines.

1
1  1
1  2  1
1  3  3  1
1  4  6  4  1
1  5  10  10  5  1
1  6  15  20  15  6  1
1  7  21  35  35  21  7  1
1  8  28  56  70  56  28  8  1

It has really interesting properties. For example, the suns of the rows are powers of two.

1 = 1
2 = 1  1
4 = 1  2  1
8 = 1  3  3  1
16 = 1  4  6  4  1
32 = 1  5  10  10  5  1
64 = 1  6  15  20  15  6  1
128 = 1  7  21  35  35  21  7  1
256 = 1  8  28  56  70  56  28  8  1

And, if you select the numbers by odd and even, you get something like Sierpinski's triangle, which will be shown in the next chapter. Here, I'll make a diagram. White will be even. Black will be odd.


⚫ ⚫
⚫ ⚪ ⚫
⚫ ⚫ ⚫ ⚫
⚫ ⚪ ⚪ ⚪ ⚫
⚫ ⚫ ⚪ ⚪ ⚫ ⚫
⚫ ⚪ ⚫ ⚪ ⚫ ⚪ ⚫
⚫ ⚫ ⚫ ⚫ ⚫ ⚫ ⚫ ⚫

It's really cool. It's a triangle made out of triangles made out of triangles made out of triangles...

Until next time...

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