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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Mathemadness
RandomI like math. When I was a kid, numbers were my version of toy cars. Equations, of action figures. Things I could break down and put back together. I come off as weird. I prefer unique. "Ew, you like math? How nerdy." "Yeah yeah. Now. How much were y...
