What are triangular numbers, pentagonal numbers, etc?

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What are triangular numbers, pentagonal numbers, etc?

Mathematics
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Triangular numbers are of the form \[1+2+...+n=\frac{n(n+1)}{2}\]
Square numbers are \[1,4,9,...\]
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Basically, if you were to draw out the shape, and fill it with dots, that would be your "____" number where you fill in ____ with triangular, square, pentagonal and so on.
Is that really all it is? I thought that it was more complex for some reason...thank you :)
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are they ment to start at n=0 or at n=1?
That's really there is. So the hexagonal numbers would be modeled by|dw:1344055645318:dw|and you get exactly 15 dots which is the third hexagonal number.
Alright. I just wanted to know because my textbook gave me a formula for the xth number of an n-gon, but I had no idea what it was talking about. Again, thank you :)
is zero a triangular/square/pentagonal,.... number???
I don't think 0 is usually listed as one of these numbers. But formally, I think it is a triangular/square/pentagonal number .

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