## Calcmathlete 3 years ago What are triangular numbers, pentagonal numbers, etc?

1. KingGeorge

Triangular numbers are of the form $1+2+...+n=\frac{n(n+1)}{2}$

2. KingGeorge

Square numbers are $1,4,9,...$

3. UnkleRhaukus

|dw:1344055445671:dw|

4. ashelz

5. KingGeorge

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.

6. Calcmathlete

Is that really all it is? I thought that it was more complex for some reason...thank you :)

7. UnkleRhaukus

|dw:1344055538341:dw|

8. UnkleRhaukus

are they ment to start at n=0 or at n=1?

9. KingGeorge

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.

10. Calcmathlete

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 :)

11. UnkleRhaukus

is zero a triangular/square/pentagonal,.... number???

12. KingGeorge

I don't think 0 is usually listed as one of these numbers. But formally, I think it is a triangular/square/pentagonal number .