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Calcmathlete

  • 2 years ago

What are triangular numbers, pentagonal numbers, etc?

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  1. KingGeorge
    • 2 years ago
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    Triangular numbers are of the form \[1+2+...+n=\frac{n(n+1)}{2}\]

  2. KingGeorge
    • 2 years ago
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    Square numbers are \[1,4,9,...\]

  3. UnkleRhaukus
    • 2 years ago
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    |dw:1344055445671:dw|

  4. ashelz
    • 2 years ago
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  5. KingGeorge
    • 2 years ago
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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.

  6. Calcmathlete
    • 2 years ago
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    Is that really all it is? I thought that it was more complex for some reason...thank you :)

  7. UnkleRhaukus
    • 2 years ago
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    |dw:1344055538341:dw|

  8. UnkleRhaukus
    • 2 years ago
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    are they ment to start at n=0 or at n=1?

  9. KingGeorge
    • 2 years ago
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    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
    • 2 years ago
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    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
    • 2 years ago
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    is zero a triangular/square/pentagonal,.... number???

  12. KingGeorge
    • 2 years ago
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    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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