Talk:Centered polygonal number

Karl, it's very nice to have this article. But the changes you made to the linked articles seemed very wrong to me for some reason:


 * A centered k-agonal number is a figurate number that represents a k-agon ...

So I changed them to


 * A centered k-agonal number is a centered figurate number that represents a k-agon ...

Anton Mravcek 21:13, 27 Jul 2004 (UTC)

Anton, I agree with your changes. Further thought, suggests that Centred number should be moved to Centred polygonal number like Polygonal number.

User:Karl Palmen 12:15 28 Jul 2004 (UTC)

Proposed merger

 * Oppose. I think it's a terrible idea, especially for centered hexagonal numbers. For the others, a case can be made, but still not likely to convince me. PrimeFan 21:38, 15 March 2007 (UTC)

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"The difference of the n-th and the (n+1)-th consecutive centered k-gonal numbers is k(2n+1)." Is unclear. When I solve the the difference between (n+1)-th centered k-gonal number and n-th centered k-gonal number I get k(2n). More generally, if you solve for difference of (n+p)-th centered k-gonal number and n-th k-gonal number you get $$C_{k,n+p}-C_{k,n} =\frac{kp}{2}(2n+p-1)$$. Returning to $$ k(2n+1)$$, I'm assuming you can simply say that $$k=\frac{kp}{2}$$ and $$ 1=p-1$$, which is satisfied by p=2, not p=1. Is the original phrase supposed to mean the difference in $$ C_{k,n+1}-C_{k,n}$$ or something else entirely? Hiruki8 (talk) 22:07, 12 January 2024 (UTC)