in reply to Triangle Numbers

Well I can't add much to the Perl solutions given by YuckFoo and particle. Heck, I'm having fun just working through them to understand the code and learn some more.

I do find Triangle Numbers interesting though. Here's a bit more about them on MathWorld. Extend the triangles into the third dimension and you get Tetrahedral Numbers. I wonder if a similar statement could be made with tetrahedral numbers.

Owl looked at him, and wondered whether to push him off the tree; but, feeling that he could always do it afterwards, he tried once more to find out what they were talking about.

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Re^2: Triangle Numbers
by Anonymous Monk on Dec 03, 2005 at 21:56 UTC
    I'm looking at triangular and tetrahedral numbers for a paper for my Computational Number Theory class. If you look at how many triangular numbers (1/2*n*(n+1) n in N) are tetrahedral numbers (1/6*n*(n+1)*(n+2) n in N) you find that there are only 5. 5?!?! Everyone I've talked to thought there would be an infinite number of them. But why restrict ourselves to 3-d? Given any number n in a dimension d we can find the d-th dimensional analogue of the n-th triangular number given by binomial(n+d-1, d). Then things start to get strange... Robert Weston OSU Math Major westonr at onid dot orst dot edu
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