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**robinhouston** @robinhouston · Jan 8

Because it's 2025, we're all thinking about the identity $(\sum_{i = 0}^{n} i)^{2} = \sum_{i = 0}^{n} i^{3}$

I'm now wondering how closely this is related to the similar (but in a way simpler) identity
$(\int_{0}^{n} x d x)^{2} = \int_{0}^{n} x^{3} d x$

Is the former a direct consequence of the latter?

Greg Egan @gregeganSF@mathstodon.xyz

I said some hand-wavy things about that here, but there are some nice pictures of 4-dimensional stacks of cannon balls:

**robinhouston** @robinhouston · Jan 8

robinhouston @robinhouston

@gregeganSF Thanks! That whole discussion is interesting.

**John Carlos Baez** @johncarlosbaez · Jan 9

John Carlos Baez @johncarlosbaez

@robinhouston @gregeganSF - it's been so long I've forgotten most of the details!

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