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Comment by ClashTheBunny | Hacker News Reader

Volume of a hypercube?

That's sort of what I figured, that it was necessarily hyperdimensional. But then I don't see why geometers of this era would have been willing to ponder hyperdimensional solids, but aren't willing to admit arbitrary exponents. Path-dependent historical attitude, I guess.

I think it was probably the first hints of polynomials that could stand on their own without a sane geometric interpretation. As in, "this makes no geometric sense, but I can use the same geometry-based techniques I used on squares and cubes, and it all works out, so let's just go with it."

Another way to interpret it could be, "okay, take this cube with a volume, take that volume and pretend it's actually the width of another special mega-cube and never mix mega-cubes and regular cubes".

Volume of a hypercube? I swear, there's something about maths that makes your brain work in the strangest ways.

A square of a square is a square made up of squares :)

(like a Sudoku puzzle)

Not really. A sudoku puzzle is a set of squares arranged inside another, bigger square. If it were a square of squares, it would mean that you square the initial square's volume including the unit. But in this case, you're only multiplying with a count (or rather, a squared count, since we're talking about two dimensions).

? We're not talking about any units, we're talking about numbers. There are 3^4 squares in a Sudoku puzzle. You don't need a hypercube or any unit of measurement to see that's true.

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