4 ms·

Volume of a hypercube?

• honkhonkpants 10y ago
  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.
  • roywiggins 10y ago
    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".
  • phaemon 10y ago
    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)
    • majewsky 10y ago
      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).
      • phaemon 10y ago
        ? 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.