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I'm not a geometer but I thought I remembered a theorem that said they hyperbolic plane can't be embedded in euclidean 3-space [1] (I can't really remember the

• theoh 10y ago
  The surface has negative curvature, which is all it takes to create a hyperbolic geometry. It doesn't have to extend to infinity and include the whole of hyperbolic space to exemplify the geometry. So it's hyperbolic, but not the whole of hyperbolic space. On a tangent, but commenting on the article: Even something as simple as the surface of a sphere has an intrinsic geometry which is non-Euclidean. So it's frankly a bit ridiculous for Wertheim to affect wonderment at the apparent "intelligence" implied by the sea slug's production of a surface with a non-Euclidean intrinsic geometry. It's disingenuous at best. Take the example of a falling rock: it doesn't know anything about elegant 19th C formulations of mechanics. It doesn't need to, but humans nevertheless make leaps of understanding of unchanging phenomena.
  • soVeryTired 10y ago
    That's a fair point. I guess you can reasonably describe a wall as 'planar' without requiring that it extends out to infinity too.