Comment on xkcd #3077: de Sitter

• Hamartiogonic@sopuli.xyz ⁨10⁩ ⁨months⁩ ago

  If you draw a triangle on different parts of a toroid, would you get different angles?

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  • knightly@pawb.social ⁨10⁩ ⁨months⁩ ago

    Yup! That saddle is a shape of constant negative curvature. On a toroid, the inside of the hole would have negagive curvature and the outside would have positive curvature.

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    • Hamartiogonic@sopuli.xyz ⁨10⁩ ⁨months⁩ ago

      Wow. That would be truly bizarre kind of space to live in.

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  • WalrusDragonOnABike@reddthat.com ⁨10⁩ ⁨months⁩ ago

    Same is true for a sphere. For example, if you draw a triangle with 1 vertex at the north pole and the other two on the equator, all the angles are 90 degrees. But if you move, say, the north pole vertex to be closer to the two in the equator, then you’d get a smaller sum.

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    • Hamartiogonic@sopuli.xyz ⁨10⁩ ⁨months⁩ ago

      Hmm… that’s a good point. Basically anything other than a flat surface will have these bizarre properties.

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