Comment on Under what circumstances or axioms do spheres (the shape) have infinite surface area?

• LifeInMultipleChoice@lemmy.world ⁨2⁩ ⁨days⁩ ago

  I read it as surface area, thus being the amount of space on the sphere itself.

  A=4πr2 is the formula if I remember correctly, so I just figure only r can be altered to match infinity

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  • thebestaquaman@lemmy.world ⁨2⁩ ⁨days⁩ ago

    I believe the surface area of an n-dimensional hypersphere is (n - 1) pi r^{n - 1}. In that case (I may have some factors wrong here, just going off memory), an infinite-dimensional hypersphere has infinite surface area as long as it has non-zero radius.

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    • loppy@fedia.io ⁨1⁩ ⁨day⁩ ago

      It does indeed scale with r^(n-1), but your factors are not close at all. It involves the gamma function, which in this case can be expanded into various factorials and also a factor of sqrt(pi) when n is odd. According to Wikipedia, the expression is 2pi^(n/2)r^(n-1)/Gamma(n/2).

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      • thebestaquaman@lemmy.world ⁨1⁩ ⁨day⁩ ago

        While I’m completely open that my factor is likely wrong here, the expression you provided is definitely wrong in both the 2D and 3D case (I’m assuming the r superscript on the pi was a typo), since it gives neither n = 2 => A = 2 pi r nor n = 3 => A = 4 pi r^2.

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• Knock_Knock_Lemmy_In@lemmy.world ⁨1⁩ ⁨day⁩ ago

  Math is weird. You can have infinite circumference but finite radius.

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