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niktemadur@lemmy.world to Ask Science@lemmy.worldEnglish · 2 years ago

If a 1D figure has length, a 2D figure has area, and a 3D figure has volume, are there names for what's inside 4D, 5D figures and so on?

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If a 1D figure has length, a 2D figure has area, and a 3D figure has volume, are there names for what's inside 4D, 5D figures and so on?

niktemadur@lemmy.world to Ask Science@lemmy.worldEnglish · 2 years ago
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  • mumblerfish@lemmy.world
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    2 years ago

    You’d just continue saying ‘volume’, alternatively ‘k-dimensional volume’ or ‘volume of the n-dimensional object’. Like for spheres: https://en.m.wikipedia.org/wiki/Volume_of_an_n-ball

    The n-dimensional volume of a Euclidean ball of radius R in n-dimensional Euclidean space is:[1]

    • {isplaystyle V{n}(R)={rac {i ^{n/2}}{amma {igl (}{frac {n}{2}}+1{igr )}}}R^{n},}
  • chknbwl@lemmy.world
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    2 years ago

    A popular example of a four-dimensional polytope is the Tesseract, which is just a 4D cube. Four dimensional and beyond polytopes have what is called a hypervolume. This can be calculated by using Lebesgue measure, which is beyond my understanding of mathematics.

    Fun fact: four-dimensional analysis is common in the development of modern parallel supercomputing!

  • Apytele@sh.itjust.works
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    deleted by creator

  • Num10ck@lemmy.world
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    2 years ago

    4D ounces

    • Cadeillac@lemmy.world
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      2 years ago

      To freedom

      • edgemaster72@lemmy.world
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        2 years ago

        is the only chance I have

  • EleventhHour@lemmy.world
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    2 years ago

    4D also has duration

    • Bassman1805@lemmy.world
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      2 years ago

      In specific applications where it is useful to consider time as a 4th spacial dimension.

      So if you’re not talking about relativity, it’s probably not.

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