Volume of a sphere in n-dimension Calculator
Calculates the volume and surface area of a sphere in n-dimensional space given the radius. | ||
| n=1: V=2r (diameter), S=2 n=2: V=πr^2 (circle\ area), S=2πr (circumference) n=3: V=4/3*πr^3 (volume), S=4πr^2 (surface area) A sphere in 4-dimensional space or more is used by statistical mechanics, quantum mechanics, etc. |
Volume of a sphere in n-dimension
| [1-10] /10 | Disp-Num |   |
- Purpose of use
- Looking for a general formula for the surface of a "sphere" in an n-dimensional space, where n is "any" number. For one thing was wondering if there is a 4/3 power relationship for any particular value of n.
[1] 2022/12/28 01:41 60 years old level or over / Others / Very /
- Purpose of use
- Calculate the relative volume enclosed by the unit hypersphere of the [77x768] prompt Tensor for Stable Diffusion when inputs are treated as a flat 59136D space - in explanation of the vastness of the latent space whilst walking off the text-embedding manifold (random walks)
- Comment/Request
- Short simple and sweet, useful and quick. Very helpful - keep it up! Will likely come back to quickly check my working on mobile whilst doing other arithmetic afk. Thanks!
[2] 2022/11/15 22:28 20 years old level / Self-employed people / Very /
- Purpose of use
- Checking if the volume of a 1-d ball was indeed 2 (yes)
[3] 2022/01/19 10:52 Under 20 years old / High-school/ University/ Grad student / Useful /
- Purpose of use
- Compare the volume of a 22 dimensional sphere with the fine structure constant. Close, but no cigar.
- Comment/Request
- The only place on the web that has a calculator for hyperdimensional spheres. Thanks for making it free!
[4] 2021/12/09 12:43 50 years old level / An office worker / A public employee / Very /
- Purpose of use
- Research
[5] 2019/06/26 06:35 20 years old level / High-school/ University/ Grad student / Useful /
- Purpose of use
- Writing my own code that will be able to calculate this. Checking my numerical results with this :)
[6] 2015/10/15 22:40 Under 20 years old / High-school/ University/ Grad student / Very /
- Purpose of use
- I was learning my alphabet today. and this helped me fill in the sphere for the full-stop
- Comment/Request
- I want more bugs on this page
[7] 2014/11/07 02:21 60 years old level or over / Elementary school/ Junior high-school student / Very /
- Purpose of use
- Keeping my mind sharp at 78 years old
[8] 2014/09/20 16:06 60 years old level or over / An engineer / Very /
- Purpose of use
- Calculate the dimensions of a hypothetical pile of soil
[9] 2013/04/24 17:32 50 years old level / An office worker / A public employee / Very /
- Comment/Request
- Excellent Please include other formulae also
[10] 2009/10/05 07:15 50 level / Self-employed people / Very /
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