Timeline for Formula for volume of $n$-ball for negative $n$
Current License: CC BY-SA 4.0
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| Nov 23, 2023 at 11:08 | history | edited | Anixx | CC BY-SA 4.0 |
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| Nov 23, 2023 at 10:58 | history | edited | Anixx | CC BY-SA 4.0 |
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| Nov 23, 2023 at 6:48 | history | edited | Anixx | CC BY-SA 4.0 |
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| Oct 10, 2020 at 13:22 | history | edited | Anixx | CC BY-SA 4.0 |
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| Oct 10, 2020 at 13:11 | comment | added | Anixx | @JamesPropp a periodic lattice in -1-dimension is both a ball and a a cube. That's why I confined my answer to the dimension -1 only. If we take the dimension -2, the square lattice would be a cube, but not a sphere, and I cannot tell how a ball in this dimension should look like | |
| Oct 10, 2020 at 12:57 | history | edited | Anixx | CC BY-SA 4.0 |
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| Oct 10, 2020 at 12:48 | history | edited | Anixx | CC BY-SA 4.0 |
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| Oct 10, 2020 at 12:42 | history | edited | Anixx | CC BY-SA 4.0 |
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| Oct 10, 2020 at 2:47 | history | edited | Anixx | CC BY-SA 4.0 |
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| Oct 10, 2020 at 1:21 | history | edited | Anixx | CC BY-SA 4.0 |
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| Apr 19, 2020 at 22:06 | comment | added | Anixx | @JamesPropp also, take a look at this: tglad.blogspot.com/2017/08/… | |
| Apr 19, 2020 at 17:25 | comment | added | Anixx | @JamesPropp And, in general, when we are talking about negative dimensions, the bodies in them are littices, spectrums and other (infinite but countable) collections of dots, but their volumes are determined based on their overall density (or the infinite part of numerocity if you prefer), not on the number of dots they include. | |
| Apr 19, 2020 at 17:10 | comment | added | Anixx | @JamesPropp This answer is specifically about the dimension -1, and the generalization to other dimensions may require efforts. Particularly, because in dimension -1 the periodic lattice is both a sphere and a cube. | |
| Apr 19, 2020 at 17:03 | comment | added | James Propp | I do not see why “the unit sphere is a pi-periodic lattice” (and I doubt that it is a “known fact”). Also, Anixx’s style of answer is unlikely to discriminate between even and odd (negative) dimensionalities, so I think it’s on the wrong track. | |
| Apr 19, 2020 at 16:34 | history | edited | Anixx | CC BY-SA 4.0 |
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| Apr 19, 2020 at 16:33 | comment | added | Anixx | @JamesPropp oh yes, i missed a mistake | |
| Apr 19, 2020 at 16:31 | comment | added | James Propp | This proposed value of the “volume” of the (-1)-ball does not agree with the formula given in the original post. | |
| Apr 18, 2020 at 3:58 | history | edited | Anixx | CC BY-SA 4.0 |
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| Apr 18, 2020 at 3:48 | history | edited | Anixx | CC BY-SA 4.0 |
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| Apr 18, 2020 at 3:32 | history | answered | Anixx | CC BY-SA 4.0 |