Are there $\pi$ -Dimension ? When I was thinking of dimensions such as about n-balls. I asked myself why isn't there a $\pi$-Ball. we always talk about n being a natural number. I know the illustration is difficult but the same applies for the 4th or 5th dimension. Thank you very much.

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    $\begingroup$ Consider this en.wikipedia.org/wiki/Fractal_dimension $\endgroup$ – Sonal_sqrt Jan 14 at 14:50
  • $\begingroup$ Ahh thank you. Didn’t know that, great! $\endgroup$ – Maths Jan 14 at 14:52
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    $\begingroup$ @Sonal_sqrt So, what is a $\pi$ dimensional ball? $\endgroup$ – Berci Jan 14 at 16:22
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    $\begingroup$ @Berci: That would be a metric space homeomorphic to, say, $B^3$, and having Hausdorff dimension equal to $\pi$. $\endgroup$ – Moishe Kohan Jan 14 at 19:50
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    $\begingroup$ The "Canonical π dimensional space?" is essential this question, but not specifically about a ball. The answer there gives examples of $\pi$-dimensional (in the sense of fractal dimension aka Hausdorff dimension) objects. For some examples of fractal dimensions $\in[0,3]$ see this wikipedia article. $\endgroup$ – Vepir Jan 14 at 19:53

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