# Are there $\pi$ -Dimension?

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.

• Consider this en.wikipedia.org/wiki/Fractal_dimension – Sonal_sqrt Jan 14 at 14:50
• Ahh thank you. Didn’t know that, great! – Maths Jan 14 at 14:52
• @Sonal_sqrt So, what is a $\pi$ dimensional ball? – Berci Jan 14 at 16:22
• @Berci: That would be a metric space homeomorphic to, say, $B^3$, and having Hausdorff dimension equal to $\pi$. – Moishe Kohan Jan 14 at 19:50
• 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. – Vepir Jan 14 at 19:53