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A well known isoperimetric inequality for closed curves in $ \mathbb{R}^2$ can be generalized to closed curves in $ \mathbb{R}^{2n}$ , see: https://mathoverflow.net/a/321505/121665. I have two questions: Question 1. Is it possible to prove a reasonable isoperimetric inquality for closed curves in $ \mathbb{R}^{2n+1}$ ? Questions 2. Can an inequality from https://mathoverflow.net/a/321505/121665 be generalized toRead more

I’ve just been told in a comment of this question I posted two days ago that there exists a Matlab function that computes the centroid of any convex polytope in $ \mathbb{R}^n$ . The user who pointed out that Matlab function knows of no equivalence in Mathematica. Therefore, my question is: do we have anyRead more

Consider a “curve” defined by a list of points in finite dimension (here, four): pts = Table[{Cos[t], 0, Sin[2 t], Sin[t]}, {t, Subdivide[0, 1, 99]}] What would be a good approach to compute the local curvature? Several possibilities I thought of: interpolating pts and using ArcCurvature (introduced in Mathematica 10) using $ n+1$ consecutive pointsRead more

For any sequence in a compact set $ K$ of $ \mathbb{R}^n$ , it is well known that there is a subsequence that is convergent to a point in $ K$ . Is this true that for any sequence in a compact set $ K$ of $ \mathbb{R}^n$ , there is a partition of thisRead more