Marcos Cossarini
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 Oct 5 comment A question about simple closed curves in 3-dimensional Euclidean space For an alternative ending, consider the oriented volume of the tetrahedron of vertices $C(0+t)$,$C(1/4+t)$, $C(1/2+t)$, $C(3/4+t)$. When $t$ goes from $0$ to $1/4$, the volume goes from one value to its opposite. So it must be zero for some $t\in[0,1/4]$. At that time the four points are coplanar. Sep 27 answered A family of convex bodies in Banach-Mazur position Sep 27 comment A family of convex bodies in Banach-Mazur position @VictorProtsak: $\log r$ is a distance in the usual sense, however for this case it is usual to leave the $r$ as it is, so for example, the triangle inequality is $d(K,L)\leq d(K,J)\,d(J,L)$. Apr 9 revised Why worry about the axiom of choice? added 2 characters in body Apr 9 revised Why worry about the axiom of choice? edited body Feb 20 awarded Yearling Feb 2 comment Examples of common false beliefs in mathematics A Finsler metric (symmetric or not) can always be bounded between two Riemannian metrics, and induces the same topology that the manifold already has before considering any metric. This topology is metrisable. Oct 14 revised Does for every vector field there always exist a volume form for which the vector field is a homothety? added 15 characters in body Oct 14 revised Does for every vector field there always exist a volume form for which the vector field is a homothety? added 40 characters in body Oct 14 answered Does for every vector field there always exist a volume form for which the vector field is a homothety? Oct 14 revised Manifolds admitting flat connections edited body Oct 14 revised Manifolds admitting flat connections added 8 characters in body Oct 14 revised Manifolds admitting flat connections added 8 characters in body Oct 13 comment Manifolds admitting flat connections I corrected the "symmetric flat" thing. I like the idea of using Cartan-Hadamard to prove that spheres don't admit torsionfree flat connections. This saves the task of proving that only toruses admit free $\mathbb R^n$ actions, which is something I didn't do in my answer. Oct 13 revised Manifolds admitting flat connections added 164 characters in body Oct 12 answered Manifolds admitting flat connections Sep 24 awarded Autobiographer Sep 12 comment Does anyone know an intuitive proof of the Birkhoff ergodic theorem? If $f\equiv 1$ and $T=I$ we have $M_T'\equiv+\infty$, so the recurrence formula is $+\infty + f=+\infty$, which is useless. Am I missing something? Aug 23 awarded Nice Answer Aug 12 revised real symmetric matrix has real eigenvalues - elementary proof added 391 characters in body