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Feb
20
awarded  Yearling
Feb
17
awarded  Nice Answer
Feb
17
revised Can the unsolvability of quintics be seen in the geometry of the icosahedron?
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Jan
8
awarded  Nice Answer
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?
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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