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Oct
7
comment Why is there no theory of $G$-ic varieties, for linear algebraic groups $G$?
By torus, I mean R^n/Z^n. It is compact but not finite. And you are right, this does not answer the question, because I missed the G↪X part.
Sep
24
answered Why is there no theory of $G$-ic varieties, for linear algebraic groups $G$?
Jun
7
comment Limit of the lengths $=$ lengths of the limit
Thanks for the video.
Jun
7
answered Limit of the lengths $=$ lengths of the limit
Jun
7
comment Equal perimeters of squares and right angled isosceles triangles
No. You also need that the sequence of path derivatives converges to the derivatives of the path. Otherwise the limiting path will have every where a different direction than the target. This is the case in the example, the limiting path looks like the diagonal, but under a magnifing glass, the direction of any of the segments of the limit is either horizontal, either vertical, never at 45°.
Jun
7
comment Equal perimeters of squares and right angled isosceles triangles
You are perfectly correct, except when you say that the perimeter of the limit is the limit of the perimeters.
Jun
7
comment Linear Algebra: Span
Take any vector in the pane. Then another one which is not a multiple of the first.
Jun
7
comment Is $i$ irrational?
If is it not real, it cannot be rational [no joke] gweigt.net
Jun
7
comment Given $E=\mathbb{R}^3$, let $f$ be an endomorphism of $E$ defined by the matrix $A=(a_{i,j})$ on the canonic basis. Let $v,w$ be two eigenvectors.
2) Hint: How many eigenvectors can you find for a multiple eigenvalue?
Jun
7
comment Given $E=\mathbb{R}^3$, let $f$ be an endomorphism of $E$ defined by the matrix $A=(a_{i,j})$ on the canonic basis. Let $v,w$ be two eigenvectors.
1) Correct: You can generalize your proof to show that any subspace generated by eigen-vectors is invariant [by the way you do not need to show they map the whole plane]
Jun
7
answered Multivariable calculus max/min
Mar
16
awarded  Yearling
Jan
1
revised When is the moment of inertia of a smooth plane curve is maximum?
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Jan
1
revised When is the moment of inertia of a smooth plane curve is maximum?
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Jan
1
revised When is the moment of inertia of a smooth plane curve is maximum?
deleted 252 characters in body
Jan
1
comment When is the moment of inertia of a smooth plane curve is maximum?
c) No Robjohn and Achille did not took into account that the curve length is constant. They use ∫ds = L, not d(∫ds)=0. In facts, if you follow their reasoning to search the curve maximizing the include area (or the lowest center of gravity), you also find straight lines, not circles (or catenaries).
Jan
1
comment When is the moment of inertia of a smooth plane curve is maximum?
b) You are write, I am on the wrong question. I was looking for the curve minimizing the moment on inertia about an axis ("chosen" as Ox). I'll edit in the post.
Jan
1
answered When is the moment of inertia of a smooth plane curve is maximum?
Jan
1
comment When is the moment of inertia of a smooth plane curve is maximum?
Of course, I am choosing the origin at the center of mass, computations are difficult enough.
Dec
31
answered When is the moment of inertia of a smooth plane curve is maximum?