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Jun
13
comment Minimum sphere containing a tetrahedron
@zamazalotta: I doubt it. Consider a flat "cap-shaped" tetrahedron with one large equilateral face, and the fourth vertex somewhere just slightly above that face. The circumcenter is way off near infinity, and the incenter is just underneath the fourth vertex, but the center of the minimal enclosing sphere is precisely the center of the large equilateral face and doesn't change as you move the fourth vertex.
Jun
13
revised Generalization of ellipse equation to higher dimensional surfaces
equation was getting cut off in Linux
Jun
12
comment The comparison theorem for matrices
@PZZ: I think Erick meant that $A \succeq B$ is commonly used in describing semidefinite matrices. I'll grant that it would seem an unusual parsing of his statement, if not for the fact that I have always seen $A \succeq B$ used to denote the positive semidefiniteness of $A - B$ in optimization texts.
Jun
12
comment Minimum sphere containing a tetrahedron
Your edit conveys no information; any 4 points lie on a sphere.
Jun
12
answered Minimum sphere containing a tetrahedron
Jun
12
comment Minimum sphere containing a tetrahedron
Sure, the minimum of the circumradius and $\sqrt{3/8}$ times the length of the longest edge is an upper bound on the radius of the minimal enclosing sphere.
Jun
12
comment Minimum sphere containing a tetrahedron
By the way, you should be aware there are algorithms to compute the smallest enclosing sphere of an arbitrary number of points in linear time. There's a little more info in the comp.graphics.algorithms FAQ.
Jun
12
comment Minimum sphere containing a tetrahedron
If you want me to be notified of a comment, you need to put the syntax "@Rahul" somewhere in it. (You always get notified of comments on your own questions.) Anyway, think about it for a minute: does the barycenter of the vertices work for the example I just mentioned?
Jun
12
comment Minimum sphere containing a tetrahedron
The answer to the last sentence is no. Consider a "spire-shaped" tetrahedron with an equilateral base and a large altitude; the insphere is centered near the base, but the smallest enclosing sphere is centered about halfway up the altitude.
Jun
12
comment $\operatorname{arsinh}$ vs $\operatorname{arcsinh}$
@Arturo, does anybody write $\sin^{-1}x$ to mean $(\sin x)^{-1}$ (or even $\sin^{-2}x$ to mean $(\sin x)^{-2}$)? I do love the usual convention, but I feel it is restricted to positive exponents.
Jun
12
revised Generalization of ellipse equation to higher dimensional surfaces
added 66 characters in body; added 33 characters in body
Jun
12
answered Generalization of ellipse equation to higher dimensional surfaces
Jun
12
revised What did Cantor take to be the relationship between the countable ordinals and the power set of the naturals?
edited tags
Jun
12
revised Covering points on a sphere with a disk
bump :(
Jun
11
answered Covering points on a sphere with a disk
Jun
11
comment On minimizing the area of an enclosing surface subject to nonnegative Gaussian curvature
@Leonid: Thanks!
Jun
11
comment On minimizing the area of an enclosing surface subject to nonnegative Gaussian curvature
@Leonid, I know what $C^1$ and $C^2$ mean, but what is $C^{1,1}$?
Jun
11
comment On minimizing the area of an enclosing surface subject to nonnegative Gaussian curvature
@yasmar: Thanks for pointing out that there exist nonconvex polyhedra with positive angle defect, in particular ones whose area is less than that of the corresponding convex hull. I just realized that this is very relevant for my original motivation for this question.
Jun
11
comment How to check if a matrix is positive definite
Gerry's point is that no, you can't say that the matrix is not positive definite just because you found an $x_1x_2$ term.
Jun
11
accepted On minimizing the area of an enclosing surface subject to nonnegative Gaussian curvature