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Jan
13 |
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Proving the existence of good covers
@Misha The two page triangulation proof by Cairns (1961) is flawed: see more discussion here: mathoverflow.net/questions/139339/… |
Jul
27 |
answered | Voronoi cells and the dual complexes in Riemannian manifolds |
Jun
25 |
awarded | Yearling |
Jul
25 |
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Techniques for refining or constraining a Voronoi diagram?
If you have the Voronoi diagram then farthest point sampling (Delaunay refinement) seems like the obvious choice. The farthest point from a station will always be a Voronoi vertex, (or a point where a Voronoi edge intersects your quadrilateral boundary, or a corner of your boundary). Insert a new "station" at that point, and continue until the farthest point is close enough to a station. |
Jul
7 |
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Are properties of geodesics on a cylinder unique to cylinders?
Could we not graft a cylinder (with $z$-axis) to the $xy$-plane (with disk removed) in such a way that no geodesic can self-intersect? |
Apr
9 |
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How to show that the “bing's house with two rooms” is contractible?
An update to jc's comment above: Ken Baker made a subsequent post that describes a deformation retraction: sketchesoftopology.wordpress.com/2010/06/23/… |
Feb
25 |
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Examples of eventual counterexamples
Another relevant blog post: scottaaronson.com/writings/bignumbers.html |
Feb
2 |
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Conic neighborhoods ⇔ Polyhedral
I guess in the definition of a cone you meant to say that $r\alpha$ is the distance from $\xi$ to $\zeta$ in $\Sigma$? |
Jan
23 |
answered | Delaunay triangulations and convex hulls |
Nov
2 |
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Why is the half-torus rigid?
The rigidity of the punctured torus is listed as an open problem (number 13) by Ghomi here: people.math.gatech.edu/~ghomi/Papers/op.pdf . I guess either the list is wrong, or I am missing a distinction between things I don't understand. |
May
22 |
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Is there a combinatorial analogue of Ricci flow?
D. Glickenstein has done some work that might interest you, "Combinatorial Yamabe flow in three dimensions" arxiv.org/abs/math/0506182 |
May
5 |
awarded | Commentator |
May
5 |
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Sexy vacuity …
de Boor's "An empty exercise" on vacuity in linear algebra: ftp.cs.wisc.edu/Approx/empty.pdf or here: dx.doi.org/10.1145%2F122272.122273 |
May
5 |
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Sexy vacuity …
There is a neat article by de Boor An empty exercise (doi), where he argues for the inclusion of $0\times n$ and $m \times 0$ matrices in Matlab. He discusses definitions of span and determinant etc. I found this from a link on the Wikipedia page for determinant. |
Apr
23 |
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How to respond to “I was never much good at maths at school.”
A thoughtful answer. There is an arithmetical error on the first page of the short article linked at the end of the post. It is quite amusing in its context, so I am not entirely sure it isn't intentional. |
Apr
17 |
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Conformal structure determined by principal curvatures
This metric is sometimes used in constructing an approximating inscribed polyhedron for the surface. There are some optimality results, e.g. K. Clarkson (2006) "Building triangulations using epsilon nets" and the works of P. M. Gruber cited therin. |
Feb
18 |
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Gaussian curvature radius
By smaller I mean that $\rho_K(x) \leq \rho_G(x)$ for all $x$, where $\rho_G$ is the original definition. They agree everywhere except when the curvature is negative and $\rho_G$ provides no bound. I would be surprised if you found this to be a useful way to capture the geometry of negatively curved surfaces. Since it is purely intrinsic, you will never be able to control triangle normals this way, for example. It is not clear to me what is represented by the bound you're proposing to introduce. I don't recall seeing it anywhere previously. |
Feb
18 |
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Hypersurfaces and Elliptic Points
In a response to his own question here: mathoverflow.net/questions/31222/… Joseph O'Rourke linked to a paper by Zalgaller: springerlink.com/content/hu76g212137g2864 which describes a PL embedding of a flat torus in $R^3$. I am curious to know where that paper sits in the line of successive rediscoveries. |
Feb
17 |
answered | Gaussian curvature radius |
Dec
7 |
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Is there a complex structure on the 6-sphere?
A topical preprint has been posted on ArXiv (asserting that $S^6$ has a complex structure): front.math.ucdavis.edu/0505.5634 |