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Questions tagged [triangulations]

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19
votes
0answers
486 views

Homeomorphisms of the sphere mapping a geodesic triangulation to another one

Consider the standard Riemannian 2-sphere $S$, equipped with a geodesic triangulation $T$. Let $L(S,T)$ be the space of homeomorphisms of $S$ which map $T$ to a geodesic triangulation. What is the ...
11
votes
2answers
2k views

Proving the Gauss-Bonnet theorem for embedded surfaces using triangulations

I heard this really neat elementary proof of the "Gauss-Bonnet Theorem" : Let $S$ be a surface embedded in $\mathbb{R}^3$. Now take a triangulation of that surface, and approximate the surface with a ...
5
votes
1answer
137 views

Does this iterated Delaunay triangulation process always “explode”?

Let $P$ be a set of three noncollinear points in $\mathbb{R}^2$. Iteratively form the Delaunay triangulation $\cal T$ of $P$, and then augment $P$ by the circumcircle centers of all triangles in $\...
2
votes
2answers
613 views

Euclidean triangulation of the plane with degree 7 at each vertex.

Hyperbolic plane has a beautiful triangulation by congruent hyperbolic triangles where all the vertices of the triangulation have degree 7, this is of course not possible in the euclidean plane, even ...