# Questions tagged [triangulation]

For questons about triangulation, that is a) the subdivision of the plane or other topological spaces into triangles (or, more generally, simplices) or b) the methods used in surveying for locating points by measuring angles and accessible lengths of triangles

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### Triangulation trigonometry

I’ve been looking at triangulation calculations, and I’ve become a bit stumped as to how the authors of the attached document have come to the following calculations. In the page it explains how one ...
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### Can one compute the location of the unseen point?

My question is quite simple. I have two images, on the first one I know the location of points $P1, P2, P3$, and $P4$. In the second image, I know the location of $P2'$, $P3'$, $P4'$, and point $Q'$. ...
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### Ordered Delaunay triangulations

I would like to show that, given n points in the plane $q_1 ... q_n$ such that the distance between $q_0$ and $q_i$ is smaller than or equal to the distance between $q_0$ and $q_j$ for every $i < j$...
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### Do two triangulations of a smooth manifold have a common subdivision?

The Hauptvermutung (ie. the question in the title) is known to be false for PL manifolds and topological manifolds, but I can't find a result for smooth manifolds (with boundary), though I recall ...
1 vote
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### Why are there only finitely many simplicial maps from one polyhedron to another?

I don't understand why for two polyhedra $|X|$ and $|Y|$, there are finitely many choices of simplicial maps $$s: |X^m| \rightarrow |Y|$$ for some large enough $m \in \mathbb{N}$. Multiple sources say ...
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### Why isn't this a correct triangulation of the torus/projective plane?

This is to be proven an incorrect triangulation of the torus: And this is to be proven an incorrect triangulation of the projective plane: I would like to know what part of the definition of ...
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### Upper triangulation of a matrix versus diagonalization

I am trying to google this question, but could not find any hints. This is important to me because of I am dealing with 3-4D matrices. It's true that an upper triangulation (Gauss elimination) of a ...
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Problem: Let there be $N$ points $P_i(x_i,y_i,z_i)$ and a $\mathbf M$ the $NxN$ matrix of distances $d_{ij}$ between each point. Lastly, let's consider that the 3 of the N points $P_1$, $P_2$ and $... 4 votes 1 answer 269 views ### Fast algorithm to embed a triangulation into plane Let$G = (V, E)$be a planar graph such that$|E| = 3|V| - 6$(so$G$must be a triangulation without Kuratowski subgraphs). Given the adjacent matrix$A$of$G$, please design an algorithm to embed$...
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I'm studying triangulations of the hyperbolic plane and have come across the following theorem: If we are given a triangle $\Delta_0$ with angles $\pi$/l,$\pi$/m,$\pi$/n, where the integers l, m, n ...