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Results tagged with mg.metric-geometry
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user 32389
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
3
votes
Minor theorems of Pappus and Desargues in "old school" geometry?
The converse of the Hessenberg’s theorem is not true. In the quaternionic projective plane the Desargues' theorem is true but the Pappus's is false. See historical notes in http://www.sciencedirect.co …
- 16.5k
3
votes
Weyl tube formula for manifolds with boundary
I think Alfred Gray's book "Tubes" https://www.springer.com/gp/book/9783764369071 is relevant. See also https://www.sciencedirect.com/science/article/pii/0040938382900052 (Comparison theorems for the …
- 16.5k
14
votes
If a triangle can be displaced without distortion, must the surface have constant curvature?
Already Riemann in his famous "On the Hypotheses Which Lie at the Bases of Geometry" concludes that the spaces of constant curvature are precisely those in which figures can move without distortion. H …
- 16.5k
4
votes
Egg-ovoid rolling down an inclined plane
This paper https://jeb.biologists.org/content/221/19/jeb178988 contains an experimental investigation of egg rolling. Theoretically, it seems "the relationship of egg shape to egg movement (e.g. rolli …
- 16.5k
3
votes
Geometric proof of the Vandermonde determinant?
Ira Gessel used transitive tournaments in graphs to prove Vandermonde’s determinant identity: http://onlinelibrary.wiley.com/doi/10.1002/jgt.3190030315/abstract
This proof certainly has some geometric …
- 16.5k
10
votes
volume over a hypercube, over simplex: twist by Euler numbers
This is only a partial answer. The Beukers-Kolk-Calabi change of variables
$$x_1=\frac{\sin{u_1}}{\cos{u_2}},\;\;x_2=\frac{\sin{u_2}}{\cos{u_3}},\ldots,
\;x_{n-1}=\frac{\sin{u_{n-1}}}{\cos{u_n}},\;\;x …
- 16.5k