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Results tagged with spherical-geometry
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user 1441
10
votes
Accepted
Convex cones and self-duality
For convex figure $\Sigma$ in $\mathbb S^2$,
the isoperimetrical inequality should look like
$$\left(\frac{\mathop{\rm perim}\Sigma}{2\cdot\pi}\right)^2+\left(1-\frac{\mathop{\rm area}\Sigma}{2\cdot\p …
- 45k
7
votes
Triangle area on surfaces of constant curvature
All the "elementary derivations of that type" are cheating (it may look nice but it proves nothing).
The only elementary way to introduce area is adding it as an axiom (which is already kind of chea …
- 45k