# Tagged Questions

geometry as on the surface of a sphere, where "lines" are great circles and any pair of lines must intersect

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### The furthest point to this torus

Recall that the (geodesic) distance on the unit sphere $S^n$ is given by $$d(p, q) = \arccos \langle p, q \rangle.$$ Let $f_r = f : \mathbb{R}^2 \to S^3$ be defined by f(\theta, \phi) = \left(r \...
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### Showing there is no local isometry between spheres of different radii

I wish to show there is no is no local isometry between 2-dim spheres of different radii, without the use of curvature, as it is not in my knowledge yet. Could you provide directions? If such ...
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### Spherical circle - Area

I am looking at the following exercise: The spherical circle of centre $p \in S^2$ and radius $R$ is the set of points of $S^2$ that are a spherical distance $R$ from $p$. If \$0 \leq R \leq \frac{\...
I know that the following theorem is true: Theorem: Provided that all faces of a polyhedron are regular poygons, the statement all the dihedral angles are congruent'' is equivalent to saying ...