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Results tagged with spherical-geometry
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user 86625
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Maximum number of half great circles of length $\pi$ can be drawn on a sphere without any in...
Here is another way to interpret Gjergji's answer.
Imagine a satellite orbits a spherical Earth in low orbit along a circular path whose maximum north and south latitudes are some angle $<90°$. These …
- 2,370
25
votes
Accepted
What is the largest subset of the sphere such that inner product of any two points in the se...
You can go slightly beyond the positive orthant. In the case of a 2-sphere in 3-dimensional space, you can render a cap with angular radius $45°$. This has a surface area of $2\pi(1-\sqrt{1/2})\approx …
- 2,370
0
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Packing twelve spherical caps to maximize tangencies
As an extension of the problem (which turns out to have some physical significance), we may consider what would happen if we were to allow the twelve vectors to "land" within the unit ball rather than …
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Tetrahedra with prescribed face angles
One observation to be made is a tetrahedron does not necessarily exist with an arbitrary set of dihedral angles. As the exercise shows below, we must have the dihedral angles at each vertex sum to at …
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