4 ms·
How does the enclosed sphere's radius changes with the number of dimensions, if the enclosing spheres are the following: 2D: 3 mutually touching 2-spheres (cir
by badmintonbaseba 2y ago
How does the enclosed sphere's radius changes with the number of dimensions, if the enclosing spheres are the following:
2D: 3 mutually touching 2-spheres (circles)
3D: 4 mutually touching 3-spheres (or spheres)
...
This variation of the problem doesn't rely on an artificial construct of a hypercube, I wonder if this yields a similarly unintuitive result.
- badmintonbaseba 2y agoIf my calculations are correct, then for this variation the enclosed n-sphere's radius converges to sqrt(2)-1 from below, and remains enclosed in the bounding hyper-tetrahedron.
- pfortuny 2y agoBuf, you may be right but I just cannot visualize it. It took me quite a while to do for the cube, imagine a tetrahedron. But you might be right.
- Hugsun 2y agoVery interesting, I've considered doing something similar with other regular polyhedra, like the n-simplex (the one you analyzed) and n-orthoplex. What was the side length in your calculation? did you find an equation for the size of the center n-ball?