- #1
bob012345
Gold Member
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- TL;DR
- A 2D problem is extended to 3D and beyond. Perhaps even to infinite dimensions!
Here is an interesting geometry problem given for general interest. In the figure, compute the fraction that is shaded. Then extend that to a sphere snugly packed in an octant of a larger sphere. That means the smaller sphere is tangent to each plane and to the larger sphere in the most compact way possible. Those who are brave can extend that further to four dimensions or higher and make some interesting observations about how things change at higher dimensions. Have fun!
