Defining Hyperspheres
A circle can be defined uniquely using 3 distinct points that are not colinear. A sphere can be defined uniquely using 4 distinct points that are not coplanar. Can a 4-dimensional hyper-sphere be uniquely defined using 5 distinct points that do not lie in the same 3-dimensional space?
BONUS: How many distinct points that lie in an (n-1) dimensional space are required to uniquely define an n-dimensional hyper-sphere?
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