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A comment on Counterintuitive Properties of High Dimensional Space. Parent comment
II. Hypercube: abs(max(v)) <= 1
Clearly II implies I, therefore the hypersphere is inside the hypercube.
The points where they touch are: length(v) = abs(max(v)) = 1, the solutions of which are the points with exactly one ±1 coordinate.
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II. Hypercube: abs(max(v)) <= 1
Clearly II implies I, therefore the hypersphere is inside the hypercube.
The points where they touch are: length(v) = abs(max(v)) = 1, the solutions of which are the points with exactly one ±1 coordinate.