How can one describe the unit ball in $\mathbb{R}^{3}$ as an intersection of supporting halfspaces?
2026-03-30 11:58:53.1774871933
How to describe the unit ball as an Intersection of hyperplanes?
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Let $B_3\subset \mathbb{R}^3$ denote the unit ball. By supporting halfspace, I assume you mean an affine half space containing $B_3$ such that its boundary contains at least one boundary point of $B_3$. Taking $$B_3=\bigcap_{|x|=1}\{x+z:\langle z,x\rangle\leq 0\}$$ should work. Here is a good picture of the lower dimensional case; can you visualize what this looks like in $\mathbb{R}^3$?