We define the polar dual of a polytope $P$ as the set $$\{x\in \mathbb{R}^n: x \cdot a\geq 1 \text{ for all } a\in P\}$$ Why do we require $1$ instead of $2$ or any other constant?
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
closed as off topic by Ryan Budney, Jon Bannon, Will Sawin, Noah Stein, Benoît Kloeckner Aug 31 '12 at 8:43Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question. 


It is just a normalization. If you were to pick any other constant (say, $c$, where $c$ is positive), then it would only scale the set by a factor of $1/c$. 

