What is the smallest (either in terms of perimeter or area) convex shape in $R^2$ such that all curves of length 1 are properly contained within it ? I'm thinking a right triangle with sides of $1/\sqrt(2)$, but I'm not sure how to reason about this rigorously. Any pointers would be appreciated.
2026-03-31 14:15:09.1774966509
Tightest convex set containing curves of length 1
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