Is it true that the perimeter of any convex polygon in the unit disk on the Euclidean plane is less than the circumference $2\pi$ of the circle? Thanks. [The OP has solved it]
Bound for perimeter of convex polygon?
3
$\begingroup$
euclidean-geometry
-
0Since the upper bound $2\pi$ cannot be attained by the perimeter of a convex polygon, a better word than "maximum" in your title would be "supremum", i.e. least upper bound. (Which is $2\pi$, as you've asked in the body of the question.) – 2012-12-07