Talk:Blaschke–Lebesgue theorem

Is this also true for non-convex curves?
In the current article, "the Reuleaux triangle has the least area of all curves of given constant width".

But in Curve of constant width: "the Reuleaux triangle has the least area of any **convex** curve of given constant width."

Which of the two statements is the more accurate? --Erel Segal (talk) 09:47, 19 May 2014 (UTC)
 * They both are. All curves of constant width are convex. —David Eppstein (talk) 05:45, 5 January 2019 (UTC)