The diameter of a closed, topologically bounded region of the plane is the greatest distance between two points in the region. Example: the diameter of a rectangle is the length of its diagonal. Of all the regions whose diameter equals 1, one of them, call it R_{max}, encloses the largest area.

Can you prove, or disprove, that R_{max} also encloses all other regions of diameter 1? That is, that all other regions of diameter 1 can be made to fit inside R_{max}?

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## bonanova

The

of a closed, topologically boundeddiameteris the greatest distance between two points in the region. Example: the diameter of a rectangle is the length of its diagonal. Of all the regions whose diameter equals 1, one of them, call itregion of the planeR, encloses the largest area._{max}Can you prove, or disprove, that

Ralso encloses all other regions of diameter 1? That is, that all other regions of diameter 1 can be made to fit inside_{max}R?_{max}## Link to comment

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