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}?
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}?
Share this post
Link to post
Share on other sites