22-Jan-1995
Unsolved Problem 4:
Can a closed curve in the plane have more than one equichordal point?
The line joining two points on a curve is called a chord.
A point inside a closed convex curve in the plane is called
an equichordal point if all chords through that point
have the same length. For example, the center of a circle is
an equichordal point for that circle.
It is not known if there is a closed curve that has two distinct
equichordal points.
Reference:
- [Lay 1982]
- Steven R. Lay,
Convex Sets and their Applications.
John Wiley and Sons. New York: 1982.
Page 92.
Equichordal Points
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