7-May-1995
Unsolved Problem 19:
When equal sized discs are pushed closer together,
can the area of their union increase?
By a disc we mean a circle and its interior.
The result is known to be true for two discs.
By being pushed together, we mean that the distance between
each pair of discs is smaller after the pushing.
The union of a set of discs is the area covered
by all of the discs. The discs are allowed to overlap.
Reference:
- [Klee 1991]
- Victor Klee and Stan Wagon,
Old and New Unsolved Problems
in Plane Geometry and Number Theory.
Mathematical Association of America. Washington, DC: 1991.
Page 16.
Pushing Discs Together
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