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Problem 18: Pushing Disks Together
- When a collection of
disks are pushed closer together, so that no distance
between two center points increases, can the area of
their union increase?
- Kneser (1955) and Poulsen (1954).
- Solved by K. Bezdek and R. Connelly.
their web page.
(Update as of 3 Aug. 2000.)
- Partial and Related Results
- Previously only settled
in the continuous-motion case
[BS98], for both this and
the corresponding question for intersection area decrease [Cap96].
But now both solved; see above.
- combinatorial geometry
- Entry Revision History
- J. O'Rourke, 2 Aug. 2001; 3 Aug. 2003.
Marshall Bern and Amit Sahai.
Pushing disks together - The continuous-motion case.
Discrete Comput. Geom., 20:499-514, 1998.
On the area of the intersection of disks in the plane.
Comput. Geom. Theory Appl., 6:393-396, 1996.
J. S. B. Mitchell and Joseph O'Rourke.
Computational geometry column 42.
Internat. J. Comput. Geom. Appl., 11(5):573-582, 2001.
Also in SIGACT News 32(3):63-72 (2001), Issue 120.
The Open Problems Project - September 19, 2017