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Problem 18: Pushing Disks Together
 Statement
 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?
 Origin
 Kneser (1955) and Poulsen (1954).
 Status/Conjectures
 Solved by K. Bezdek and R. Connelly.
See
their web page.
(Update as of 3 Aug. 2000.)
 Partial and Related Results
 Previously only settled
in the continuousmotion case
[BS98], for both this and
the corresponding question for intersection area decrease [Cap96].
But now both solved; see above.
 Appearances
 [MO01]
 Categories
 combinatorial geometry
 Entry Revision History
 J. O'Rourke, 2 Aug. 2001; 3 Aug. 2003.
 BS98

Marshall Bern and Amit Sahai.
Pushing disks together  The continuousmotion case.
Discrete Comput. Geom., 20:499514, 1998.
 Cap96

V. Capoyleas.
On the area of the intersection of disks in the plane.
Comput. Geom. Theory Appl., 6:393396, 1996.
 MO01

J. S. B. Mitchell and Joseph O'Rourke.
Computational geometry column 42.
Internat. J. Comput. Geom. Appl., 11(5):573582, 2001.
Also in SIGACT News 32(3):6372 (2001), Issue 120.
The Open Problems Project  September 19, 2017