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- 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 . (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.

- Appearances
- 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 continuous-motion case.

*Discrete Comput. Geom.*, 20:499–514, 1998.- [Cap96]
V. Capoyleas. On the area of the intersection of disks in the plane.

*Comput. Geom. Theory Appl.*, 6:393–396, 1996.- [MO01]
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.