A186704 The minimum number of distinct distances determined by n points in the Euclidean plane.

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6

Offset

1,4

Comments

The Mathoverflow link has an image from page 200 of Brass reference.

References

P. Brass, W. O. J. Moser and J. Pach, Research Problems in Discrete Geometry, Springer (2005), p. 200.

Links

Table of n, a(n) for n=1..13.

P. Erdős and P. Fishburn, Maximum planar sets that determine k distances, Discrete Math. 160 (1996), 115-125.

L. Guth and N. H. Katz, On the Erdős distinct distance problem in the plane, arXiv:1011.4105 [math.CO], 2010-2011.

R. Mansuy, Le problème des distances d'Erdős, Mathematik Park, Institut Henri Poincaré, Paris, 2013.

Mathoverflow, Erdos distance problem n=12

K. Schade, Softwarepraktikum, Sommersemester 2007

Example

a(4) = a(5) = 2 from the 2 distinct distances between vertices of a square and a regular pentagon.

Crossrefs

Sequence in context: A225559 A082479 A090616 * A067434 A336348 A177357

Adjacent sequences: A186701 A186702 A186703 * A186705 A186706 A186707

Keyword

nonn,hard,more,nice

Author

Michael Somos, Feb 25 2011

Status

approved