Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
open problem in mathematics
|
| gptkbp:field |
gptkb:combinatorial_geometry
discrete geometry |
| https://www.w3.org/2000/01/rdf-schema#label |
unit distance problem
|
| gptkbp:lowerBound |
floor(n/2) (for n points on a circle)
|
| gptkbp:notableAchievement |
Best known lower bound is floor(n/2)
Best known upper bound is O(n^{4/3}) |
| gptkbp:openProblem |
Exact asymptotics are unknown
|
| gptkbp:posedBy |
gptkb:Paul_Erdős
|
| gptkbp:relatedTo |
gptkb:Erdős_distinct_distances_problem
lattice points distance graph |
| gptkbp:type |
What is the maximum number of pairs of points at unit distance among n points in the plane?
|
| gptkbp:upperBound |
Cn^{4/3} (for some constant C)
|
| gptkbp:yearProposed |
1946
|
| gptkbp:bfsParent |
gptkb:combinatorial_geometry
|
| gptkbp:bfsLayer |
6
|