TOPICS
Search

Planar Distance


For n points in the plane, there are at least

 N_1=sqrt(n-3/4)-1/2

different distances. The minimum distance can occur only <=3n-6 times, and the maximum distance can occur <=n times. Furthermore, no distance can occur as often as

 N_2=1/4n(1+sqrt(8n-7))<(n^(3/2))/(sqrt(2))-n/4

times.

Finally, no set of n>6 points in the plane can determine only isosceles triangles.


See also

Distance

Explore with Wolfram|Alpha

References

Honsberger, R. "The Set of Distances Determined by n Points in the Plane." Ch. 12 in Mathematical Gems II. Washington, DC: Math. Assoc. Amer., pp. 111-135, 1976.

Referenced on Wolfram|Alpha

Planar Distance

Cite this as:

Weisstein, Eric W. "Planar Distance." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PlanarDistance.html

Subject classifications