6
votes
0answers
93 views

Biggest Little Polyhedron

The Biggest Little Polygon problem asks for the polygon with greatest area where the largest diameter is 1. Let's add a dimension and find the largest volumes. What is the biggest little polyhedron ...
4
votes
0answers
82 views

Points at Integer Distances in 3-space

With the restriction no three points in a line, no four points on a circle, there is a 7 point configuration of points on the plane such that all pairs of points are at integer distances. [1] For ...
1
vote
1answer
122 views

Upper bound for the number of open disks containing $k$ points in the plane

I hope that you can help me with this. Let P be a set of points in the plane, such that $|P|=n$, what is the maximal number of open disks containing at least $k$ points for some $k$, two discs are ...