Groemer Theorem

Given n circles and a perimeter p, the total area of the convex hull is

 A_(Convex Hull)=2sqrt(3)(n-1)+p(1-1/2sqrt(3))+pi(sqrt(3)-1).

Furthermore, the actual area equals this value iff the packing is a Groemer packing. The theorem was proved in 1960 by Helmut Groemer.

See also

Convex Hull

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Groemer Theorem." From MathWorld--A Wolfram Web Resource.

Subject classifications