Given 
circles and a perimeter 
, the total area
of the convex hull is
 |
Furthermore, the actual area equals this value iff the packing is a Groemer packing. The theorem was proved in 1960 by Helmut Groemer.
Groemer Theorem
See also
Convex HullExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Groemer Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GroemerTheorem.html