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Circle Packing -- from Wolfram MathWorld
We would like to pack as many circles of diameterd as possible into another large circle of
diameter D. We denote by N(d;D) such number.
(a) Give the upper bound for N(d;D).
(b) Give in details how we can calculate a lower bound for N(d;D). Find an explicit value for
Nwhen d = 9 mm and D = 72 mm.
To my knowledge, there is no formula that will compute N(d;D) precisely. However, Eckard Specht has compiled a table of observed packings for N up to 900 (and beyond). From his data, it's clear that D/d varies smoothly as a power function of N.
For D = 72mm and d = 9mm, N = 51.