I have two circles. Both origin at San francisco $(37.77493,-122.419415)$, The larger circle has Radius $R_1$, the smaller circle has radius of $R_2$.
What's the fewest number of additional overlapping smaller circles (/w Radius of $R_2$) that fit inside the larger one, that creates zero empty space (except near the edge of the larger circle), and the corresponding co-ordinates of each circle's origin.
I've bounced this problem across my peers, and we've decided that the circles are optimally fitted to how the Flower of Life is laid (http://en.wikipedia.org/wiki/Flower_of_Life).
Thus one unit of $R$ from the centre would produce $7$ circles ($1$ in the middle, and $6$ surrounding).
Origin = $(x,y)$
Surrounding circles: (x+cos(60x)R,y+sin(60x)R) // Guess
From here I'm stuck on how to continue to fill the circle, and how to give real-world coordinates of each of the circle's origins. With input like $R_1 = 5,000$ meters, and $R_2 = 1000$ meters.