Tricky Q: how to optimize the number of circles fitted in a bounded region.

[chantaiman]

Circle is a shape that cannot be tesselated. But how to optimize the number of circles fitted in a bounded region. Is there any relationship between the number of circles and the dimension of the regions. Design a rack with minimum area or perimeter to fit in 50 coke cans. Restrict the problem to racks in the shape of regular polygons. What kind of mathematical model can be used to make prediction?

 

[mmm4444bot]

Have you considered the can's footprint as a regular hexagon (with the circle inscribed)?