I know that I should use some kind of honeycomb structure but can't work out in which orientation I should arrange it. I've looked at a few websites now and although I have a slightly better idea of the options, I can't work out how to model the problem and therefore calculate how many circles I could cut.
Specifically I would like to know:
~ How could I model this and what mathematics are involved?
~ What is the maximum number of 51 mm-diameter circles I can cut from a 330 mm × 530 mm rectangle?
~ What is the minimum size rectangle from which I could cut 16 circles?
(As you might suspect this is a real-life problem that I must solve, the disks that I will cut are to be used in a physics experiment but the material from which they are made is very expensive. It can however be purchased in any size rectangle, up to 330 mm × 530 mm.)
OK so I just discovered this question and the Wikipedia link contained therein. Whilst it is certainly related I am no closer to solving my current queries. (Other than if I were to order a square sheet of the material measuring 204 mm × 204 mm but I'm sure a rectangle would be more efficient.)