About Roger Watkin Expertise I can answer any question regarding tactics, offensive and defensive play, serving, how to make every point count! I can also advise on the history of table tennis.
Experience I have played table tennis since 1960 and have organised table tennis clubs.
Organizations Te Rama Table Tennis Club, Wellington, New Zealand.
NZ Table Tennis Association.
Publications New Zealand Table Tennis Association website: www.tabletennis.org.nz
blayk writes on 2007-06-18 01:50:35
Almost, but not exactly correct. You can fit slightly more than that in a cubit foot, due to the fact that the highest packing density for spheres does not occur when you stack them neatly in a cubic grid.
I'll admit I'm not keen on the math or vocabulary for this, but your analysis makes the assumption that ping pong balls packed into a volume will behave as cubes rather than spheres, and that they will pack in such a way that a ball in the center will be touching six of of its neighbors, as would be the case for cubes. It is possible to pack spheres such that they touch sixteen of their neighbors. I refer you to the following wikipedia article for further explanation: http://en.wikipedia.org/wiki/Sphere_packing
By the way, I went through a similar process a little while back when my girlfriend had ordered 700 ping pong balls on the internet and was eagerly awaiting their arrival, thinking that 700 ping pong balls would be enough to fill a small room. I said I wasn't so sure and we did the math you did in your answer and realized it would be scarcely more than a cubic foot even at a non-optimal packing density. Sure enough, when the box arrived it was just about 1' by 1' by 1'.
James writes on 2008-11-12 17:01:18
That answer is a good lower bound on the number of balls you could fit, but in reality you can pack the balls much more tightly than lining then up end to end like that. You can get a better estimate by dividing the total volume of the box (1 cubic ft) by the volume of a single ping pong ball (I get .000896 cubic ft using a 40mm ball), and then multiplying that number by the sphere packing density (about .74. Check out wikipedia). Now, you're looking at 619 instead of 343. The true answer is somewhere between the two, since you won't get ideal sphere packing, but it should be closer to the high number. Go buy a carton of ping pong balls and let us know how it goes.
