what happens when my girlfriend works a friday night shift and I have no poker game to go to
Took advantage of the weather to thin some fruit off my two apple trees today. Fate denied me a cherry harvest this year but has bestowed a bumper crop of apples, which are currently only halfway ripe, but so densely packed on that the normally vertical branches are bowing so low that I'm surprised some haven't snapped yet.
If I don't cull some, they'll just pop each other off the tree as they get bigger. But I'm not very good at it: many of the ones I intended to leave on the tree came tumbling down as well, and surprisingly, getting bonked in the face by a green apple is only funny about the first dozen times.
I didn't count how many I picked, but afterward I got curious. Fortunately, I remember some math. Plus, I has internets.
I assumed that:
- the garbage can I tossed them into (not the recycle can above) is roughly cylindrical (diameter 15 inches, filled to depth of 20 inches);
- the average diameter of the apples is 2 inches, and the average volume is somewhere between that of a sphere and a spindle torus, both with a 2-inch diameter;
- the apples approximate random monodisperse close packing behavior;
- the volume fraction is probably between that of spheres (0.64) and M&Ms (0.68). In actuality it's probably higher because of the size variation of the apples, but I'm being conservative.
And there are probably at least half that many left on the trees.