Only a child can do it
A science museum in Charlotte, NC, Discovery Place has an exhibit on candy running, sponsored by Jelly Belly. Or “had”, I should say. Part of it has been taken down, and it’s all thanks to an eight-year-old boy.
The feature in question was a big pyramid filled with brand-name jelly beans. The question posed is how to estimate the number of jelly beans inside. Here’s what the plaque said:
A jelly bean has a volume of about 1 cubic cm.This container is half a pyramid.
Its base measures 46 cm by 23 cm and its height is 72 cm.
Here’s the formula to find the volume: 1/3 x base area x height.
Now divide your answer by 2 since this is half a pyramid.
Now multiply your answer by 0.9 to account for spaces between the jelly beans.
The answer should be 22,853.
Do you see the problem here? If the first formula were for the area of a square pyramid everything would be fine. However, since that term was written “base area” rather than “the area the base would have if it were a square, we’ve already taken the factor of 1/2 into account. Dividing by 2 again is extraneous.
Apparently nobody caught this until Parker Garrison came along. He’s evidently the only one who actually did the calculations and saw that the actual result of the given formula wasn’t what was printed. He knew something was funny and instead of just piping down and moving on he spoke up about it.
This sort of critical thinking and willingness to take action is just what we need more of, and the mathematical skill and interest needs to be nurtured. I don’t know if you’re out there, Parker, but if someone can put me in contact with you I’ve got a copy of Martin Gardner’s New Mathematical Diversions: More Puzzles, Problems, Games, and Other Mathematical Diversions (which has a section on the sphere packing problem) with your name on it. That should help explain where that 0.9 comes from.