Grid vs tree (with a bit of number theory on the side)
The Secret of the Fibonacci Sequence in Trees. A middle school science project by Aidan Dwyer finds that arranging an array of solar cells on branches distributed around a central trunk using a Fibonacci-based spiralling pattern works significantly better than just placing them in a flat array. Via metafilter — the metafilter discussion has some skepticism about whether his experiments really show what he claims they show, but regardless it's a neat idea.