  At a certain infamous tea party, the Mad Hatter posed the following riddle:
why is a raven like a writing-desk? We do not answer this question. Instead, we
solve a related nonsense query: why is a soap bubble like a railway? The answer
is that both minimize over graphs. We give a self-contained introduction to
graphs and minimization, starting with minimal networks on the Euclidean plane
and ending with close-packed structures for three-dimensional foams. Along the
way, we touch on algorithms and complexity, the physics of computation,
curvature, chemistry, space-filling polyhedra, and bees from other dimensions.
The only prerequisites are high school geometry, some algebra, and a spirit of
adventure. These notes should therefore be suitable for high school enrichment
and bedside reading.
