The Math of Cutting Cake and Dividing Candy

How do you cut a cake so that everyone is happy with their piece? The oldest protocol, 'I cut, you choose', is a way into what fairness can mean: proportional, envy-free, equitable, and efficient. For more people, I work through procedures from a moving knife and recursive median cuts to the Selfridge–Conway protocol for three, with interactive demos, and show how Sperner's lemma yields nearly envy-free divisions. Candy cannot be cut, so I introduce relaxations like envy-freeness up to one item, and some open problems from current research.