Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress. The formula for the volume of a cylinder leads to the mathematical joke/self-description: "What is the volume of a pizza of thickness a and radius z?" Answer: pi z z a. This result is sometimes known as the second pizza theorem. A self-recursive statement due to J. vos Post is, "This sentence contains ten words, eighteen syllables, and sixty-four letters". Math Horizons gives a number of "self-answering problems" that can be regarded as a form of self recursion.

Kolakoski sequence | look and say sequence | recursion | regression | self-recursion | Tupper's self-referential formula