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
and radius 
?" 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" (Hofstadter 1985, pp. 26-27).
Math Horizons (2006) gives a number of "self-answering problems" that can be regarded as a form of self recursion. For example:
1. In 1978, Raymond Smullyan wrote a book about logical puzzles. What is the name of this book?
2. I am the square root of 
. Who am i?
3. What would the value of 190 in hexadecimal be?
4. Twenty-nine is a prime example of what kind of number?
5. The reciprocal of 
is half of what number?
6. How many consonants are in "one"? How many in "two"? And how many in "three"?
7. What do you do to the length of an edge of a cube to find its volume?
