The Dottie Number

- The Dottie Number (≈ 0.739085…) is the unique real solution to the equation cos(x) = x — the value where the cosine function’s output equals its own input. It is famous in recreational mathematics as a surprising, irrational fixed point that emerges from repeatedly pressing “cos” on a calculator. - The number was nicknamed by the mathematician Samuel R. Kaplan after a professor named Dottie who observed the phenomenon during a lecture; it has since become a well-known curiosity in math-popularization circles. - “Fixed points” like this one are important in mathematics because they show where functions become self-referential. The Dottie Number is often the first non-trivial fixed point a student encounters outside of simple linear equations. - This post is by Lawrence C. Paulson, a noted computer scientist known for his work in automated theorem proving (especially the Isabelle proof assistant). His writing here blends formal proof with mathematical exposition, reflecting his interests in logic and verification.