**Title**: What is Crofton's formula?

**Speaker**: Miles Calabrese (Ohio State University)

**Abstract**: Using lines to approximate curves is an age-old technique in mathematics. Archimedes used it to estimate the value of pi, and it pins down calculus. In this talk, we'll explore another application: Crofton's formula, which relates the arc length of curves to the measure of infinitely many lines that intersect the curve. This result is stronger than other common arc-length formulas, and it has far-reaching consequences into Riemannian geometry, probability, and real analysis.

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The What is ...? seminar's main goal is to expose culturally ambitious participants to some mathematical notions not taught in standard courses. These topics form an important part of mathematical folklore, and may prove useful for doing research and enhancing teaching. Lectures will be given mostly by graduate and undergraduate student participants. Professors Vitaly Bergelson and Daniel Shapiro serve as coordinators/mediators.

The What is ...? Seminar is an event organized by the Mathematics Department, independent of SAMMS, but participants are encouraged to attend any meeting that seems intriguing! Let the attending mediator know you are a SAMMS participant.