**UM Math Graduate Student Seminar**

Drew Armstrong

* University of Miami *

**will present**

**Archimedes and the Existence of pi**

Friday, April 14, 2017, 5:00pm

Ungar Building Room 402

**Abstract: **

We all know that for any two circles with circumferences C,C' and diameters d,d' we have C/d=C'/d'. In modern terms we think of this common ratio as a real number and we call it pi. Yet it is surprisingly difficult to track down the history of this result. You won't find it in Euclid's Elements. In fact, even Descartes in 1637 stated that ratios between straight lines and curved paths cannot be discovered by the human mind. In this talk I will show that the identity C/d=C'/d' is an easy corollary of the work of Archimedes, even though Archimedes never stated it explicitly. I learned about this topic from a recent paper of David Richeson.

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