Graduate Student Seminar
Wednesday September 18th, 2019
Time: 1:00 PM - 2:00 PM
Title: Additional Problem No58
Speaker: Lisa Marquand, Stony Brook University
Location: Math Tower P-131
Abstract:

There is a Russian book 'Problems in Geometry (Planimetry) by I.F Sharygin, which contains around 498 problems in Planar geometry; 143 standard, 293 difficult, and 62 'additional problems'. Today, we'll discuss only one of them, an easy to state school-level problem which led to fascinating and beautiful complex mathematics.
The problem begins with a scalene triangle, for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them 'Sharygin Triangles'. The problem ends with a rigorous study of the group of rational points on a particular cubic, and we'll see what we meet on the way.