##### Oct 2-4, 2023

Los Altos High School

# Dr. Simon Rubinstein-Salzedo

Director

###### Euler Circle

#### Polygons inscribed in curves

#### Math

In this talk, we will look at several problems related to inscribed polygons in closed curves. The most famous of these is the inscribed square problem: Given a closed curve in the plane, do there exist four points on it forming the vertices of a square? But there are many other related problems that are also interesting. Of particular note is a theorem I proved together with a student, about inscribed triangles in closed curves. Given any triangle ABC and any closed curve in the plane, it is not too hard to show that there exist three points on the curve that form a triangle similar to ABC. But the corresponding question about curves in n-dimensional space is trickier. We proved that, under mild hypotheses, this is still true.

#### Meet the Speaker:

Simon Rubinstein-Salzedo received his PhD in mathematics from Stanford University in 2012, working in algebraic number theory. He has also done research in many other areas of mathematics, including algebraic geometry, combinatorics, probability, game theory, and topology. Simon is the founder of Euler Circle, a mathematics institute dedicated to teaching college-level math classes to high-school students.