Los Angeles Math Circle

3/11 -- LAMC High School: Congruent Numbers -- Yingkun Li

A rational triangle is a right triangle whose three sides are all rational numbers. A rational number is called a congruent number if it is the area of some rational triangle. It is an ancient problem to decide if an arbitrary integer is a congruent number. Surprisingly, this innocent-looking problem is still open today. In this talk, we will go through the history of congruent numbers and look at its connections to important objects in modern number theory.