Splash Biography

A positive rational number is called congruent if it is the area of a right triangle with rational sides. Since $$3^2+4^2=5^2$$, it follows that $$6$$ is a congruent number. In this class I talk about the congruent number problem and how you can win a million dollars.

Which positive integers are the sum of two integer squares? Well $$5=1^2+2^2$$, but $$7$$ doesn't seem to be a sum of two squares. In this class we will determine exactly which positive integers can be written as a sum of two squares using a relatively uncommon lattice point technique called Minkowski's theorem.