Visualizing Bézout’s theorem
Bézout's theorem says that two polynomials of degrees n and m intersect in nm points. But if we graph xy = 1 and y = x2 it looks like they only intersect at the single point (1,1) instead of at four points.
To see all four points of intersection we need to look at the corresponding homogeneous curves xy = z2 and yz = x2. Here's what this looks like: