Two main points, mostly to look at this old theorem in new ways.

1) The sides of a triangle (3-4-5) can represent portions of any shape. For example, circle area (radius 3) + circle area (radius 4) = circle area (radius 5).

Instead of radius, you could pick diameter, circumference, or any line segment and the relationship would hold.

2) You can use the Pythagorean Theorem to split any squared quantity into two smaller ones. This can yield surprising insights; is it immediately clear that a list of 50 takes as long to bubble sort as a list of 30 and 40? =)