Homer enters a bathroom and happens upon some glasses. He wears them, and in an attempt to be smart, incorrectly recites the pythagorean theorem. Someone in one of the bathroom stalls corrects his mistake.
The Wizard of Oz awards Scarecrow an honorary Th.D (Doctor of Thinkology) degree. After receiving the degree, Scarecrow incorrectly recites the pythagorean theorem.
Grover and Rosita illustrate and explain the properties of a triangle. Rosita brings over two different-looking triangles to serve as visual aids, and Grover does not consider them to be triangles. He creates an equilateral triangle and states why it is a triangle. Rosita mentions that the triangles she brought in fit his definition of a triangle, causing Grover to realize that there are different types of triangles.
English schoolteacher Andrew and his students sing a song explaining the pythagorean formula: a2 + b2 = c2. They illustrate the appearance of a right triangle several times to reinforce the concept they are singing about.