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David Stringer explains ancient Pythagoras' findings about right triangles. He illustrates the Pythagorean Theorem and explains how special right triangles with the ratio 3:4:5 can be scaled up to any size.

In this clip, Charlie uses the behavior of the hoop's shadow to pinpoint the longitude and latitude where the photos had been taken. In order to make calculations involving the position of the sun in the sky, Charlie used a technique called spherical astronomy.

Tracy helps Calvin with his geometry homework by drawing large triangles on the side of his house. He uses basketball examples to help Calvin remember the different types of triangles.

Hypatia of Alexandria explains that the center of a circle is always the same distance from any other point of the circle. She also states that a circle is a special type of ellipse.

The host of Dancing with Triangles, Tom Twinkletoes, invites contestants on stage to perform their best dance with a triangle. The contestants dance with hexagons, squares, and even an elephant, but only one dances with a triangle. Tom explains why the other geometric shapes are not 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.