AGES 10+ · SHAPES & AREA
The Butterfly’s Square
Follow a butterfly around a right triangle and watch square areas come together.
Tap the picture to pause or play, or use the controls below. Sound is off until you choose to enable it.
Look, pause, wonder
A right triangle with side lengths 3 and 4 has a hypotenuse of length 5. Squares on its sides have areas 9, 16, and 25 square units. The general rule a² + b² = c² applies to every right triangle, with c opposite the right angle. The moving tiles illustrate this example; they are not a general proof and are not pieces cut from the triangle.
Pause at the end. Why do we add areas, 9 and 16, rather than simply adding the side lengths, 3 and 4?
Read with the trio: The Triangle That Measured the Sky.
Explore the mathematics further · Back to the interactive collection