You've memorized a squared plus b squared equals c squared, but do you know why it's true?
Introduction
Why does it work?
You've memorized a squared plus b squared equals c squared. But why is it true?
- a² + b² = c²
- But why?
A right triangle
Take a right triangle. Call the short sides a and b, and the long side c.
- Short sides: a and b
- Long side: c
Four triangles, one square
Make four copies. Place them inside a big square whose side is a plus b.
- Big square side: a + b
First arrangement
Arranged one way, the triangles leave two empty squares. One has area a squared. The other has area b squared.
- Empty space: a² and b²
Rearrange the triangles
Now slide the triangles into a new arrangement. The empty space becomes one tilted square, with side c.
- Leftover: one tilted square
- Side length c
Area: c squared
Its area is c squared.
- Tilted square = c²
Same square, same triangles
But the big square never changed. The four triangles never changed. So the leftover space must be equal.
- Same total area
- So leftovers match
a² + b² = c²
That means a squared plus b squared equals c squared.
- Proven by rearranging
Follow for more proofs
No algebra needed, just a rearrangement. Follow for more beautiful proofs.
- Shapes, not formulas