Take any triangle with a perfectly square corner — a right angle. On each of its three sides, build a square. Pythagoras' theorem is the surprising claim that the two smaller squares, put together, hold exactly as much space as the biggest square.
The Squares Tell the Story
In the toy, the short leg has length a, so the square on it has area a × a = a². The other leg b gives a square of b². The slanted longest side c gives the big square c². Drag the legs to any sizes you like and the readout keeps insisting on the same thing: a² + b² lands bang on c². With legs 3 and 4 you get 9 + 16 = 25, and the big square really is 25 units across its area.
Why "squared", Not Just "the Sides"?
It's tempting to think the two short sides simply add to the long one. They don't — 3 + 4 is 7, but the long side here is 5, not 7. The neat relationship only shows up once you square each length, because you're really comparing areas of squares, not the lengths themselves. That little ² is doing all the work.
An Idea Older Than the Textbook
People were using this thousands of years ago — Egyptian rope-stretchers knotted a 3-4-5 loop to lay out perfect right angles for building. The theorem carries Pythagoras' name, but it's really a fact baked into the shape of space itself. This rung is just about seeing it; the next one gives the parts their proper names.