Pythagoras on the Move
The squares on the two short sides of a right triangle are cut into five pieces. Slide them to fill the square on the slanted side with no gaps. The same cut works for any side lengths.
Drag the pieces into the tilted gray square. You never need to turn them, only slide.
3² + 4² = 9 + 16 = 25. The slanted side is c = 5, and c² = 25.
How to play
On the right are the larger square (already cut into 4 pieces) and the small square. Drag them into the tilted gray square on the left. You never turn a piece, only slide it. Near a corner of the tilted square a piece snaps into place. On a keyboard, focus a piece, move it with the arrow keys and press Enter to settle it. Change "Side lengths" to try another right triangle. "Hint" starts with the idea and gets more specific. "Auto-solve" places the pieces one by one with a reason for each, and stops when the square is filled.
Learn more
Call the two sides that meet at the right angle a and b, and the slanted side c. Then a² + b² = c². This is the Pythagorean theorem, and here we check it with areas. Draw one line through the centre of the square on the longer side b, parallel to the slanted side, and another perpendicular to it. They cut the square into 4 identical pieces. Slide the four pieces into the corners of the tilted square, drop the small a-square into the gap in the middle, and you have exactly the square on c. The pieces only slide, never turn, so the same cut works for any a and b. The areas are checked by this site's tests for many pairs of a and b.