He turned to the blackboard and pulled on a handle at the bottom. To his pupils' surprise, the black surface shot up smartly to reveal a green, furry surface. Pythagoras placed a right-angled triangle made of thin yellow card on the felt, then three more identical yellow triangles so as to form a large square surrounding another, tilted square. He placed a red square over the blank square in the middle of the triangles. Quickly, while his pupils leaned forward in their chairs to watch, he removed the red square to another part of the felt board and rearranged the four yellow triangles in two blocks in a disjointed 'L' shape. Then he put two new squares, blue and pale green, interlocking with the triangles to form a square. After that he removed the yellow triangles and equated the blue and pale green squares to the removed red square as being two versions of the left-over area from the original large square.
“That, my friends, is one of the proofs of the theorem,” he summarised. “And one of the simplest and most beautiful. By just moving the triangles and equating the squares, we can prove that a² + b² = c². You don't need to measure any sides or angles – although you can if you wish.”
Most of the class was aghast with the neatness of the proof, but Paidia whispered to Gelio that she'd read the theorem