The Sixth Proof
This proof is the most complicated of them all. It involves a series of intricate steps, each one more convoluted than the last.
Step 1: Draw a square
Draw a square with sides of length a, b, and c. This is the foundation upon which our entire proof will be built.
Step 2: Draw two more squares
Draw two more squares, one with sides of length a and d, the other with sides of length b and e. These squares will represent our first two variables, x and y.
Step 3: Draw a third square
Draw a third square, with sides of length c and f. This square will represent our third variable, z.
Step 4: Draw two more squares
Draw two more squares, one with sides of length x and y, the other with sides of length z and w.
Step 5: Draw a final square
Draw a final square, with sides of length u and v. This square will represent our final variable, t.
Step 6: Combine all the squares
Combine all the squares, using the Pythagorean theorem to calculate the lengths of the sides of each square.
Voila! The proof is complete!
We have now proven that the sum of the squares of the lengths of the sides of a square is equal to the square of the length of the diagonal.