Scott Syplychak, age 74, of Monongahela, Penn., for his question:

WHAT IS THE PYTHAGOREAN THEOREM?

The Pythagorean theorem in geometry states that in a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides. A right triangle is one in which one angle equals 90 degrees. The hypotenuse is the side opposite the right angle.

The ancient Egyptians wanted to lay out square corners for their fields. They had few tools, but about 2000 B.C. they discovered a "magic 3, 4, 5 " triangle. A rope was knotted into 12 equal spaces. They took three stakes and stretched the rope to form a triangle around the stakes. They placed the stakes so the triangle had sides of 3, 4 and 5 units. The side of 5 units was what we would call the hypotenuse, and the angle opposite it equaled 90 degrees.

About 500 B.C. a group of Greek philosophers called the Pythagoreans used the " 3, 4, 5" formula in their theorem.