Pythagorean Theorem and Carpentry

Modern carpentry work is so much easier when the Pythagorean Theorem is applied to the task at hand. Roof framing, squaring walls, and foundations rely on this basic principle of mathematics.

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Basics of the Theorem

In geometry this theorem states, in a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides. In a right triangle one angle equals 90 degrees. The hypotenuse is on the opposite side of the right triangle.

Here is the formula for the Pythagorean Theorem. a squared + b squared = c squared In this formula, c represents the length of the hypotenuse, a and b are the lengths of the other two sides. If two sides of a right triangle are known, you can substitute these values in the formula to find the missing side.

Squaring Buildings with the Pythagorean Theorem

When laying out concrete footings for a new building, the Pythagorean Theorem is the most accurate method available for making square 90 degree angles. It is the same as the old 3 - 4 - 5 carpentry trick, only more precise, because the exact corners can be located.

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Pythagorean Theorem Origins

Around 2000 B.C. the ancient Egyptians needed a way to lay out square corners for their fields. They took a length of rope knotted into 12 equal sections and stretched the rope around three stakes arranged in a triangle. When they had 3 lengths between two stakes, 4 lengths between the next two, and 5 lengths back to the starting point the hypotenuse of the right triangle was formed.

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A man named Pythagoras became famous for formulating the Theorem, however it was certainly known earlier. He was a Greek philosopher and mathematician born around 530 B.C. He founded a brotherhood called the Pythagoreans in Crotona, Italy, among the aristocrats of that city. The townspeople became suspicious of the brotherhood and killed most of its members in a political uprising. It is not known if he fled the city before the uprising or was killed in it.