Modern House Framing and the Pythagorean Theorem

Roof Pitch

The relationship between carpentry and the Pythagorean Theorem is believed to be around 4,000 years old, even though we usually use for roof pitch and squaring. The modern house framing industry would not be possible without the use of this theorem. It is applied in nearly all aspects of home building. Some examples would be roof framing, squaring foundations, and walls to name just a few.

The Pythagorean Theorem is believed to have originated around 2,000 B.C. The ancient Egyptians needed a way not to establish roof pitch but rather to lay out square corners for their fields. The way this was accomplished is amazingly simple yet very effective. They used three stakes arranged in a triangle and a length of rope knotted into twelve equal lengths. They would then stretch the rope around the three stakes until they had three knots between the first two stakes, four knots between the next two stakes, and five knots between the last two stakes. Thus the hypotenuse of the right triangle was formed.

A Greek philosopher and mathematician, born around 530 B.C., named Pythagoras became famous for formulating the Pythagorean Theorem. Even though the historians have given him credit, it was certainly known much earlier.

When referring to a right triangle, one angle equals 90 degrees, the hypotenuse is on the opposite side and equal to the sum of the squares of the other two sides. The formula for the theorem is A squared + B squared = C squared with C being the hypotenuse. When building houses, since two sides are usually known, this method is extremely accurate when squaring footings and foundation walls or establishing roof pitch.

In conventional house framing, roof framing using roof pitch is one of the more complex issues carpenters are faced with. With the use of a framing square and a working knowledge of the Pythagorean Theorem, roof framing is more accurate and efficient. The design of the framing square is based on this principal of mathematics. On the rafter tables and brace measurement portion of the square, these numbers are generated using the Pythagorean Theorem.

When the theorem is used in conjunction with computer software to generate roof pitch, foundation, floor, wall, and roof framing plans, it will increase quality, productivity, and decrease waste. If quality and productivity are increased and waste reduced, it can only lead to one outcome, higher quality finished homes, an increased profit margin, and higher customer satisfaction. This is a definite win win situation for the builder and homeowner alike.

The author of this article has 29 years of experience working in the highly competitive housing market of the west and southwest suburbs of Chicago as a carpenter. His job titles have included Master Roof Cutter, Apprentice, and everything in between. Most of his experience is in the high end custom home marketplace, including all aspects of fine homebuilding, from footings to ridge cap. His website contains more information on House Framing and the Pythagorean Theorem and roof pitch.

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