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.
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.
Normally in carpentry points a and b are known so all you have to do is solve for c. Here is a neat little calculator that you can use to simplify the math.