Pythagoras wasn’t a carpenter, but anybody who drives nails should know his work. You have to be careful how you quote him and toss his name around, though. Eyes will glaze over.
I was working on a shed the other day when a neighbor dropped by. He checked out the project, then he asked in passing if the foundation was square. I told him that I’d measured the sides, which were exactly 11 feet 10. Then run the diagonals, which should be ....
I was losing him.
I said, “Yep, pretty square.”
When folks ask how you’re doing, they want to hear “fine.” They don’t want your latest cholesterol numbers.
The Pythagorean theorem holds that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
I have since learned that the ancient Greek might not have been completely responsible for figuring that out. But my math teacher, Mrs. Sommerfeld, gave him credit – and that’s good enough for me.
Years ago, a friend and I were framing up his new garage on a freshly poured concrete pad, which was slightly out of square. We wanted to make sure the framing was square, even though the concrete wasn’t. I asked him if his daughter’s calculator had a square root function on it.
He gave me a blank look but got the calculator.
Each side of the garage, as I remember, was 35 feet. I punched in a few numbers and told him that the diagonal was 49.49 feet. We laid the wood framing out perfectly square, even though the concrete wasn’t.
From then on, every time I’d do as much as dig a posthole, he’d wander over and ask if I wanted the calculator. Most of the time you don’t need to know exactly what the diagonal is supposed to be, only that the two diagonals are identical. If the opposing sides or a square or rectangle are the same lengths, and the diagonals are the same, the deck or garage is square.
That’s far more accurate than trying to square something with, say, a carpenter’s framing square. It works on everything from bookcases to picture frames, too.
If you ever need to use the square root function, just remember that .1 is not 1 inch. It’s 1/10th of a foot. As your calculator will tell you, that’s 1.2 inches.
Let’s just say I learned that the hard way.
When I got the walls up on the shed, and made sure the footprint was square, I checked the angles at the tops of the walls.
It’s hard to measure from corner to corner at the tops of walls when working by yourself, so I used the 3-4-5 rule, which old Pythagoras’ theory also explains.
If one side of a triangle is 3 feet, and another is 4 feet, then the corner between those legs is square if the third side is 5 feet. It works as long as the ratio is the same – say, 6-8-10.
Yes, the tops of walls can be out of square even though the base is perfectly square. I learned that the hard way, too.
So, don’t forget old Pythagoras the next time you’re building something that you want to keep square. But don’t quote him. If somebody asks how you got that cabinet perfectly square, just say an old carpenter taught you.