Carpenters always carry a ruler — a metal tape or a folding rule with brass extensions to capture inside-to-inside dimensions. These days it might even be a laser that shoots a red spot on objects 50 feet away. But there are situations when carpenters put the rulers away because there's a better route to accuracy: geometry.
The infallible right triangle
"Right" means 90-degrees, a concept that has promoted sound engineering and long-lasting construction since about 300 B.C. It's still the basis of making your home square, so doors close solidly and windows open easily. Get it right, and kitchen cabinets fit into the corner without a piece of scribed trim to cover uneven joints. The elegant math that solves so many problems in construction is the 3-4-5 triangle. The numbers indicate the relationships of the three sides. It could be inches, feet, yards, miles, but when one side is three of them, another four of them and another five of them, the two legs enclose a right triangle — exactly 90 degrees.
Here's how it works in the field: You're building a deck off the back of the house. You want it to be square, not cockeyed. (That's a parallelogram.)
•Step 1: Where the end of the deck meets the house, mark off 3 feet on the siding.
•Step 2: Wet one of the deck boards perpendicular to the house at the same starting point and mark off 4 feet.
•Step 3: Measure from the 3-foot mark on the siding 5 feet across the longest side of the triangle until it meets the 4-foot mark on the deck board. Pivot the board until the 5-foot line and the 4-foot mark meet, and the board is 90-degrees off the house.
Why not save the math and use a 24-inch framing square? Sure, over short distances. But what about a 24-by-36-foot patio where a small error in the square will be magnified? Easy solution: Multiply each unit of the ratio times six and lay out a triangle about the same scale as the patio.
More geometric solutions
Double-checking for square Before cutting, nailing, or pouring concrete, it's wise to double-check the layout using a different rule of geometry: Diagonals of a rectangle are the same length. It's also helpful in the planning stage when stakes and strings are set up to mark a footing, patio or deck. Projects that start square have a shot at staying square. Projects that start cockeyed require adjustments along the way that often cause problems between trades, aside from extra time and money. A simple check is to measure the diagonals corner to corner. If they're equal, the corners are square, if not you have a skewed box, another parallelogram.
Checking for plumb Other old-fashioned helpers include the plumb bob. It dates to the Egyptians around 2500 B.C., when they built the Great Pyramid, the tallest structure in the world for almost 4,000 years. To establish verticals and angles they used a pointed metal weight hung at the end of a long cord. Most people now use a level despite two drawbacks. First, accuracy depends on how you read a small bubble against two black lines. Is it exactly in the center or just sort of? Second, accuracy falls off when the level isn't as long as the piece you're plumbing. Use a one-foot level on a door jamb, and a 1/8-inch error becomes most of an inch on the jamb. (That's why carpenters use 4-foot models and masons 6-feet and up.) With a plumb bob you need to wait for the weight to stabilize. Once it does, the bob's point is exactly under where the string is fastened, dead vertical.