Math is fundamental to building. And while there is no escaping the need to be proficient with numbers and algebra, learning some geometry can go a long way in helping carpenters be more efficient. In this article, we’ll introduce a few methods for dividing, measuring, and laying out shapes that can save time and take some of the head scratching out of many layout jobs.

Scale. The first principle we’ll address is the idea of using a scale of known increments (such as a tape measure) to divide a line or area. In the first two examples below, we don’t need to know the width of the board we want to divide, or make any calculations. We simply hold the end of tape along one edge and run it out to the opposite edge. The distance and angle of the tape don’t matter, as long as we align the opposite edge with a number on the tape that we can easily divide by 2 or 3 (or any divisor we want). This same concept can be used to divide an uneven distance into a number of equal segments without having to pull out a calculator.

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