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The 3-4-5 Rule for Squaring


This is a Carpenter’s Method for Getting a Perfect Square Based on the Pythagorean Theorem in Mathematics

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How the 3-4-5 Method Works



This is an old fundamental item in every carpenter’s box of tips and tricks. But it wasn’t a carpenter who invented the concept. It was worked out by a Pythagoras of Soma, a wily old Greek Ionian philosopher, mathematician, scientist, and mystic in about mid 500 BC.

The rule he dreamed up is simple and brilliant all at the same time and our rule is based on that, without you having to deal with working out squares or square roots. The Pythagorean theorem says A2 + B2 = C2. While you read this explanation, refer to the graphic below for clarification. Pardon my sloppy artwork, but hey, I’m a carpenter, not an artist.

You’ll notice there is an X axis and a Y axis. One is numbered to 3 units and the other to 4. This can be any unit of measurement; inches, feet, meters, or cubits. Also, keep in mind that multiples of these units (6-8-10, for example) may be used and the formula will still work. The flexibility of this tool is convenient.

The first step is to mark one of the axis’. For the sake of illustration, let’s imagine we are laying out control lines on the floor for installing ceramic tile, although there is no limit to the actual number of situations. So, first measure out a foot from one wall in two places, close to the ends of the wall. Strike a chalk line through both marks parallel to the wall. Now you’ve got your first axis.

Referring the picture below, mark a starting point, and then measure carefully 4’ down and make a mark there. Label it “A”. Next, establish the second axis using the same method as before. You see where they intersect. Snap your chalk line and measure out 3’ and make a mark. Label it “B”. Now, if the measurement between “A” and “B” is 5’ you’re done.

If it’s more than 5, the far end of “B” needs to be moved in a bit while maintaining the point where A and B intersect (lower left hand on the picture). Logically, if it’s less than 5, the opposite needs to happen; the far end needs to be moved out. One or two iterations ought to get it perfect.

The Pythagorean Theorum

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