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Ideas from Ed: No math for good measure (Volume 6, Issue 8)

It seems like I’ve been doing a lot of construction and woodworking lately, so some of my “Ideas” columns are based on tools that I use, habits I have adopted, or things that I think just might be of interest. I suspect math is not an idea that most of you hold dear to your hearts, but being able to do simple and accurate measurements of dimensions and angles is critical to most any project.

Let’s begin with making a couple of simple statements about measurements. First, you should use the same measuring implement if you can throughout the project. In other words, don’t use a yardstick at one point, a folding rule at another, and then a retractable tape. It would be a wonderful world if every device was accurate (as it should be) but don’t count on it being so. Retractable tapes, in particular, often suffer from the “hook end” being bent from being dropped or stepped on, which of course throws things off just a bit. To be safe, when measuring, use the middle of the tape when you can. In other words, to measure 14” (for example) use the distance between the 10” and the 24” marks, which will be more accurate than using the hook end of the tape to the 14” mark.

Use a measuring tool that you are used to, with units that you understand. It’s amazing to me how so few people can accurately read a standard U.S. rule, in fourths, eighths, sixteenths, or even smaller units.If you have trouble doing so, by all means switch to something easier. Here are examples of a normal U.S. tape, one that is also divided using the metric system (centimeters and millimeters) and one that I find to be easiest, reading in inches divided into tenths.

The most accurate way of making something “fit” is often not by measuring at all, but by simply marking and cutting it. For example, to fit a board into a 25 and 9/32 inch space, it is possible to measure 25 9/32” and transfer that dimension onto the board, then cut it, OR simply position the board in place and mark that needed size before cutting. The most accurate math is no math at all.

Just for fun, though, this month I wanted to show a couple of ideas from high school geometry class that are very useful, and that also result in very accurate outcomes without the need for a scientific calculator or upper-level math work.

In the first example, I want to subdivide a piece of paper into 3 evenly-sized columns. (You can pretend it’s a board that will be cut, or a pane of glass, or whatever might seem applicable to your needs.) I chose 3 columns but it could be a different number. As you know, a standard sheet of paper is 8.5” wide. Doing it using math would be 8.5 divided by 3 = 2.8333 inches, a very awkward number regardless of which style of measuring device you use. The easy way to do it is to hold a ruler with the 0 on one edge and a number easily divisible by 3, like 9, on the other. That means holding the ruler at a skewed angle across the paper. Then you can carefully mark the locations of the “3” and the “6” thus dividing the 9 into thirds. I used just the point of a pen.

I did the same thing at the lower part of the page:

Then, connecting the dots divides the paper exactly (or at least as exactly as you positioned things) without doing anything above first-grade arithmetic!

I’ve often found it necessary to draw a line perpendicular to another line. Again, if an accurate square is handy, that’s probably what I’d use. Sometimes a little improvising is needed. In this picture, my goal is to make a right angle (90 degrees, a perpendicular line) to the right of the line I’ve drawn, starting at the point of the arrow.

A compass is an amazing tool, and with very little effort, can be used in many ways, including accomplishing the needed task. Here I placed the point of the compass at the arrow, and drew 2 arcs, each one crossing the original line exactly the same distance from the arrow.

Then, moving the compass point out to each intersection of that arc with the line, I drew two more arcs to the right of the line.

By connecting the arrow with the intersection of those two arcs, a perfect right angle is formed!

I’ll just show one more use of the compass, although there are many more. This time, I’ll be subdividing an angle of unknown measurement. This method is much more accurate than trying to measure the angle, dividing it in two, and re-drawing the bisecting line. The principle is basically the same as in the above scenario. Here’s the angle to be split:

Use a compass to mark equal distances along each line:

Then draw 2 more arcs within the angle, using the marks you just made as the point of the compass:

Connect the vertex of the angle with the new arc intersection and the angle has been split perfectly in half!

I’ve used these tricks a million times over the years, and you probably learned everything I’ve shown you in high school, but may have forgotten it! Maybe the quick refresher I’ve offered will help you design or build your next project more accurately.

I hope all your projects go well. Thanks for reading, and happy restoring!


If you’d like to download a PDF of this “Ideas” column, click here:

Ideas from Ed 2023_August_No_math_for_good_measure
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