Just when you think you only need high-school math to figure out the losses on your 401(k), along comes a reader with a question. Barry Randell plans to build a cover for a 16″-diameter cistern. The cover would have six or eight sides, and he wanted to know how long the pieces would be. My plan was to draw an octagon on paper, so here’s how that worked:
2. Draw diagonal lines between opposite corners of the square to find the center at the intersection of the lines.
3. Set a compass for the distance between one corner and the center. (You can make a crude beam compass by clamping a scratch awl and a pencil to the yardstick 16″ apart.
4. Place the point of the compass at one corner and mark where the arc (shown in red) intersects two sides of the square. Do this again at each of the remaining corners until each side has two arc marks on it.
5. If you want to stop there, you can measure the distance between two arc marks on any line to discover the length of the inside face of a mitered frame piece. Or connect the arc marks closest to a corner and repeat at each corner to create the octagonal shape.
Now, in fairness, Barry did ask for a formula and not a geometry exercise. So I’ll open the question up to anyone whose math skills are better than mine. In other words, everybody. And in the words of my high-school math teachers, remember to show your work.
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