Sunday, October 7, 2012

Dividing a Circle Into Thirds, Without a Protractor

One of the things I'm doing in preparation for the JOTA event on the USS IOWA, is (finally!) building up my new "more portable" antenna mount for my satellite antenna.

I started with a 5' surveyor's tripod I got really cheep on eBay. I have numerous "spare" Yaesu Azimuth/Elevation rotators and control boxes, so I figured I could mount one of my spares to the tripod with an adapter plate.

I bought some good 6061 1/4" thick aluminum sheet, and proceeded to cut out a 6"x6" square. I marked it, and using a set of trammels, laid out a circle the same diameter as the bolt circle for the Azimuth motor. Then I drilled and countersunk some holes to bolt it to the motor with flat-head machine screws.

Now the task was to mount the plate to the tripod, and there was the snag I hit.

The top of the tripod is triangular, and where the legs mount to it there's a lack of space on the underside of the plate to use four mounting screws. So, I decided I'd use three screws instead, and they'd have plenty of room between where the legs meet the top of the tripod.

The problem was, how do I lay out 3 equally spaced holes on the correct 3" diameter circle I just scribed using my trammels?

I remember from way back in high-school geometry (or was it trig?) that dividing a circle into thirds was a very complex, tricky task, and you were better off to just get a protractor, and lay out your marks every 120*.

A quick Google search found this very ingenious method of equally dividing a circle into three sections, WITHOUT the use of a protractor.
I was so amazed that I thought I'd share it with my friends here, in case any of you are metal cutters like I am, or perhaps woodworkers.

Enjoy the little video. I found it quite amazing!



  1. Okay, so how does one place the point on the diameter line? Move to the right or left will make the angles bigger or smaller????

  2. 1/4 of the diameter will give you 120 degrees, I don't remember the math for the rest of it though... :-(

  3. Old_NFO beat me to it. i/4 the diameter is half the radius, so I went half way between the center of the circle and one edge of it. From that point you draw a line at 90* to the radius/diameter, crossing both edges of the circle, and those two points are 120* apart.

    It's harder to describe than watching him do it.

    1. The process was easy, but I didn't know until now that the perpendicular line was set at 1/4 the diameter. Cool trick!

    2. Why not devide it into 6 parts. Easier. Thanks use 2 parts times 3.

  4. The only 'trick' to it is making your measurements VERY precisely.

    I was off a tad, and while it worked just fine for what I needed, the marks I made were not exactly 120* apart.

    After playing around with pencil and paper, I saw that an error of even a small amount would result in a larger error in the "equality" of the 120* spacing.


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