VII.  Constructing 4 or 8 parts of a circle

This one is a double feature because one leads into the other.

A couple of years back I read in the Tips and Tricks page of a magazine a tip from a reader who had discovered a very complicated way to lay out 12 equal spaces on a circle. He was using 2 framing squares to accomplish this. His ultimate reason for doing this was that he wanted to make a clock face.

I was flabbergasted at the complexity of the process, so I wrote in with my solution which is shown below. I received a check for $100 for my effort.

Draw a circle of the required size and draw a centerline through it. Set your compass at a distance approximately the diameter of the circle.

Swing intersecting arcs from both intersections in both directions.

Draw the line which is now the horizontal centerline. The circle has now been quartered. That is the first part of the solution.

Now set your compass to the radius of the circle. Swing arcs on both sides of each intersection. The result is a circle divided into 12 equal parts.

Logic tells you that if the radius can be used to lay out a 6 sided figure, that it must also be able to describe a 12 sided figure. So what would be the result if you were to divide the circle into 8 parts?

(Old trick for getting the apprentices to do something for themselves.)

December, 2005

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