Most any method is going to start with constructing a regular polygon (one where all the sides are the same length) circumscribed by the circle, like the hexagon that Bob makes, and then if needed, dividing the angles or line segments of that hexagon to get the appropriate divisions. Bisecting the angles of a hexagon easily gets you the 12 points, as Bob demonstrates in his video. If you needed 18, you could divide the resulting line into three segments, etc.

As with a lot of these constructions, it’s all sort of the basic methods (most of which are described in the links I posted below) “stacked” to get what you want, and there are often different ways to arrive at the desired result, depending on what you start with.

A 10-sided shape is more complex than twelve, because you can’t start with that easy hexagon. You need to start with a pentagon, and then divide each of those segments in half to get the 10 sided shape you want.

Here’s links to drawing pentagons from one of the websites I mentioned before:

http://www.mathopenref.com/constinpentagon.html

It might be easier to follow if you click the link below the movie to the printable instructions:

http://www.mathopenref.com/printinpentagon.html

Because the construction is not symmetrical, you can set the dividers between two points on the pentagon, and then use that to step off another set of points along circle, starting on the opposite side of the original line. I.E., the “peak” of the pentagon is at the top of the circle, along that first line dividing the circle in half the way they make it – once you can set the dividers to the distance between points on the circle, you can step one off starting at the bottom of the circle, on the other side of that original line – that will get you 10 points, without having to divide every angle or line segment in half.

Hope that last bit made sense, I’m not the best at describing these without being able to make pictures.

]]>-Shawn

]]>I bumped into those some time ago when trying to figure out how to divide circle into innumerable bits and pieces. Lot’s of stuff that can be done with a set of dividers and a straightedge.

Best regards,

Albert A Rasch

I have an overabundance of dividers, and in learning about them, I found this series of flash videos :

http://www.mathopenref.com/constructions.html

and

http://www.mathsisfun.com/geometry/constructions.html

Pretty useful when I was looking for stuff. Lots of cool tricks. I think learning to layout an ogee with dividers from Roy’s show was what started me on this trek. There’s lots more info online, as well – looking for “compass and staightedge constructions” pulls up a lot of neat info.

I particularly liked the trick for dividing a line into any number of parts without measuring or constant stepping off and adjusting, which I don’t think I saw in your article, and has proven pretty useful to me a couple of times:

http://www.mathopenref.com/constdividesegment.html

Pretty quick if you have more than one divider so you don’t have to reset one over and over.

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