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### Sixteen-sided Window

```
Date: 08/05/97 at 23:56:14
From: Robert Richards
Subject: Lengths of a sixteen-sided circle

I am trying to cut a window for my twin girls' playhouse and would
like to make a sixteen-sided window to go in the second floor hallway.
I have tried to lay it out on cardboard using about every increment I
can calculate for the total but it still doesn't work out. Can you
help me out so I can tell where I am going wrong?
```

```
Date: 08/12/97 at 13:22:10
From: Doctor Rob
Subject: Re: Lengths of a sixteen-sided circle

You want the length of the side of a regular 16-sided polygon, right?

Draw a circle of diameter d.  Pick a point on the circle to be the
starting point.  Mark off points around the circle at regular
intervals, to be connected up to make your 16-gon.  You want to know
what the length of these sides will be.

The answer is d*Sqrt[2 - Sqrt[2 + Sqrt[2]]]/2.  This is approximately
0.19509*d.  The central angle that each side corresponds to is 22.5
degrees.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
High School Practical Geometry
High School Triangles and Other Polygons

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