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Date: 05/04/97 at 15:18:59
From: Mike S.
Subject: decagons

What does a decagon look like?

I have serched the internet and the encyclopedia and found nothing.

Date: 05/04/97 at 17:02:23
From: Doctor Mike
Subject: Re: decagons


It's nice to hear from another Mike.  There are lots of us!
I'm sure you have seen a stop sign. If you haven't looked at one
carefully before, go out and find one. It is an octagon, which means 
it has 8 sides. Not only that, it is a "regular" octagon, which means 
that all 8 sides are the same length. I'm telling you this because a 
decagon is like an octagon, but with 10 sides, not 8. 

If you draw lines from each point of a stop sign to the center of it, 
the angle between each pair of neighboring lines is 45 degrees, or 
1/8 of a 360 degree circle.  If you draw lines from each point of a 
regular decagon to the center of it, the angle between each pair of 
neighboring lines is 36 degrees, or 1/10 of a full circle.
An octagon and a decagon are both polygons. Some of the most 
interesting polygons are the regular ones, whose sides are all the
same length. A square is one; an equilateral triangle is another. 

You might be able to find a picture of a regular pentagon (5 sides) in 
an encyclopedia article on the U.S. military, because their 
headquarters building in the Washington D.C. area has that shape. In 
fact, it is called "The Pentagon."  

You will be able to find a picture of a regular hendecagon (11 sides) 
in a coin-collecting book or catalog, because the Susan B. Anthony 
dollar coin has a regular hendecagon shape on it. I'm pretty sure 
there is also a Canadian coin in that shape.  
Another interesting regular polygon is called the dodecagon, which has 
12 sides of equal length. You can draw one of these easily if you 
have a picture of a clock face with a dot showing each hour. If you 
draw a straight line segment from the dot for 12 to the dot for 1, 
then a line segment form the dot for 1 to the dot for 2, et cetera all 
around the picture of the clock face, you will have constructed a 
regular dodecagon. If you draw lines from each point for an hour (a 
point of the regular dodecagon) to the center of the clock face, the 
angle between each pair of neighboring lines is 30 degrees, or 1/12 of 
a full circle.  So, in the hour between eight o'clock to nine o'clock, 
for instance, the hour hand sweeps out an angle of 30 degrees.    
You might be wondering where all these strange names come from. We can 
help with that because that is one of our Frequently Asked Questions, 
which is answered in our FAQ section of the Dr. Math archives:   

I think you will find that info interesting. I hope this helps.      

-Doctor Mike,  The Math Forum
 Check out our web site!   
Associated Topics:
Elementary Geometry
Elementary Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons

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