[Woodcarver] Geometry question for the group

[Classic Carving Patterns]

Opps .. It would have been nice if I had included the formula in the
earlier e-mail ... My apologizes.

A circle's circumference is equal to the diameter divided by pi (3.14).
C=pi/d  My computer doesn't have a pi key.
Radius is one half of the diameter.  d=1/2r

The circumference of a circle is 13 inches. What is the diameter? 
   
Solution:  
  13 inches = 3.14 · diameter
  13 inches ÷ 3.14 =  diameter  = 4.140 inches diameter = radius of 2.07
inches

For multiples of 13 use 26 or 39 and then use 2" spacing for 26"
circumference or 3" spacing for 36".
  26 inches = 3.14 / diameter = 8.280 inches diameter = radius of 4.140
inches
  39 inches = 3.14 / diameter = 12.420 inches diameter = radius of 6.21
inches 

I note this only because the I believe that those of 800 years ago had a
touch more than just straight edges and compasses.  I would expect that
they had defined measuring units (rulers) and they had some excellent
higher math skills.

Susan

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-----Original Message-----
From: woodcarver-bounces at six.pairlist.net
[mailto:woodcarver-bounces at six.pairlist.net] On Behalf Of Victor
Hamburger
Sent: Thursday, September 30, 2004 8:53 AM
To: [Woodcarver]
Subject: Re: [Woodcarver] Geometry question for the group


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Tom Clarke wrote:
> 
> Are just some of what's out there. Using the formula's given a side
> length or taking an exterior circle one could then draw the polygon
for any sided.
> Problem with one with 13 sides is the angle isn't a whole number.
Probably give you
> fits.

Tom, and Ivan,

Thanks for the comments, I had found the DrMath site but didn't try the
math. 
13 is a prime number, indivisible except by 1, causing some of the
problem. 
What I want to understand is how, using only a compass and straightedge,
do you 
lay out the 13 point star.  I have various solutions for 4,5,6,8 and 12
point 
stars.  I can bisect any of those sides to create a star with twice
those 
points, but 13, being prime, has got to be done by itself.

The builders 800+ yrs ago knew how to do it with a compass and
straightedge, and 
I would like to duplicate that.  As I said, I can lay it out with a CAd
program 
no problem, I just like the challenge of doing it with the simple tools
of the 
master craftsman of earlier times.  The pyramids and Greek Temples and
Roman 
empire were built with these tools, I am curious to try a more complex
figure 
for myself.

Thanks,  Vic H


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