[Woodcarver] Geometry question for the group

[Joe Dillett]

Hi Vic,

Laying out a 13-point star is easier to divide the 360-degree circle into 26
equally spaced lines, because an even number uses straight lines
intersecting through the center of the circle. You need 26 equally spaced
points to determine both the outer points and the inner points of the star.
Draw two circles determining the diameter for the outer and inner points.

If I was to divide a circle into 26 equal points I would use the formula for
the circumference of a circle C= 3.1416 X Dia. By setting my dividers at an
arbitrary distance of 1 inch between the 26 points I would approximate the
circumference of the circle to be 26-inches (slight difference because of
the arc between the 1-inch distance). The diameter of the circle is
(26-inches divided by 3.1416) = 8.27-inches. By drawing a circle 8.27-inches
diameter you can divide it into 26 equal points (with as error of about
.06-inch because of the approximation). Use every second point for the outer
points of your 13-point star.

Trig will get you closer without the need to approximate.


Joe Dillett
The Carving Shop
645 E. LaSalle St. Suite 3
Somonauk, IL. 60552
(815) 498-9290 phone
(815) 498-9249 fax
http://www.thecarvingshop.com
jdillett at thecarvingshop.com
http://www.carvingmagazine.com Carving Magazine web site and Readers Forum
http://community.webshots.com/user/joe_dillett
**************************************************


----- Original Message ----- 
From: "Victor Hamburger" <VHamburg at bellatlantic.net>
To: "Woodcarver" <Woodcarver at six.pairlist.net>
Sent: Wednesday, September 29, 2004 10:03 PM
Subject: [Woodcarver] Geometry question for the group


> To make a DONATION to the Mailing List using PayPal OR regular mail, click
this link: http://wwwoodcarver.com/WWWList/WWWList.html
>
> I did well in geometry in High School, but that was more than a while ago
now.
> I am interested in learning to draw a 13 point star geometrically.  I know
I can
> lay one out with a CAD program, but the Cathedral at Chartres, built
700-800 yrs
> ago, has a labryinth laid out on the floor.  To correctly design the
labyrinth,
> you need to know how to lay out a 13 point star.  In those days, some
builder
> knew how to lay out a 13 point star to do this........
>
> I have googled around and not found anything on 13 point stars and
geometry, at
> least not that I can see on the links!  Any googling on labyrinths gets me
lots
> of info except how to lay out the star for this one.
>
> BTW, a labyrinth is a path, laid out in a geometric figure such as a
circle
> (Chartres) or other figure.  It has an entrance and end point in the
middle and
> to get in and out again you follow the singular path.  A maze on the other
hand
> has a path but with multiple turns that are wrong turns and dead ends.
The
> point of the labyrinth is to enter and walk the path, allowing your mind
to be
> free to pray, chant, or otherwise let go of your usual thoughts and let
your
> inner thoughts take over. You can learn more by googling on labyrinths and
Grace
> Cathedral in San Francisco.  They have an extensive set of links and
details
> there to more info on labyrinths.
>
> What has this got to do with carving? Well, beside the rosette
possibilities for
> chip carving a 13 point star, there are finger labyrinths you can carve so
you
> don't need a 45' circle in your house or garden......only an 18" sq board.
I
> may never carve one, but it is worth the mental challenge to pursue it.
>
> Thanks,  Vic H
>
>
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