[Woodcarver] geometry - labyrinth layout

[Byron]

Hi Sean,
Using math is not the difficult part of the problem. The difficult is to 
NOT using numbers. Use just a straight edge and a pair of dividers. Neither 
have any units measurement on them. It is very easy to do with 4 or 8 
points, but 13 points is different matter. According to a couple of places 
I've looked, it can't be done. Now there's a problem for your math students.

Byron


At 09:02 PM 9/30/04, you wrote:
>To make a DONATION to the Mailing List using PayPal OR regular mail, click 
>this link: http://wwwoodcarver.com/WWWList/WWWList.html
>
>'Lo Vic
>Sorry I didn't read your question sooner.  I'm a math major, and I can help
>a bit.  What you're looking for is a chord length to help you lay this thing
>out, and a chord is any line segment connecting two points on a circle.
>Y'all have already figured out what your central angle is, which is 360/13.
>The formula of a chord is 2r sin(theta/2), where r is your radius and theta
>is the central angle in radians (instead of 360/13, think 2pi /13).  For an
>18" square board, your max radius is 9", so according to my calculator 2 *
>9" * sin (2pi/26) = 4.3076", which is a little less than 4 5/16".  Just set
>your compass to 4 5/16", draw a line from the center of the circle to the
>edge of it, put the sharp point of the compass where the line and circle
>meet, and draw an arc that intersects the circle.  Draw a line from the
>center of the circle to where the arc intersected the circle.  You have just
>created a 1/13th division of the circle, so repeat as neccessary with your
>compass and fairly soon you'll have it all laid out.
>Thanks, by the way, for asking this question.  My future students will have
>one killer extra credit problem now ;-)
>
>Sean
>
>
>_______________________________________________
>Woodcarver mailing list
>Woodcarver at six.pairlist.net
>http://six.pairlist.net/mailman/listinfo/woodcarver