Long Forgotten Trig and Geometry

[JR]

Simple geometry

In a hexagon configuration each length will describe an equilateral triangle with respect to the center of circle. Bisecting that triangle defines the radius (r), and makes a right triangle including the side (h) and the side (h/2).

Therefore, using pythagoras' law, root-r = (h-squared) - ((h/2)-squared)



JR

[sacherjj]

You're not correct in this instance.
The round object needs to fit within the hexagon which means that the
radius applies not at the points of the hexagon but at the center of the edges of the hexagon.

Oh, I was thinking fit the polygon inside the circle. I need to read better. In that case, the tangent formula seems right.

tan(360/2n) = l/2r
L = 2*r*tan(360/2n) Yeah, thats right for surrounding a circle.

8 sides and 6" L = 4.97"

Sketchup Verifies (I find myself checking trick measurements in Sketchup more and more):

[Wood_workur]

Yeah, for an 18" pot you would need*:

10.5" sides (measured on the inside of the boards) or 11.375" (measured on the oustide of the boards) for 6 sides.

or

7.5" sides (measured on the inside of the boards) or 8.125" (measured on the oustide of the boards) for 8 sides.

And only use one of the measurements, sine they are rounded up slightly, you might have some problems with the pieces not aligning.

I checked with autocad, and yes, the polygon was circomscribed aroung the circle. (for those who remember geometry)

PM me if you need anyother dimentions.

*measurements guarenteed accurate

EDIT:
steve-norrell has a very good table attached to his post, but it only gives the meausrements for the inside edge of the board. Makesure you always do a double check on good old paper (draw it out) with a ruler before you do any cutting.

[JimD]

I didn't try to derive a formula but I would approach it like JR. Regardless of the number of sides, you know one side of the triangle because it is the radius of the pot and you know the angle. If it is an 8 sided structure, the angle is 1/2 of 360/8 or 22 1/2 degrees. Now the tangent of 22 1/2 degress = the opposite over the adjacent or 1/2 the length you want over the radius of the pot. Multiplying the radius times the tangent of 22 1/2 and then taking the result times two will get you the distance. The only thing that changes for different sided structures is the angle you take the tangent of. It will always be 1/2 of 360 divided by the number of sides. For 6 sides it is 30 degrees, for instance. For four sides, it would be 45.

For me picturing the triangles is much easier than trying to derive a formula. Once you do it once, however, it also would be pretty simple to write it as a formula.

Jim

[pierhogunn]

wow, I need some of you guys in my little compound when I go to start my own country in Montana

[LCHIEN]

wow, I need some of you guys in my little compound when I go to start my own country in Montana

Is this going to be a real country? Like Branch Hogunn?
Do we get automatic weapons? and 4 wives?

[mschrank]

Kind of a late reply and sounds like you got it figured out, but I finally found the webpage I was looking for when I was your OP:

http://woodworking-woodworking.com/polygons.html

Might come in handy next time!

PS-Thanks to forum member Joe Lyddon, I found this from links on his site.