Replies

1. 
   Ribeye | Nov 22, 2005 10:38pm | #1

   Since "Hexa" equals "Six", just divide 360-degrees by six and deal with the complementary angles as necessary ...

   -- sure beats a trip to the used book store :-)

   -- Steve

   Enjoy life & do well by it;

   (it might well be the only chance you get.)

1. 
   user-54856 | Nov 23, 2005 12:29am | #2

   True, and penta- means 5, hepta- means 7, dodeca- means 12, etc., but, in the absence perhaps if an Incra jig, you'll need a good protractor and I think you'll end up with a lot of trial and error in making the cuts. Furthermore, just cutting the angles is not the same as laying out the polygon. There are lots of books on the subject but this little book is cheap and a lot of fun.Edited 11/22/2005 4:32 pm ET by Troost Avenue

   Edited 11/22/2005 4:40 pm ET by Troost Avenue

1. 
   byhammerandhand | Nov 23, 2005 09:33pm | #3

   Years ago, Jim Cummins (RIP) had a discussion on this in his "small shop projects FWW Video." Since Jim ran a picture framing shop 40" matboard trimmings were plentiful. Using 1000 mm (1 meter), slightly less than 40", as the base of a triangle, he would use the arctan function on a scientific calculator (or your computer's version) to compute the altitude (other leg) of the triangle in terms of mm. Draw the hypotenuse and cut the end of the triangle off to make an angle gauge. He, and I, as a trial, made a 31-sided figure using this method with no discernable error. No measuring, just stick the angle guide up to the saw blade and sight it in.

1. 
   user-54856 | Nov 24, 2005 07:11am | #4

   Good thinking. Sister Honorious didn't teach trigonometry. I think that was Sister Cornileus.

2. 
   highfigh | Nov 24, 2005 08:57pm | #5

   If you want to make polygonal pieces, with an ACCURATE protractor, a compass, some drafting vellum (you can get it at any artist's supply store) and a piece of melamine covered particle board (or MDF), you can make a pattern for whatever job you are doing. Knowing the diameter of the circle encompassing the shape, draw the circle and, using the protractor and a calculator, mark the angles. Connect the points on the circle where the rays from the center intersect, and you have the polygon of the correct size. The melamine can be easily cleaned of pencil marks, so mistakes are easy to eliminate. Once the correct angles and diameter are found, you can repeat it on the vellum and use low-tack cement to stick it onto the pieces if needed. Most of the angles will be easy enough to create since the angle will be a whole number. For odd numbers of sides, like 7, 11, 13, 14, 17, 19 and any other number that gives a fractional angle, the chance of using that number of sides is probably slim.Another great resource ignored by a lot of people who work with wood is drafting skills and books. This is all covered in drafting books and classes, although there are less pencil-on-paper classes now since most designs are done with CAD, which is another great resource since it can do fractional angles with extreme accuracy.BTW, all of the polygons (5,6,7,8,9 sides) in the original question are evenly divided into 360 degrees, with 7 being the exception.
   "I cut this piece four times and it's still too short."

   Edited 11/24/2005 1:01 pm by highfigh

1. 
   PlaneWood | Nov 25, 2005 02:04am | #6

   For a polygon frame where all sides are to be of equal length and N is the number of sides to the polygon.  The angle to cut on the end of each frame piece is 360/N*2. 

   PlaneWood by Mike_in_Katy (maker of fine sawdust!)PlaneWood

1. 
   highfigh | Nov 25, 2005 08:37am | #7

   So you're saying that, for a 7 sided polygon, it would be (360/7)(2), or 102.857°. That doesn't work. It should be 360°/7, or 51.43°. The outside angles would be greater than 90°, not the cut angles.
   "I cut this piece four times and it's still too short."

2. 
   PlaneWood | Nov 26, 2005 12:39am | #8

   The end of each frame piece would be cut at 360/(N*2) or 25.71 degrees.

   i.e. starting with a triangle - 60, 45, 36, 25.71, 22.5, 20, 18, etc.

   I guess it don't make sense without the parenthesis!

   PlaneWood by Mike_in_Katy (maker of fine sawdust!)PlaneWood

3. 
   highfigh | Nov 26, 2005 01:55am | #9

   I was referring to the angle at each joint. To make this easier for what we are trying to do, the angle at the corner should be determined by dividing 360/n, with n=number of sides. For a heptagon, the angles are 51.43° at each corner. This is the angle that needs to be set on the miter gauge. The complementary angle doesn't even matter. Divide 360° by 8 and you get 45°. If you set the miter gauge to this and cut each end of the pieces, you get an octagon. Doing it your way, the result is 22.5°, which is fine if you have 16 sides.
   "I cut this piece four times and it's still too short."

4. 
   user-58937 | Nov 29, 2005 05:07am | #10

   Mind your arithmetical grammar. The parenthesis command the that the operation within happens first. By the way your math is correct. There are graphical methods of subdividing an object, for instance a circle. The tools needed are a compass, a straight edge, a rule, and a triangle (a drafting triangle or a nice square would suffice). The method is simple. First draw a circle of any size, aim for large as comfortable with your compass. Next, using your straight edge, draw a line outside of the circle, at any angle ands longer the the diameter. Next, with scale in hand divide the straight line by even increments for the number of sides of the figure plus one ( consider the plus as the zero if need be) Next, draw parallel lines from the subdivided straight line through the circle. the key here is parallel.  Try clamping or taping the straight edge down and sliding the square along it. You should now have a circle evenly divided. Sometimes it takes a little practice setting off the tick marks to get a large number of divisions, this is why the large circle works. At this point extend lines from the center to the edge of the divided circle and lines from corner to corner. The final step before cutting stock is carefully copying one section of the pie to a scrap as a cutting guide. wallah circle division without angles, calculator or the dread geometry tables. Any one for racing interpolation.

2. 
   corners | Dec 09, 2005 06:47am | #11

   In your CAD program select the polygon tool, tell it how many sides, tell it how big, save the file in a 1 to 1 scale and next time you pass a Kinko's or other service provider have them print it full size and use it as a pattern.

   This technique works well for any other shape or pattern.

    

1. 
   user-54856 | Dec 09, 2005 09:53pm | #12

   I don't have access to CAD but somehow I think I would probably be more comfortable with Euclid.

1. 
   Ruth | Dec 15, 2005 05:04pm | #13

   Here's a fantastic Euclid site -- scroll down the page, and try Book 4, propositions, for construction of polygons.

   http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Ruth DobsevageTaunton New Media

1. 
   user-54856 | Dec 16, 2005 01:22am | #14

   Thanks. Memories again of Sister Honorious. Do kids today still study geometry. If not, what a shame.