Mitre question???

On 7/24/2005 11:35 AM Leon mumbled something about the following:

I've done triangles, but I had to do lap joints, since I couldn't come up with the cut, no matter how I positioned the board. Obviously, I was doing something wrong if it can be done.

You absolutely have to do them backwards to normal thinking including the angles. Did you check my PDF file on A.B.P.W. ? That illustrates how to cut the angles for a triangle on the TS.

There, you said it, sort of. Odd number of sides

I think the problem with all of this is we're (all)attempting to make one rule fit all situations. Obviously it doesn't work on all triangles and your rule that allows different length sides on a polygram but keeps the angles identical throughout will only work on a polygon with an EVEN number of sides. Once you have five, seven or nine sides to your polygon then you're right back to length of sides and angles must be identical.

On 7/24/2005 12:25 PM Leon mumbled something about the following:

Yes, I checked it out, but something still isn't clicking on the angles for me. Not to worry, I don't have to worry about triangles very often, so it isn't that critical :)

Yes you can: A rectangle with two sides one length, and two another [opposite sides are equal] will have all four angles each 90 degrees. A "Regular" polygon is defined as one having all sides equal. Then equal angles follow from that. However, the opposite does not follow, as you see from the above example. That is IF all sides are equal, THEN all angles will be equal. However, IF all angles are equal, it does not follow that all sides are necessarily equal.

I really don't know why all the fuss. You are looking at definitions and at properties of these figures. You can use one property or another to advantage, and it really doesn't matter which, except to keep it simple, and except to your personal preference. The main idea is that a polygon can be divided into a number of triangles from a convenient point inside joined to the edges. [Actually, the main idea is to build stuff.] The sum of angles in each is 180. If there are "n" triangles, there will be a total of 180n degrees. Subtracting the angles around the center point, 360, or 2*180, you wind up with 180n -

If the polygon is regular, there will be n equal angles [following from n equal sides], so each will be (n-2)*180/n. To find the miter angle, divided by 2 to get (n-2)*180/(2n).

Now, for three sides, or for four, you can set the miter to that angle. However, if a greater number of sides, you have to use the complementary angle [90 - the found angle.] This will give you 180/n when simplified. That is the measure of half the exterior angle, which is the outer angle formed when you extend one of the sides of the polygon.

So, the gentleman who said to use 180/n was dead on accurate, and as should be done, he kept it simple. That's always the best practice. You can use a CAD program to draw an ellipse. I can draw one in the same time using two concentric circles. "Layout", as it's called is usually based on firm math, but the entire idea is to keep the process simple. The math can be very complicated, even more ocmplicated than calculating each point using coordinates instead of the layout technique. It's layout that cause the invention of 3D drafting techniques. Again, the entire idea is to keep it simple. So ...I go for 180/n, and set the miter to the complelentary angle if needed.

Thanks to all for adding confusion to what I thought was a simple explaination, even if it had been mentioned previously.

I do wonder how many WRECKERS actually work with wood. Some obviously do and are very experienced. But, judging by the number and frequency of letters I suspect the only tools some use are a keyboard and mouse!!

Oldun

I don't think so. I've posted an example to abpw.

-- Morris Dovey DeSoto Solar DeSoto, Iowa USA

Correct

Once you have five, seven or nine sides to your

Actually not all have to be the same length as illustrated by Morris Dovey's post in a.b.p.w.

Yeah.. LOL.

RE: Subject

My 80+ year old, at the time, high school math teacher, Olive Bowers, all 4'-10" and 85 lbs of her would roll over in her grave observaving this discussion.

You guys can do better.

Lew

You *are* confused! Albeit somewhat understandably so.

Try a hexagon, with sides of 1,2,3,1,2,3 All the angles can be 60 degrees.

With a pentagon, it *is* also doable, Take a regular pentagon, and draw lines parallel to two _adjoining_ faces, at say halfway down the sides. You get a shape vaguely reminiscent of a squatty ice-cream cone. The bottom of length "a", two 'sides' of length "b", and the two top parts of length "c". All inside angles _are_ the same 72 degree measure.

Quantitatively, given the bottom (a) as of length 10, the sides (b) are then of length (5), and the 'top' parts (c) are of length 8.0902+.

Wrong. a regular polygon requires that all sides be of equal length

WRONG! Look up a "rhombus",

Disproof by counter-example an object with corners at (0,0), (sqrt(2),0), (1+sqrt(2),1), and (1,1)

length of each side is "sqrt(2)". angles are *not* equal.

A regular polygon, *by*definition* (and by definition =ONLY=) has n equal angles *and* n equal-length sides.

You're right, of course. [Head hung in shame.] I must have taken the wrong pill [the dumb one instead of the smart one.]

What saw are you using? All of my saws have a range of 90 degrees to

That's just not right. The sum of the interior angles of a triangle- any triangle, is 180 degrees. What Odinn is saying is that your formula doesn't work because you're looking for the angle you need to cut, not the total interior angle of the polygon. If you're making a triangle out of planks of wood, you need to cut the miters at 30 degrees, so that when the joint goes together, you end up with a total of 60 degrees. Cutting the wood at 60 degrees will give you a hexagon.

BTW, for the other poster (and it may have been you, I forget who it was) who said that you can just flip a piece that is cut at

I admit, it has been a long time since I took geometry, but I kinda remember Mr. Darby telling us that triangles had ony 189 degrees.

Glen

Welcome to USENET.

Definitions: USENET -- open mouth, insert foot. Echo internationally.

You don't get it. I used to teach math! I've solved some awfully difficult problems in my day, and love geometry in particular, applying it constantly to woodworking as well as other things. I really, really!! fell asleep at the wheel on this one.

"The mind goes second. I can't remember what goes first."

Make that 180 degrees!

Glen