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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.

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

Wrong. a regular polygon requires that all sides be of equal length***and*** all angles be of equal measure. You ***can*** have _either_one_
in the absence of the other.

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.

[..munch..]]

***FALSE*** reasoning. see above for disproof of the reasoning..

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

Welcome to USENET.

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

***GRIN***

You***are*** confused! Albeit somewhat understandably so. <grin>

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+.

It certainly does work with a triangle. However you will be hard pressed to find a saw that will cut at 60 degrees. The solution if using a TS would be to set the saw at 30 degrees and put the board on end and run through the saw.

Yeah.. LOL.

And I will mention again that you will not find 67.6 degrees on your saw.

#### Site Timeline

- posted on July 24, 2005, 7:12 pm

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.

- posted on July 24, 2005, 11:23 pm

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

- posted on July 24, 2005, 5:36 pm

On Sun, 24 Jul 2005 15:56:17 GMT, Unquestionably Confused

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 -
2***180 = (n-2)*180.

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.

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

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.

- posted on July 25, 2005, 1:25 am

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

[..munch..]]

A regular polygon,

- posted on July 25, 2005, 3:05 am

On Mon, 25 Jul 2005 01:25:06 -0000, snipped-for-privacy@host122.r-bonomi.com
(Robert Bonomi) wrote:

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

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

- posted on July 25, 2005, 1:07 pm

Welcome to USENET.

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

- posted on July 25, 2005, 8:31 pm

On Mon, 25 Jul 2005 13:07:16 -0000, snipped-for-privacy@host122.r-bonomi.com
(Robert Bonomi) wrote:

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."

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."

- posted on July 25, 2005, 1:17 am

You

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

With a pentagon, it

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+.

- posted on July 24, 2005, 2:50 pm

It certainly does work with a triangle. However you will be hard pressed to find a saw that will cut at 60 degrees. The solution if using a TS would be to set the saw at 30 degrees and put the board on end and run through the saw.

- posted on July 24, 2005, 5:48 pm

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 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

- posted on July 24, 2005, 7:15 pm

Yeah.. LOL.

- posted on July 20, 2005, 2:35 am

Gotta hand it to you, you sure know how to make things complicated.

- posted on July 19, 2005, 4:43 pm

On Tue, 19 Jul 2005 10:22:14 -0400, snipped-for-privacy@webtv.net (JAKE) wrote:

Asked and answered just recently, so my first impression was that this is a troll. A Google would bring the result. However, since it has been answered several ways, I'll suggest yet another method, still based on the same principles.

8 sides = 8 triangles to the center. The center angle is then divided 8 ways = 360/8 = 45 Each triangle has two angles at the outside that are equal, and the angles in a triangle add to 180, so they add to 180 - 45 = 135. Being equal, they are each 67.5 degrees.

Do the same sort of calculation for any number of sides [oteh thsan 8.]

Asked and answered just recently, so my first impression was that this is a troll. A Google would bring the result. However, since it has been answered several ways, I'll suggest yet another method, still based on the same principles.

8 sides = 8 triangles to the center. The center angle is then divided 8 ways = 360/8 = 45 Each triangle has two angles at the outside that are equal, and the angles in a triangle add to 180, so they add to 180 - 45 = 135. Being equal, they are each 67.5 degrees.

Do the same sort of calculation for any number of sides [oteh thsan 8.]

- posted on July 19, 2005, 7:37 pm

(JAKE) wrote:

As you can see by using math you've come up with a completly wrong answer. By using common sense the angle for the skirt cuts would be 22.5. This is not rocket science.

As you can see by using math you've come up with a completly wrong answer. By using common sense the angle for the skirt cuts would be 22.5. This is not rocket science.

- posted on July 19, 2005, 7:43 pm

(JAKE) wrote:

Which as I mentioned to another poster is the same thing. 22.5 and 67.5 are complimentary angles. It's just a matter of which side of the line you're cutting.

Which as I mentioned to another poster is the same thing. 22.5 and 67.5 are complimentary angles. It's just a matter of which side of the line you're cutting.

- posted on July 19, 2005, 7:48 pm

Secret Squirrel wrote:
...

You've the wrong "compliment" here (BTW, I didn't post until after I read the second time, just to be sure...). :)

Angles are "complementary", we give each other "compliments" for good work, etc., ... :)

You've the wrong "compliment" here (BTW, I didn't post until after I read the second time, just to be sure...). :)

Angles are "complementary", we give each other "compliments" for good work, etc., ... :)

- posted on July 19, 2005, 10:03 pm

And I will mention again that you will not find 67.6 degrees on your saw.

- posted on July 25, 2005, 7:31 am

On Tue, 19 Jul 2005 22:03:58 GMT, "Leon"

What saw are you using? All of my saws have a range of 90 degrees to 45 degrees (maybe a little less in some cases) To get 22.5 requires cutting a complementary angle or using a jig.

What saw are you using? All of my saws have a range of 90 degrees to 45 degrees (maybe a little less in some cases) To get 22.5 requires cutting a complementary angle or using a jig.

- posted on July 19, 2005, 6:17 pm

If the table top is accurately cut, then 22.5degrees

John

On Tue, 19 Jul 2005 10:22:14 -0400, snipped-for-privacy@webtv.net (JAKE) wrote:

John

On Tue, 19 Jul 2005 10:22:14 -0400, snipped-for-privacy@webtv.net (JAKE) wrote:

- posted on July 19, 2005, 9:36 pm

snipped-for-privacy@webtv.net (JAKE) wrote in
3134.bay.webtv.net:

As stated, this question cannot be answered, as there are infinitely many possible arrangements of 8 sides which result in a closed surface.

However, assuming that what you really meant was "I want to make an octagonal table top", the answer is 22 1/2 degrees.

John

As stated, this question cannot be answered, as there are infinitely many possible arrangements of 8 sides which result in a closed surface.

However, assuming that what you really meant was "I want to make an octagonal table top", the answer is 22 1/2 degrees.

John

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