?on miter cut.

[Graham Walters]

PLEASE read the OP

Bob's not asking for the angle in the piece of wood he's just cut

Bob's asking what degree would he need to cut the 2 x 4's. He needs an angle of 36.

Graham

[Chris Melanson]

Go build one then start making some since CHRIS

[Doug Miller]

Which causes the saw to cut at an angle of (90 - 36) = 54 degrees.

Think about it: what do you set your miter gauge at to make a cut at 90 degrees? Unless you have a really unusual miter gauge, you'll set it at zero.

I think the confusion arises from careless use of terminology.

For *any* closed polygon of n sides, the sum of the exterior angles is (n - 2) * 180 and the measurement at each angle of a regular polygon is (n - 2) * 180 / n. To cut a mitered frame in the shape of a regular polygon of n sides, the angles at each end of each piece are (n - 2) * 180 / (2n).

However, to cut a board at the angle p, one must set the miter gauge to (90 - p) because miter gauges measure angle from a line *perpendicular* to the edge of the board being cut. For example, to cut a board square (90 degrees), you set the miter gauge at zero.

So....

To cut a mitered frame in the shape of a regular polygon of n sides, the _miter_gauge_ setting is (90 - p) where p is (n - 2) * 180 / (2n), or 90 - [(n - 2) * 180 / (2n)] simplifying... = 90 - [(180n - 360) / (2n)] = 90 - [(180n / 2n) - (360 / 2n)] = 90 - [90 - 180/n] = 180/n

Thus, to cut a mitered frame in the shape of a regular pentagon (n = 5), the _miter_gauge_ setting is 180/5 = 36 degrees. Which produces a 54-degree angle.

-- Regards, Doug Miller (alphageek-at-milmac-dot-com)

For a copy of my TrollFilter for NewsProxy/Nfilter, send email to autoresponder at filterinfo-at-milmac-dot-com

[Chris Melanson]

Read the OP And then try and build one using 54 I would like to see what yo end up with

CHRIS

[Leon]

The funny thing about this is that you set the saw to 36 degrees. 54 degrees is the measured result. 90 degrees -36 degrees = 54 degrees. You always count the number of cuts you need and divide that number into 360.

[Bruce]

There is no mistake in the drawing Chris.

Yes, if that is the question, then you have to set your saw at 36 degrees to achieve the required 54 degree angle.

I didn't know CAD programs had a bad name? If someone interprets that drawing WRONG and sets the saw to 54, that isn't my fault.

[Graham Walters]

20

[Wood Butcher]

I've never seen so much bickering and misinformation in my life as there is in this thread.

Even Doug who is usually right on target is off a bit on this one. Doug's formula is for the sum of the INTERIOR angles.

The sum of the EXTERIOR angles = 360° for any regular polygon of ANY number of sides. Including triangles and squares. The EXTERIOR angle of said polygon is 360° / n The INTERIOR angle is = 180° - (360° / n)

Art

[Mo' Sawdust]

Chris,

Have you family ties with B.A.D.? Or just blood brothers?

[Wood Butcher]

That's the setting on the miter guage. The angle on the side of the board is 70°.

Art

[CW]

I would suggest you do a little rethinking before you make yourself out to be this ignorant.

3.33333333333333333

[Danny Boy]

He's mixing it up with the exterior angles which always add to 360.

Dan.

[Danny Boy]

You mean the sum of the "interior" angles is (n-2)*180. Otherwise OK. The exterior always all add to 360.

Dan.

[Chris Melanson]

You are the one who has interpreted the information wrong by reading it as 54 when in order to make that cut it is in reality 36 what you would have to set your saw to. And yes CAD programs do have a bad name in the millwork industry and are generally pretty pictures with overall sizes on them . Unless you have somebody with experience in joinery as a draftsperson. You cannot trust CAD drawings in the real world. That is why cabinetmakers do full size layouts most of the time.

CHRIS

[Chris Melanson]

Go and make one before you start calling me ignorant and do a little of your own rethinking as to why when you set your saw to LOL 54 degrees you do not come up with a pentagon. By the way what is your occupation??? I will bet you are not a cabinetmaker.

CHRIS

[Danny Boy]

That is also false.

I'm tired of this, so here's the proof:

For any closed polygon, pick any point in the interior. Draw lines from there to all vertices of the polygon. If you have n sides, you now have n triangles. Add all angles, and you have n*180, the sum in all of the triangles (**). However, that includes all of the angles at the interior point. They add to 360, so subtract that [360 =

2*180] So you sind up with the angles at the vertices, the "interior" angles, adding to (n-2)*180.

Draw lines to continue each side in the same direction each time to look like one of those wheeled firecrackers. The small angles so obtained are what are referred to as the "exterior" angles of a polygon. Now, all of the outside anlges add to each inside angle to produce n lines, or n*180.

So, the exterior angle sum is found by subtracting: (n-2)*180 - n*180 = 2* 180 = 360.

If the polygon is "regular', all sides are the same length and all interior angles are the same measure. So divide by the number of sides = number of angles to get the size of each one.

(**) Proof for the triangle, the basis for all of this, depends on the fact that angles on paralallel lines crossed by a line are the same. It is the start, not the end. The others are built from triangles.

Period.

Dan.

[Graham Walters]

My reply was in context with rest of the thread

[Danny Boy]

OOps! Too much of a hurry. The other away around: n*180 - (n-2)*180 = 2*180 = 360.

Dan.

[Wood Butcher]

Exactly.

[Greg Neill]

I would build a correct pentagon. My pieces would have

54 degree angles as measured between the outside face and the cut face:

-------------------- / \ / \ cut face / \ / \

----------------------------- outside face