In article ,
"Swingman" writes:
"Jeffrey Thunder" wrote in message
On Fri, 12 Mar 2004 04:51:15 +0000 (UTC), Andrew Barss
wrote:

No you don't. Unless they are at an exact 45 degrees, one will be
longer
than the other.

B.) Many miters have one side longer than the other. Think
rectangular box, trimming the base of a bookcase, etc...

I think you're thinking of perfect squares only.

I won't claim to know what Andrew was/is thinking, but when the
angle isn't 45 degrees, one cut will be longer than the other.
(If this isn't clear, you can draw a simple picture to see
what is meant.) This will most often give a result which few would
argue is a "perfect miter."

The length of the sticks being joined isn't the point of contention,
it's the joint which will look bad.

Yabbut, with the miter jig as described, whereby complementary angles are
used to arrive at a 90 degree joint, the angle discrepancy is generally so
small that it doesn't make a tinker's damm about the length of one side
versus the other.

You don't understand. Yes, the resulting angle when you join
the pieces is indeed 90 degrees. But the joint won't look right.

Here's a simple thing anyone can try. Take two strips of
paper (cheaper than wood for these experiments) of equal width.
Cut one "miter" at an angle larger than 45 degrees (don't
try to get it close to 45 degrees) on one of the strips and
cut a complementary "miter" on the other strip. Join them
together. Sure enough, they form a 90 degree angle. But
where they join looks terrible. One cut is longer than
the other. You can either have the outside corners meet
or the inside, but not both.

Another way to do it is to take a sheet of paper and make a
cut at one corner. Now cut equal width strips from the
adjoining sides.

IOW, anyone who has ever used a properly made jig of this type will testify
that there is nothing wrong with the appearance of the resulting miter
joint.

If the jig is not set very close to 45 degrees, the appearance
of the resulting miter most definitely looks bad. That
is what is wrong with Barry's contention in his post (essentially
that as long as one cuts at complementary angles,
the result is "perfect miters").

--
Jeff Thunder
Dept. of Mathematical Sciences
Northern Illinois Univ.
jthunder at math dot niu dot edu