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
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.
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 *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
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!!
On Tue, 19 Jul 2005 10:22:14 -0400, email@example.com (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
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., ... :)
firstname.lastname@example.org (JAKE) wrote in
As stated, this question cannot be answered, as there are infinitely
many possible arrangements of 8 sides which result in a closed
However, assuming that what you really meant was "I want to make
an octagonal table top", the answer is 22 1/2 degrees.
HomeOwnersHub.com is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here.
All logos and trade names are the property of their respective owners.