Fine. So when the wings are at 179.999 degrees then they are at an angle
but when they extend .001 degree more then their position becomes undefined
because 180 degrees is not an angle.
As for their being "solid figures", the most complex technologies usually
exist as lines on flat paper before they exist as "solid figures".
Reply to jclarke at ae tee tee global dot net
Yep at 179.999 its an angle, but 179.999 degrees to what? 180 degrees
doesn't mean undefined, it means a continous line. I thing swing
wings angles are measured not against the other wing but from a line
at right angles to the body, so 180 degrees isn't possible. That is,
when the wings are straight out you would call it 90 degrees to the
body, or a swing of 0 degrees (from straight out). More than likely a
60 degree fold means the wings tips are closer to the tail than at 30
degrees; in other words, 180 degrees is never used.
By solid figures what I meant was that a door and a frame are
continuous at only two or three points (the hinges) and there is no
need to have the hinges in a straight line with the door and the
casing when the door is closed. So, except at the point of contact
(hinges) between the door and the casing when the door is closed, the
door and the casing exist as two lines. Although there are two lines,
there still does not have to be an angle. This is the same as the
swing wing, when the door is slightly open it will be open 3-4
degrees not 176-177 degrees. So when it is closed the angle is 0
degrees and 0 means none, not some, i.e., there is no angle.
When you measure swing of something you normally give the acute angle
and not the obtuse, i.e., no swing is 0 degrees not 180 degrees, and
your use of 180 degrees in these situation is neither natural nor
common practice and is entirely a straw horse constructed for the sake
of argument. OTOH the outline of a solid body that doesn't change
shape, but is complex could be measured in various ways.
Then the lines are parallel and there is no angle! You couldn't
figure that out?
It is not magical, it is simply a fact by definition. If you want to
change the language of map ok, but call it Clarke's math. Your
arguement also applies to O, so you are saying when the "angle" is 0
degrees that an angle doesnt doesn't cease to exist? What the hell
does 0 mean then?
Okay, okay... dig back into 2nd semester college trig....
18 inches. I made that arbitrary point up.
The axis point is arbitrary if you think of a 180 degree angle as a
straight line (which it is for practical purposes). In the mathematical
realm, however, the axis point is where the two sides of an angle meet.
In this case it is wherever you put it along that line---a quality
which is unique to 180-degree angles. Do I win a prize?
Nope, no prize. You defined the problem -- two sides, or another way
of saying to lines get an angle. But there is only one line. It axis
isn't arbitrary, because there is no axis point. As other you can go
off on a tangent of infinite pieces and get to calculus but that adds
nothing to the concept of a line and that a single line can not form
On Sat, 31 Jul 2004 05:00:01 GMT, "George E. Cawthon"
Reverse the argument. Take two arms, and swing one around, measurig
the increasing angle. Do you stop measuring when they line up? Any
measure prior to that is less than 180 degrees, and any measure past
that is greater than 180 degrees. So, the measure of that *must* be
It's like an argument about zero:
What's 5 - 3 ........Ans: 2
What's 5 - 2 ........Ans: 3.
What's 5 - 5 ........Ans: "I dunno."
If there is no agreement for 180 then there could be more argument
about zero, with such nonsense as "You can't measure what doesn't
exist." Besides, we are not going to solve the problems of
mathematics in this conference. There's little enough here about
woodworking, so let's stick to something we know, like the difference
between a "tri square' and a "try square". :-)
P.P.S. 0/0 is "indeterminate" = "undefined". Something is well
defined, or not. "indeterminate" means not "well defined". That is;
if you can not determine it exactly, it can not be well defined, and
so is undefined.
1/0 = "not finite"; that is, not part of the finite arithmetic number
I've already answered that in other responses, but just to be caustic
why would you have a pivot in a straight edge, and if you did, it
would be a straight edge would it? it would be an angle finder.
Ah but "we" collectively, apparently, don't know that.
Woodworkers like to eat lunch, so what time is it one minute after
I thought "bevel" described a shape not the tool. There is no need to
copy 180 degrees, since it is just a straight line. Beside if the
line describes what you call 180 degrees, then it is just a single
line and a single line cannot define an angle. You have to have two
Interesting. Lots of poor education practices exist in all sorts of
places, often characterized by rote memorization and lack of actual
I think you misinterpreted what I said, or I didn't explain clearly.
180 degrees is certainly useful in rotating something on an axis or on
a coordinate system. But my point is that when a line is fixed on an
axis and a second line is rotated on the same axis to 180 degree from
the fixed line, the rotated line is no longer at an angle to the
original because the original and the rotated line form a single line
with the length equal to the sum of the rotated and nonrotated lines
and when the rotated line reaches 360 degrees a single line is formed
with the dimension of the longest line. The latter, is true because
two lines cannot occupy the same space. In the abstract, lines have
no width and are continuous (no breaks). In the practical, lines do
have widths and breaks (spaces between molecules). Whether in the
abstract or in practical carpentry, a straight line or a straight edge
is not considered as having breaks, is therefore a single line, and
discussion of an angle of 180 degrees or any angle has no meaning.
On Mon, 02 Aug 2004 07:04:00 GMT, "George E. Cawthon"
The measure of angle has nothing to do with the measure of length,
except as inferred by ratio in trig relations. Your use of "a second
line is rotated on the same axis to 180 degree from the fixed line" is
inconsistent with your " the rotated line is no longer at an angle to
the original" You can't have your cake and eat it. The measure of
that angle is 180 degrees, period. If you rotate it 180 degrees, it
forms a 180 degree angle, even though it becomes collinear with the
stationary line segment. In fact, "collinearity" is the key here.
When you use a try-square to make your jointer table guide at 90, do
you say you can't do it because when it lines up the space between
disappears? Or is it that both angles [the try-square and the
fence-to-table] are now equal, being 90, and so adding to 180?
It's actually called a straight angle, which makes no sense at all. a
180 degree "angle" isn't an angle based on the basic definition of an
angle. The terminology used for 180, 360, and 0 degrees is
ridiculous. The rotated at 180 degrees and non rotated lines become
a single line.
I don't understand what you are saying. Are you talking about the
fence being set up at 90 degrees. If so, when you draw this the
vertical line indicating the fence and the vertical line of the try
square would be a single line. And the horizontal line indicating the
face of the jointer and the horizonal line indicating the horizontal
leg of the try square would be a single line. You still have an
intersection of 90 degrees between the jointer face and the fence as
well as 90 degrees between the legs of the try square. Maybe I
misunderstood you, but I don't see your point. Or are you confusing
lines on a paper and the representation of solid objects in real life.
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