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 system.Bill.
I'm no mathematician, but a line (note A line, meaning one line) doesn't have to have a dimension so of course it can be any length. It needs two points and then it can go off forever. As far as the center of the circle, well the circle is twice as big as the radius but the radius in infinite so the center has to be half of the infinite diameter. Yeah right.
Not infinite at all, not even existent. As I understand it, an angle requires two lines. If you take two lines and place them in same plane and the same direction and they touch at any point, you define a single line by definition. The only thing that has changed is the dimension of the line, but it is A line. If you have a straight edge, it is ideally defined by the two end points, and whatever is in between is just a mechanical holder or a visual aid. If it is a single line, then there is no axes and no angle formed.
You wouldn't, nor could you. The door and the wing-sweep actuator are not lines, they are solid figures and you are considering two solid figures in reference to each other (door-wall) and (actuator-whatever). But if you want to visualize them as lines in a single plane, then when they are at 180 degrees you have two lines that are separated by a space, or if they touch you have a single line.
I forgot to add that a straight edge theoretically doesn't move and is continous. Thus a single line.
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 an angle.
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
11:59 a.m.?
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".
"We" call it an adjustable bevel, and it can copy any angle ...including 180.
Bill.
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.
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 lines.
Oops. What I said still stands, but I just realized you may have misinterpreted my statement about we collectives, which refered to try-tri spelling controversy.
I think this " a straight line is a 180 degree angle" discussion is well past burial time and wasting bandwidth. So enough said.
Except when it is.
And when it is open completely so that it is flat against the wall?
The "straw horse for the sake of argument" is your contention that somehow magically there is a singularity at some point between 179 degrees and 181 degrees in which angles cease to exist.
You went to high school in the US didn't you?
A good point, but wrong, I'm afraid. The bevel is also a tool. You are thinking of a "bevelled edge" being also called a "bevel", and a "bevelled cut". The word "bias" also comes to mind.
I taught math for over thirty years [and it comes in *really* handy in woodworking]. A straight line is not only an angle, but it can be used as the basis for measuring angles:
Pi radians = 180 degrees.
That is used [constantly] to change back and forth between radian and degree measure of angles.
Bill.
I think people could save a *lot* more bandwidth by making the effort to edit text before replying. :-)
However, I agree, especially since some efforts are not really on the mark.
Bill.
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?
Your point?
My dictionary also says bevel is an adjustable tool for drawing angles. But if you go to a tool store and as for a "bevel" the tool many will as "bevel what?" The dictionary also has bevel square which is the more common (maybe the correct) term for an adjustable tool used for drawing angles and adjusting work.
Practical or abstract, geometry or trig? Which of those are you talking about? A line that include the points A and C and also includes B is still just a line even if a-b and b-c are segments. My only point through this whole thing, is that fact. When you rotate a line around a coordinate system, when you get to 180 degrees you have just one line. And when you continue to rotate to 360 (or 0) you just have one line because two lines cannot exist in the same space. Do you want to debate that? Neither do I.
Characteristic of the US education system--nothing means anything unless the student "sees" it. Hence this totally ludicrous discussion of whether 180 degrees is an angle.
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