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George E. Cawthon wrote:

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".

"J. Clarke" wrote:

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.

Seems to me that's what I said. Oh, well, thus it is written.

Bill.

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.

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- posted on August 1, 2004, 1:52 am

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".

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- posted on August 1, 2004, 5:54 am

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.

- posted on August 1, 2004, 7:53 am

George E. Cawthon wrote:

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.

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.

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- posted on August 1, 2004, 11:42 pm

"J. Clarke" wrote:

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?

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?

- posted on August 2, 2004, 9:34 pm

http://mathworld.wolfram.com/StraightAngle.html

Enjoy.

Enjoy.

- posted on August 3, 2004, 12:24 am

Seems to me that's what I said. Oh, well, thus it is written.

Bill.

- posted on July 31, 2004, 11:35 pm

"J. Clarke" wrote:

I forgot to add that a straight edge theoretically doesn't move and is continous. Thus a single line.

I forgot to add that a straight edge theoretically doesn't move and is continous. Thus a single line.

- posted on July 31, 2004, 6:28 am

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?

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?

- posted on July 31, 2004, 11:44 pm

Elwood Dowd wrote:

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.

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.

- posted on July 31, 2004, 12:55 pm

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
180 degrees.

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". :-)

Bill.

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

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". :-)

Bill.

- posted on July 31, 2004, 6:23 pm

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.

- posted on July 31, 2004, 11:54 pm

Bill Rogers wrote:

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.?

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.?

- posted on August 1, 2004, 2:32 am

On Sat, 31 Jul 2004 23:54:51 GMT, "George E. Cawthon"

"We" call it an adjustable bevel, and it can copy any angle ...including 180.

Bill.

"We" call it an adjustable bevel, and it can copy any angle ...including 180.

Bill.

- posted on August 1, 2004, 6:01 am

Bill Rogers wrote:

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.

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.

- posted on August 1, 2004, 7:54 am

George E. Cawthon wrote:

You went to high school in the US didn't you?

You went to high school in the US didn't you?

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- posted on August 1, 2004, 11:43 pm

"J. Clarke" wrote:

Your point?

Your point?

- posted on August 2, 2004, 2:07 am

George E. Cawthon wrote:

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.

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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- posted on August 2, 2004, 7:04 am

"J. Clarke" wrote:

Interesting. Lots of poor education practices exist in all sorts of places, often characterized by rote memorization and lack of actual thought.

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.

Interesting. Lots of poor education practices exist in all sorts of places, often characterized by rote memorization and lack of actual thought.

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.

- posted on August 2, 2004, 12:27 pm

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?

Bill.

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?

Bill.

- posted on August 2, 2004, 8:35 pm

Bill Rogers wrote:

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.

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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