What is the difference between superposition and intersection?

[phya]

The spherical geometry thought that in the surface does not have the parallel line, actually this idea is wrong, should say: In the spherical surface does not have the straight line parallel line, but in the spherical surface has the curve parallel line.

Is very actually good about the curve parallel concept understood. If we acknowledge any thing own and oneself always parallel, then we can not but acknowledge that the curve and the curve are also parallel. For instance a straight line, it own and oneself is parallel. Similarly, a circle, it own and oneself is also parallel. Therefore the curve and the curve are may mutually parallel.

In the spherical surface, the latitude parallel is mutually parallel. Therefore may not remove the parallel postulation in the spherical surface.

What is the parallel essence? The parallel essence is the distance maintains invariable. The curve parallel definition is, if two curve's distances maintain invariable, then these two curves are parallel. In curve parallel, does not intersect was not equal to that is parallel.

 

[HallsofIvy]

The spherical geometry thought that in the surface does not have the parallel line, actually this idea is wrong, should say: In the spherical surface does not have the straight line parallel line, but in the spherical surface has the curve parallel line.

This is incorrect. Spherically geometry defines great circles (circles on the sphere whose center is the center of the sphere) as "straight lines".

Is very actually good about the curve parallel concept understood. If we acknowledge any thing own and oneself always parallel,

If, by this, you mean that an object and itself are always parallel, I have said, in another of your threads, that this NOT true. An object and itself are NEVER paralllel.

then we can not but acknowledge that the curve and the curve are also parallel. For instance a straight line, it own and oneself is parallel. Similarly, a circle, it own and oneself is also parallel. Therefore the curve and the curve are may mutually parallel.

In the spherical surface, the latitude parallel is mutually parallel. Therefore may not remove the parallel postulation in the spherical surface.

Except for the equator a "line of latitude" is not a great circle and so is not a "line" in the sense of spherical geometry.

What is the parallel essence? The parallel essence is the distance maintains invariable. The curve parallel definition is, if two curve's distances maintain invariable, then these two curves are parallel. In curve parallel, does not intersect was not equal to that is parallel.

That is a very bad "essence". As I said, again, in another of your threads on this same subject, it is ONLY in Euclidean geometry that the set of points at a constant distance from a given line (and on one side of it) is a line at all.

Further, depending on exactly how you define "distance" between two sets, it is possible to have "equidistant" sets that intersect one another. Not intersecting seems to me to be much more the "essence" of "parallel" than does "equidistant".

 

[CRGreathouse]

Not intersecting seems to me to be much more the "essence" of "parallel" than does "equidistant".

Exactly.

 

[phya]

Today I did not reply first your question, I ask a question again: If in the spherical surface the great-circle is the straight line, then on the circular conical surface, what is a straight line?

 

[CRGreathouse]

Today I did not reply first your question, I ask a question again: If in the spherical surface the great-circle is the straight line, then on the circular conical surface, what is a straight line?

I don't know what you mean by "circular conical surface"; is that "cone"?

It's not obvious that there's a version of neutral geometry that is modeled by the surface of a cone.

 

[phya]

If in the spherical surface the great-circle is the straight line, then on the circular conical surface, what is a straight line?

 

[phya]

I don't know what you mean by "circular conical surface"; is that "cone"?

It's not obvious that there's a version of neutral geometry that is modeled by the surface of a cone.

You as if have not understood my meaning.

 

[CRGreathouse]

You as if have not understood my meaning.

That's what I said -- I don't understand what you mean by "circular conical surface". Care to enlighten?

 

[phya]

That's what I said -- I don't understand what you mean by "circular conical surface". Care to enlighten?

I ask a your question: A straight line own and is parallel?

 

[CRGreathouse]

I ask a your question: A straight line own and is parallel?

What you wrote isn't a valid English sentence, let alone one conveying mathematical content. My guess is that you mean, "Is a line parallel to itself?". If that's the case, then the answer is no.

 

[phya]

What you wrote isn't a valid English sentence, let alone one conveying mathematical content. My guess is that you mean, "Is a line parallel to itself?". If that's the case, then the answer is no.

Sorry, my English is not good. My meaning is: Whether a straight line is parallel to oneself?

 

[phya]

"Is a line parallel to itself?".
Yes, this is my meaning.

 

[phya]

NO？
Why？

 

[phya]

If has moving point a and moving point c, straight line B through a and c, the direction which a and c move is always vertical to B, and a and the c straight line's distance maintains invariable, then a and the c path is a parallel line, regardless of this path is a straight line, or is the curve.

 

[Mentallic]

NO？
Why？

Because it's obvious?

For example, in coordinate geometry when trying to find the intersection of two lines, we need to consider 3 cases and that is if they are parallel (thus no solution) if they are not parallel (thus 1 solution) and if they are the same line (infinite solutions). Just saying the two lines are parallel doesn't distinguish between the two cases.

 

[phya]

Because it's obvious?

For example, in coordinate geometry when trying to find the intersection of two lines, we need to consider 3 cases and that is if they are parallel (thus no solution) if they are not parallel (thus 1 solution) and if they are the same line (infinite solutions). Just saying the two lines are parallel doesn't distinguish between the two cases.

f has moving point a and moving point c, straight line B through a and c, the direction which a and c move is always vertical to B, and a and the c straight line's distance maintains invariable, then a and the c path is a parallel line, regardless of this path is a straight line, or is the curve.
？

 

[phya]

In spherical surface, given a line L and a point p outside L, there exists no line parallel to L passing through p. attention, here line is not a straight line.

 

[Mentallic]

I made a mistake, I actually shouldn't have made a post here.

I'm not getting into this argument again.

 

[phya]

I made a mistake, I actually shouldn't have made a post here.

I'm not getting into this argument again.

Regret

 

[phya]

This is incorrect. Spherically geometry defines great circles (circles on the sphere whose center is the center of the sphere) as "straight lines".


If, by this, you mean that an object and itself are always parallel, I have said, in another of your threads, that this NOT true. An object and itself are NEVER paralllel.


Except for the equator a "line of latitude" is not a great circle and so is not a "line" in the sense of spherical geometry.


That is a very bad "essence". As I said, again, in another of your threads on this same subject, it is ONLY in Euclidean geometry that the set of points at a constant distance from a given line (and on one side of it) is a line at all.

Further, depending on exactly how you define "distance" between two sets, it is possible to have "equidistant" sets that intersect one another. Not intersecting seems to me to be much more the "essence" of "parallel" than does "equidistant".

No, the parallel essence is the distance constant invariable, because the non-concentric circle does not intersect, but their each other is not parallel.

 

[phya]

I made a mistake, I actually shouldn't have made a post here.

I'm not getting into this argument again.

You had not understood. After being similar to Einstein's theory comes out, also many people did not understand.

 

[phya]

Because it's obvious?

For example, in coordinate geometry when trying to find the intersection of two lines, we need to consider 3 cases and that is if they are parallel (thus no solution) if they are not parallel (thus 1 solution) and if they are the same line (infinite solutions). Just saying the two lines are parallel doesn't distinguish between the two cases.

In analytic geometry, we all know, as the slope of the line are parallel, if only a straight line, its slope is only one, so the line is parallel with himself.

 

[HallsofIvy]

No, that is not true. Two distinct lines are parallell if and only if they have the same slope, but a line is NOT parallel to itself. Saying that a line is parallel to itself contradicts the basic definition of "parallel" that they do not have any point in common.

You seem to be insisting on using "equidistant" for parallel in spite of repeated explanations of why the is NOT appropriate.

 

[phya]

No, that is not true. Two distinct lines are parallell if and only if they have the same slope, but a line is NOT parallel to itself. Saying that a line is parallel to itself contradicts the basic definition of "parallel" that they do not have any point in common.

You seem to be insisting on using "equidistant" for parallel in spite of repeated explanations of why the is NOT appropriate.

If has straight line parallel line A and B, in A infinite approaches B in the process, they always parallel, when they superpose in together time, they no longer were parallel? They certainly parallel,

 

[phya]

No, that is not true. Two distinct lines are parallell if and only if they have the same slope, but a line is NOT parallel to itself. Saying that a line is parallel to itself contradicts the basic definition of "parallel" that they do not have any point in common.

You seem to be insisting on using "equidistant" for parallel in spite of repeated explanations of why the is NOT appropriate.

You the understanding have the question to the definition, a body is not the intersection, the part intersection, the part does not intersect is intersects.

 

[Mark44]

You the understanding have the question to the definition, a body is not the intersection, the part intersection, the part does not intersect is intersects.

Does anyone other than me get the impression that the responses by phya are computer-generated? See ELIZA.

 

[G037H3]

I just assumed phya has aspergers and is making assumptions about geometry without studying it seriously.

 

[Upisoft]

I'm expecting new thread entirely dedicated to the sixth and the seventh sides of the triangle. And what happens if they are parallel...

Anyway it looks like computer translated language, but not generated. Computers cannot be so... eh... insistent.

 

[HallsofIvy]

Does anyone other than me get the impression that the responses by phya are computer-generated? See ELIZA.

I get the impression that Phya's native tongue is not English and that he has difficulty constructing an intelligible sentence.

What bothers me more is his insistence that he is right and everyone else is wrong.

 

[CRGreathouse]

I get the impression that Phya's native tongue is not English and that he has difficulty constructing an intelligible sentence.

What bothers me more is his insistence that he is right and everyone else is wrong.

It would be so much easier if we only had to cope with one of those.

 

[phya]

Straight line is circle,Of course, the circle radius is infinite, Therefore, the parallel circle,
So also concentric circles. So the concentric circles is parallel.

 

[CRGreathouse]

Straight line is circle,Of course, the circle radius is infinite, Therefore, the parallel circle,
So also concentric circles. So the concentric circles is parallel.

If you're careful, you can describe a line as a circle with infinite radius (or at least the limit of a circle as its radius expands without bound). But that doesn't mean that you can apply properties of lines to all circles!

That would be like saying that since a square is a kind of rectangle, rectangles have four congruent sides.

 

[phya]

If you're careful, you can describe a line as a circle with infinite radius (or at least the limit of a circle as its radius expands without bound). But that doesn't mean that you can apply properties of lines to all circles!

That would be like saying that since a square is a kind of rectangle, rectangles have four congruent sides.

In analytic geometry, we all know, as the slope of the line are parallel, if only a straight line, its slope is only one, so the line is parallel with himself.

 

[phya]

If you're careful, you can describe a line as a circle with infinite radius (or at least the limit of a circle as its radius expands without bound). But that doesn't mean that you can apply properties of lines to all circles!

That would be like saying that since a square is a kind of rectangle, rectangles have four congruent sides.

If has straight line parallel line A and B, in A infinite approaches B in the process, they always parallel, when they superpose in together time, they no longer were parallel? They certainly parallel, therefore the straight line own and oneself is parallel, the curve is also so.

 

[CRGreathouse]

If has straight line parallel line A and B, in A infinite approaches B in the process, they always parallel, when they superpose in together time, they no longer were parallel? They certainly parallel, therefore the straight line own and oneself is parallel, the curve is also so.

My best guess as to your meaning:

If A and B are parallel lines, and (something about a limit), then A and B are always parallel. Certainly they are always parallel, so a line is always parallel to itself, and thus a curve is also always parallel to itself.​

This isn't clear enough for me to understand. You may need to talk to a math educator (ideally, a high-school math teacher or the equivalent) who speaks your own language. He or she should be able to clear up your misconceptions.

Your reasoning is flawed, but it's hard to point out the exact flaw without a better understanding of what you're actually saying.

 

[CRGreathouse]

In analytic geometry, we all know, as the slope of the line are parallel, if only a straight line, its slope is only one, so the line is parallel with himself.

Your definition is wrong.

 

[phya]

My best guess as to your meaning:

If A and B are parallel lines, and (something about a limit), then A and B are always parallel. Certainly they are always parallel, so a line is always parallel to itself, and thus a curve is also always parallel to itself.​

This isn't clear enough for me to understand. You may need to talk to a math educator (ideally, a high-school math teacher or the equivalent) who speaks your own language. He or she should be able to clear up your misconceptions.

Your reasoning is flawed, but it's hard to point out the exact flaw without a better understanding of what you're actually saying.

You had not understood that my meaning, has a chart in the appendix, in the chart has two mutually parallel straight lines, moves a straight line, in the motion process, maintains two lines parallel, until their overlapping. Therefore, the straight line own and oneself is also parallel. Similarly, the curve own and oneself is also parallel, therefore the curve is also may be each other parallel. This is my meaning.

 

[phya]

Your definition is wrong.

Why？

 

[HallsofIvy]

For exactly the reason you have been told repeatedly- two lines are parallel if and only if they never intersect. Since a line intersects itself everywhere a line is not parallel to itself. As I said before, you should have "two distinct lines have the same slope if and only if they are parallel".

 

[phya]

In the analytic geometry,
Supposition
the straight line L1 equation is y=kx,
the straight line L2 equation is y=kx+c,

then L1∥L2 is parallel,
if reduces c, then still L1∥L2.
When c=0,
L1 and L2 superposition, still L1∥L2,
if L1 and L2 not parallel, then L1 and L2 will not superpose, will intersect.
Therefore the straight line own and oneself is parallel, otherwise the straight line will not be a straight line, will intersect.
The curve is also so, the curve is also own and own parallel, therefore the curve is also may mutually parallel.
Does my this logic have what question?

 

[Mentallic]

When c=0,
L1 and L2 superposition, still L1∥L2,

You didn't even consider hallsofivy's response, you just explained it to us in a different way - which by the way, we already understand what you were trying to say. We didn't need another example to clarify it.

 

[phya]

You didn't even consider hallsofivy's response, you just explained it to us in a different way - which by the way, we already understand what you were trying to say. We didn't need another example to clarify it.

Then you whether to think the straight line own and own parallel?

 

[phya]

You didn't even consider hallsofivy's response, you just explained it to us in a different way - which by the way, we already understand what you were trying to say. We didn't need another example to clarify it.

I have not replied him? No, my new example is replying him.

 

[Mentallic]

No I don't think a line is parallel to itself because as Hallsofivy has said,

Since a line intersects itself everywhere a line is not parallel to itself.

 

[phya]

No I don't think a line is parallel to itself because as Hallsofivy has said,

Hallsofivy？

 

[phya]

No I don't think a line is parallel to itself because as Hallsofivy has said,

Your view definitely is wrong, because of you indecipherable following logic:
When c=0,
L1 and L2 superposition, still L1∥L2,
if L1 and L2 not parallel, then L1 and L2 will not superpose, will intersect.
Therefore the straight line own and oneself is parallel, otherwise the straight line will not be a straight line, will intersect.

 

[Mentallic]

Hallsofivy？

The guy that you replied to just before.

Ok then we're at a disagreement and damned if I'm the one to convince you otherwise.

When c=0,
L1 and L2 superposition, still L1∥L2,
if L1 and L2 not parallel, then L1 and L2 will not superpose, will intersect.
Therefore the straight line own and oneself is parallel, otherwise the straight line will not be a straight line, will intersect.

How can you say "therefore" when your previous line has nothing to do with the dispute. You haven't explained why or how two superimposed lines are still separate. As far as logic tells me, in 2 dimensions, two lines are parallel unless they intersect each other. Not only are two superimposed lines intersecting each other infinite times, they are now just 1 line since they are not distinct. No distinction means there is just one...

 

[phya]

The guy that you replied to just before.

Ok then we're at a disagreement and damned if I'm the one to convince you otherwise.

sorry.

 

[phya]

The guy that you replied to just before.

Ok then we're at a disagreement and damned if I'm the one to convince you otherwise.


How can you say "therefore" when your previous line has nothing to do with the dispute. You haven't explained why or how two superimposed lines are still separate. As far as logic tells me, in 2 dimensions, two lines are parallel unless they intersect each other. Not only are two superimposed lines intersecting each other infinite times, they are now just 1 line since they are not distinct. No distinction means there is just one...

Obvious:
if L1 and L2 not parallel, then L1 and L2 will not superpose, will intersect.
Because does not have not to superpose, has not intersected, Therefore the straight line own and oneself is parallel, otherwise the straight line will not be a straight line, will intersect.

 

[HallsofIvy]

You seem to be saying that a straight line "superposes" on itself rather than "intersecting" and only "intersecting" lines are not parallel. It is your distinction between "superposing" and "intersecting" that is incorrect. "Superposing" is "intersecting". A straight line is not, in the usual definition of the word, "parallel" to itself. It "lies in the same direction" as itself but that is not the same as "parallel".