Concentric circles are parallel?

[phya]

Is a circle phya-parallel to the dot at its center? If so, then can I say the center-dot is parallel to the circumference? Can a dot then also be parallel to an ellipse?

Please note, my words were such say:Circumference is parallel to the center of the circle, so the circle became a circle, because the ellipse is not parallel, so the ellipse as the ellipse.

 

[Mentallic]

I'm done with this thread.

Considering you landed smack bang on the 200^th post, I hope you truly are done with it

I've been able to argue for weeks at a time over the net with others, but those were on controversial topics such as global warming and what-not. This is just getting ridiculous though... I could never see myself reading that entire book which proves 1+1=2, and simultaneously I could never see myself pursuing this discussion any further than I already have.

If you feel like you have just theorized the relativity of mathematics, then by all means take your findings and present them to a professor or something.
Oh and then get back to us on the verdict

 

[phya]

What about two spirals, occupying 3 dimensions? Does phya-parallel include spirals of different wavelengths, of different radius? Are two squares, one within the other, phya-parallel? Then why not two triangles? Why not two houses? Are Russian dolls phya-parallel to each other? Where do I end?

You had not understood that the concentric spherical surface was certainly each other parallel.

 

[phya]

What about two spirals, occupying 3 dimensions? Does phya-parallel include spirals of different wavelengths, of different radius? Are two squares, one within the other, phya-parallel? Then why not two triangles? Why not two houses? Are Russian dolls phya-parallel to each other? Where do I end?

Starts, the red straight line and the blue color straight line is parallel, afterward they became the spiral line, if their distance were invariable, therefore they were each other parallel. This is not the very simple truth?

 

[phya]

That didn't answer the question. Even this many pages into the thread, you still haven't told us what you mean by parallel (what the rest of us call phya-parallel).

I'm done with this thread. If someone is able to formalize a definition for phya-parallel, feel free to message me and I'll check back to see what it is. Until then, have fun!

If a line (straight line either curve) to another line (straight line or curve) the distance maintains invariable, then these two lines (straight line or curve) are parallel.

 

[HallsofIvy]

If a line (straight line either curve) to another line (straight line or curve) the distance maintains invariable, then these two lines (straight line or curve) are parallel.

I suspected that you did not know what a mathematical definition was. What you are giving, over and over again, are "characterizations" or "examples', not definitions. You seem to be saying that two "lines" (which, in your definition can be curves) are parallel if and only if they "maintain" a constant distance. But for that to be a complete definition, You must tell exactly how you are defining the "distance" between two curves- and there are a number of quite different ways of doing that. And, as I said before, depending on exactly how you define that distance, you might find that there are examples of curves that are "parallel" in your definition but also intersect!

 

[phya]

you might find that there are examples of curves that are "parallel" in your definition but also intersect!

Please give an example!

 

[HallsofIvy]

A "conchoid" is a curve that loops back on itself. Another conchoid, just slightly distant from the first, where the "distance" is defined along a mutual perpendicular, will have constant distance yet intersects- the points of intersection on the curves not having a mutual perpendicular so that, even though the curves intersect, the "distance" between them is not 0. As I said, you have to be careful how you define the "distance" between two curves.

 

[phya]

A "conchoid" is a curve that loops back on itself. Another conchoid, just slightly distant from the first, where the "distance" is defined along a mutual perpendicular, will have constant distance yet intersects- the points of intersection on the curves not having a mutual perpendicular so that, even though the curves intersect, the "distance" between them is not 0. As I said, you have to be careful how you define the "distance" between two curves.

You said right, on the exploration path, we must be careful. In the plane, between two curve's distances to be vertical to two curve line segment length.

 

[phya]

A "conchoid" is a curve that loops back on itself. Another conchoid, just slightly distant from the first, where the "distance" is defined along a mutual perpendicular, will have constant distance yet intersects- the points of intersection on the curves not having a mutual perpendicular so that, even though the curves intersect, the "distance" between them is not 0. As I said, you have to be careful how you define the "distance" between two curves.

The attention, is must simultaneously be vertical to two curves.

 

[AC130Nav]

To add concentric circles to our definition of "parallel lines," you would have to prove all the rules for parallel lines apply. One of those rules has to do with parallel lines intersecting other parallel lines (corresponding angles are equal). Can you show me even one that works? (ALL should work if what you say should be accepted.)

 

[phya]

To add concentric circles to our definition of "parallel lines," you would have to prove all the rules for parallel lines apply. One of those rules has to do with parallel lines intersecting other parallel lines (corresponding angles are equal). Can you show me even one that works? (ALL should work if what you say should be accepted.)

The straight line parallel has the phase angle to be equal, generally, the curve parallel does not have the corresponding angle to be equal.