Asymptotic lines:Differential Geometry

[amjadsuhail]

Find asymptotic lines of the surface Z=X^2+Y^2

please give some definitions and suggestions.

[Mr Skeptic]

Looks like a homework problem... Otherwise you would know you are talking about a circle.

[MrSandman]

Looks more like pothagerean thorem with different letters, however you get twice the product. Maybe he should explain more. Maybe its for trying to find the length of a side that is in creased by 100% from the orginal shape. Any number of possibilities here.

[Bignose]

It's not a circle, nor a Pythagorean theorem, it is a 3-D curve. It is a parabolic "bowl" shaped curve that extends upward. Any slice taken along a constant value of z will be a circle, but the radius of the circle will increase as z increases.

 

Anyway, amj, it does look like a homework problem and as such, the rules of this forum forbid us from giving you direct answers. However, we can give you suggestions, and help point out where you might have made mistakes.

 

Do you know the definition of asymptotic? Basically, it means approaching a value or a curve arbitrarily closely as some sort of limit is taken. See this entry in mathworld: http://mathworld.wolfram.com/Asymptote.html

 

and the others related to it.

[MrSandman]

cool I gotta look that up sometime.

[Country Boy]

It's not a circle, nor a Pythagorean theorem, it is a 3-D curve. It is a parabolic "bowl" shaped curve that extends upward. Any slice taken along a constant value of z will be a circle, but the radius of the circle will increase as z increases.

 

Anyway, amj, it does look like a homework problem and as such, the rules of this forum forbid us from giving you direct answers. However, we can give you suggestions, and help point out where you might have made mistakes.

 

Do you know the definition of asymptotic? Basically, it means approaching a value or a curve arbitrarily closely as some sort of limit is taken. See this entry in mathworld: http://mathworld.wolfram.com/Asymptote.html

 

and the others related to it.

 

You are right that it is not a circle, but it also is not a curve! It is a surface: specifically, a "paraboloid". Frankly, I don't believe it has any asymptotes! The parabola in 2 dimensions doesn't.

[the tree]

HallsofIvy, "3D curve", whilst being sloppy terminology, is at least correct in terms of what he meant to say, no?

 

I'm fairly sure that it doesn't have asymptotes as well.

[Bignose]

Yes, sorry for the sloppy terminology. I also agree that it doesn't have any asymptotes, but since it looked like a homework problem, I didn't want to say that. I wanted the OP to do their own work -- since this really looked like a homework problem.

[the tree]

It'd take a cruel tutor to send the OP on such a wild goose chase, perhaps he misunderstood the assignment?

[Country Boy]

HallsofIvy, "3D curve", whilst being sloppy terminology, is at least correct in terms of what he meant to say, no?

 

I'm fairly sure that it doesn't have asymptotes as well.

No, it's not. A "3D curve" would be a one-dimensional object in three dimensions: a line in space or a spiral, for example. A surface, lke this paraboloid, is a 2-dimensional object.