Results 1 to 3 of 3

Math Help - Parametric surfaces

  1. #1
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641

    Parametric surfaces

    My book skipped this section, but I think it is important, and I am having difficulty finding resources online. So if this is incorrect bare with me.

    Say we have a curve defined by

    z^2=x^2+y^2

    Now we want to parametrize this, but we do not want z's parameter to be dependent on x and y's. So is this how you would paremetrize it?

    Let z=v

    and x=v\cos(t)

    and y=v\sin(t)

    I chose this because

    x^2+y^2=v^2\cos^2(t)+v^2\sin^2(t)=v^2=z^2

    Is this correct?

    And secondly how do we integrate restrictions into this, for example

    z=x^2+y^2

    I believe that what I would do is let

    z=v

    and

    x=\sqrt{v}\cos(t)

    and

    y=\sqrt{v}\sin(t)

    So we would get

    x^2+y^2=v\cos^2(t)+v\sin^2(t)=v=z


    But what if the quetion also stated that it is the portion of this curve below z=4?

    If someone could tell me if I am doing this right, and then maybe give me a hint for how to do the last part, that would be great.

    Thanks in advance,
    Mathstud
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Quote Originally Posted by Mathstud28 View Post
    My book skipped this section, but I think it is important, and I am having difficulty finding resources online. So if this is incorrect bare with me.

    Say we have a curve defined by

    z^2=x^2+y^2

    Now we want to parametrize this, but we do not want z's parameter to be dependent on x and y's. So is this how you would paremetrize it?

    Let z=v

    and x=v\cos(t)

    and y=v\sin(t)

    ...
    Uuuh... If you define z=v and x=v... and y=v... wouldn't z be dependent on x & y ?


    This would help ya, depending on what exactly you're looking for : Cylindrical coordinate system - Wikipedia, the free encyclopedia

    x=r \cos(t)

    y=r \sin(t)

    z=z

    huh ? This is weird, the English version of Wiki isn't the same as the French one... Coordonnées cylindriques - Wikipédia (French)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by Moo View Post
    Hello,



    Uuuh... If you define z=v and x=v... and y=v... wouldn't z be dependent on x & y ?


    This would help ya, depending on what exactly you're looking for : Cylindrical coordinate system - Wikipedia, the free encyclopedia

    x=r \cos(t)

    y=r \sin(t)

    z=z

    huh ? This is weird, the English version of Wiki isn't the same as the French one... Coordonnées cylindriques - Wikipédia (French)
    Yeah, its hard to find on the internet, but kind of what I was saying is if we have that


    x=x(t)
    y=y(t)
    and
    z=z(t)

    We would not be describing the whole surface, to describe any point on the surface we must let the last part be any real number, therefore it would be delegated its own parameter.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Parametric Surfaces
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 21st 2010, 04:37 PM
  2. Surfaces
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 28th 2010, 12:31 PM
  3. surfaces
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 6th 2010, 12:24 PM
  4. Calculus 3--parametric surfaces/surface area
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 18th 2009, 06:11 AM
  5. Surfaces
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 2nd 2007, 06:34 AM

Search Tags


/mathhelpforum @mathhelpforum