Results 1 to 12 of 12
Like Tree5Thanks
  • 2 Post By chiro
  • 1 Post By Hartlw
  • 1 Post By chiro
  • 1 Post By chiro

Math Help - Parameterization of a curve.

  1. #1
    Junior Member
    Joined
    Jan 2013
    From
    australia
    Posts
    39

    Parameterization of a curve.

    Hi all,

    I have the following problem for homework:

    A curve is represented by the two equations. Parameterize this curve such that your parameter increases from (0, 0, 0) to (1, 1, 1). What is your parameter value for the point (−1, 1, −1)?

    How do I start this question?

    I tried to make x the subject of both and solved for y.





    then made z=t and substituted in getting:


    Is this at correct? if not how do I solve such a question?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,694
    Thanks
    618

    Re: Parameterization of a curve.

    Hey mcleja.

    If you parameterize using t, then the function is (t,t^2,t^3) for x,y,z respectively. If you are using some extra constant to give a specific parameterization to get a particular vector when t = 1, then you need to account for this. (In your case, you don't need to change anything).

    What you have is spot on.
    Thanks from topsquark and mcleja
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Aug 2010
    Posts
    961
    Thanks
    98

    Re: Parameterization of a curve.

    Isn't it already parameterized with parameter x?
    When x=-1, y=1 and z=-1
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,780
    Thanks
    1521

    Re: Parameterization of a curve.

    Quote Originally Posted by mcleja View Post
    Hi all,

    I have the following problem for homework:

    A curve is represented by the two equations. Parameterize this curve such that your parameter increases from (0, 0, 0) to (1, 1, 1).
    Go back and reread the problem. What you have written makes no sense. The parameter is a number and so cannot "increase from (0, 0, 0) to (1, 1, 1). I suspect they are asking you to find a parameterisation so that when the parameter is 0, the point is (0, 0, 0) and when the parameter is 1, the point is (1, 1, 1).

    What is your parameter value for the point (−1, 1, −1)?

    How do I start this question?

    I tried to make x the subject of both and solved for y.


    Yes, what you give is a good parameterisation. Personally, seeing that y and z are given as functions of x, I would have used x itself as parameter: x= t, y= t^2, z= t^3.


    then made z=t and substituted in getting:


    Is this at correct? if not how do I solve such a question?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Banned
    Joined
    Aug 2010
    Posts
    961
    Thanks
    98

    Re: Parameterization of a curve.

    Quote Originally Posted by HallsofIvy View Post
    Go back and reread the problem. What you have written makes no sense. The parameter is a number and so cannot "increase from (0, 0, 0) to (1, 1, 1). I suspect they are asking you to find a parameterisation so that when the parameter is 0, the point is (0, 0, 0) and when the parameter is 1, the point is (1, 1, 1).
    That's what post #3 says.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jan 2013
    From
    australia
    Posts
    39

    Re: Parameterization of a curve.

    The question states "Come up with your own parametrisation for this curve, such that your parameter increases as you proceed from the point (0, 0, 0) to (1, 1, 1). What is your parameter value for the point (−1, 1, −1)?"

    Have I done the question correctly?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Banned
    Joined
    Aug 2010
    Posts
    961
    Thanks
    98

    Re: Parameterization of a curve.

    Quote Originally Posted by mcleja View Post
    The question states "Come up with your own parametrisation for this curve, such that your parameter increases as you proceed from the point (0, 0, 0) to (1, 1, 1). What is your parameter value for the point (−1, 1, −1)?"

    Have I done the question correctly?

    Thanks.
    Yes. You can make either x, y or z the parameter. x is easiest because it is already done. Setting the one you choose equal to t is unnecessary- it's just renaming the parameter. It changes the variables x,y,z to x,y,t.
    Thanks from mcleja
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Jan 2013
    From
    australia
    Posts
    39

    Re: Parameterization of a curve.

    So if i parameterise in x i get (x,x^2,x^3). Is this correct? I dont understand what the question means by "What is your parameter value for the point (−1, 1, −1)?"? Does it mean substitute -1 for x?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,694
    Thanks
    618

    Re: Parameterization of a curve.

    Basically it means you need to solve for the particular value of your parameter.

    In my post I used t and in your post above you used x. Basically its asking you that given a point, you give the corresponding value of t (or x).
    Thanks from mcleja
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Jan 2013
    From
    australia
    Posts
    39

    Re: Parameterization of a curve.

    Would the value of the parameter x be -1? giving (-1,-1^2,-1^3)=(-1,1,-1)?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,694
    Thanks
    618

    Re: Parameterization of a curve.

    Yes that is correct.
    Thanks from mcleja
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Junior Member
    Joined
    Jan 2013
    From
    australia
    Posts
    39

    Re: Parameterization of a curve.

    OK.

    Thanks everyone!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. help with parameterization
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 13th 2013, 01:59 PM
  2. Curve Parameterization to Position Along Curve
    Posted in the Calculus Forum
    Replies: 0
    Last Post: August 17th 2011, 03:38 PM
  3. Parameterization
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 22nd 2010, 09:02 AM
  4. One-to-one parameterization
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: October 27th 2009, 03:57 AM
  5. parameterization of a curve
    Posted in the Calculus Forum
    Replies: 14
    Last Post: February 8th 2009, 06:25 PM

Search Tags


/mathhelpforum @mathhelpforum