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Math Help - Math function for parabola

  1. #1
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    Math function for parabola

    Hello. I need to find an implicit function that plots a parabolic tube with a circular cross-section of radius 3. Even if you know only the function of the parabola, it would be a great hint.



    Thank you in advance.

    EDIT: well, first post, first wrong forum. I think this should go in the trigonometry forum.
    Last edited by TyTiKi; May 15th 2012 at 10:04 AM.
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  2. #2
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    Re: Math function for parabola

    Quote Originally Posted by TyTiKi View Post
    Hello. I need to find an implicit function that plots a parabolic tube with a circular cross-section of radius 3. Even if you know only the function of the parabola, it would be a great hint.



    Thank you in advance.

    EDIT: well, first post, first wrong forum. I think this should go in the trigonometry forum.
    Let x = t. Then the orange line consists of all points (t, t, 0)

    The length of the orange line segment from (0, 0, 0) to (85, 85, 0) is 85 \cdot \sqrt{2}

    The equation of a parabola with it's vertex at (0, 0, 30) is

    p=a \cdot s^2 + 30

    where s is the unit on the orange line when x and y increases by 1. So s = t \cdot \sqrt{2}

    Determine the value of a if p = 0 at (85, 85, 0).

    I've got a = -\frac3{1445}

    So the equation of the parabola is p:\left\lbrace\begin{array}{l}x = t \\ y = t \\ z = -\frac6{1445}(t )^2+30 \end{array}\right.
    Attached Thumbnails Attached Thumbnails Math function for parabola-parab3d.png  
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  3. #3
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    Re: Math function for parabola

    Thank you very much for your help earboth. However I need an implicit function that I could write in Imp View 3D.



    It would be fantastic if you could help me.
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  4. #4
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    Re: Math function for parabola

    I found a way.

    (0.75-sqrt(y^2+z^2/3))^2+x^2<0.030

    gives me a parabolic tube. Now I need something that rotates it by 45 degrees. Any hint?
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