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Mathematical name of time dilation curve

  1. Aug 16, 2014 #1
    In mathematics, what is the name (type) for a curve given by velocity and time dilation?

    Specifically, I want to find a name for the curve [itex]y=1/(1-x^2)^{1/2}[/itex]

    This curve is derived from the equation of a unit circle [itex](x-a)^2+(y-b)^2=r^2[/itex]
    where [itex]y=(1-x^2)^{1/2}[/itex]
     
  2. jcsd
  3. Aug 17, 2014 #2

    Simon Bridge

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    It's called a hyperbola. Well - sort of.

    The general equation is: ##(x^2-h)(y^2-k)=m##

    Your relation has ##k=0, h=-1, m=-1##

    This is a rectangular hyperbola in ##(x^2,y^2)##

    You can get much more general than that by just taking the product of two polynomials... $$P_n(x)P_m(y)=\text{const.}$$
     
    Last edited: Aug 17, 2014
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