Mathematical name of time dilation curve

  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. Simon Bridge

    Simon Bridge 15,474
    Science Advisor
    Homework Helper
    Gold Member

    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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