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Mathematical name of time dilation curve

Tags: curve, dilation, mathematical, time
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Aug16-14, 07:29 PM
P: 39
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]
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Simon Bridge
Aug17-14, 12:02 AM
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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... $$P_n(x)P_m(y)=\text{const.}$$

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