# interference: Hyperbolas transition to ellipses

Hyperbolas have the same equation as ellipses and transition to each other. The only difference is the sign of the second component with y^2, when the denominator becomes negative because t^2 becomes > 1.

**Teaser**

Lorentz transformation invariant has hyperbola equation:

ds^2 = (cdt)^2 - (dx)^2

although I prefer this form:

ds^2 = (cdt)^2 - (vdt)^2 Hyperbolas, rotated by 45 degrees, give us (cdt)*(vdt) = const or dt*dx = const equations. These are actually y = 1/x, no kidding :) And they look like this:

Sorry, I couldn't help myself. Explanation of stretched rectangles that are spanned on rotating axes will come in the future post.

This will probably break the rules :D

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