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The geometry of hyperbolas is the key to understanding special relativity.
The Lorentz transformations of special relativity are just hyperbolic
rotations, yet this point of view has all but disappeared from the standard
physics textbooks. This approach replaces the ubiquitous $\gamma$ symbol of
most standard treatments by the appropriate hyperbolic trigonometric
functions. In most cases, this simplifies the resulting formulas, while
emphasizing their geometric content.