They have a great deal in common. A space rotation is a is a mixing , while a Lorentz transformation is a mixing . The Lorentz transformation, however, has an apparently much more complicated form. There also appears to be nothing that looks quite like an angle. The apparently complicated nature of the Lorentz transformation arise because we have insisted in writing them in terms of the velocity.
Velocity is sort of the slope of the rotated coordinates.
If we were to write a rotation in terms of the slope of the rotated coordinates then the formulas for a rotation are given by Note the similarity of this expression to the Lorentz transformations. This awkward form for rotations is not very useful, and the standard form for Lorentz transformations is often not useful. Our goal is to make Lorentz transformations look more like rotations. First, we must discuss a little math, namely hyperbolic functions. It is similarly possible to define the hyperbolic functions coth, sech, and csch.