An interesting quirk of this, is that the description of the path of a particle under constant proper acceleration in special relativity is mathematically very

An interesting quirk of this, is that the description of the path of a particle under constant proper acceleration in special relativity is mathematically very close to that of a simple harmonic oscillator. Now, just as you can use rotation in the complex plane (i^2 = -1) to describe a simple harmonic oscillator in 2D space, x + iy = e^(it) It's possible to use a rotation in the split-complex plane[1] (j^2 = 1) to describe the motion of a particle undergoing constant proper acceleration, x + jt = e^(ajτ)/a - 1 [2] This is because multiplying by e^(jτ) preserves the split-complex modulus (|x+jt|^2 = (x + jt)(x - jt) = x^2 - t^2), which is equivalent to the Minkowski norm. Expanding the above gets you, x = cosh(aτ)/a - 1 t = sinh(aτ)/a which are the more traditional expressions you would typically see. [1]: https://en.wikipedia.org/wiki/Split-complex_number https://en.wikipedia.org/wiki/Split-complex_number [2]: There's a line of reasoning that allows you to write this down almost immediately, or in maths-speak makes it trivial, but I can't remember it at the moment. I spent a good deal of time thinking about this for a university assignment years ago in order to avoid spending 2 minutes doing an integral.