Given the fact that we could derive trigonometric functions from a unit circle and on the other hand hyperbolic functions from the unit hyperbola. Could we derive similar functions from example the unit parabola or the unit ellipse or any given shape? and if the answer yes why haven't we done that for every known shape and why only for those 2 shapes?
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An interesting question, but I feel like the answer is probably bland and uninspiring - I imagine it probably has been tried before, and the results either too hard to derive or utilize for some reason, or just not very useful (unlike the circle/hyperbola case). I would be pleasantly surprised to hear otherwise though! – PrincessEev Apr 08 '19 at 23:59