Hyperbolic functions

I've been working on it for past three days, so I'll let you feel some of the beauty as well ;-) But it's more or less finished by now, else I'd turn crazy of it. Now I can start doing the Physics project for SOČ. *laughing crazily*
Hyperbolic functions are to hyperbola the same what trigonometric functions are to circle. Also, as hyperbolic functions are composed of exponentials, one may connect them to the trigonometric ones through Euler's formula. Therefore, a lot of relations between trigonometric functions are similar for the hyperbolic ones. Actually, most of the seminar work of mine (that I've been working on) is about proving the relations (including derivatives); no matter it was proved many times before :-)
Back to the beauty (I may consider the counting itself very appealing, yet I fear some of the readers do not).
Hyperbolic cosine is "is the shape of a hanging flexible chain or cable when supported at its ends and acted upon by a uniform gravitational force (its own weight)." Not hyperbola, as one may think. The curve is therefore also called "catenary". It has some more interesting properties as well.
With some more playing with the functions, one can obtain the plot of Poinsot's spirals.
Cute, isn't it? ;-)