A quick note: If you just want a curve which is in the shape of dfyb's rope picture, you'll get it using hyperbolic functions (which are somehow similar or analogious to trigonometric functions.) Don't ask me how, cause I heard this from my math teacher in hi school, and he didn't tell me anything more about hyperbolic functions. If some math guru knows more about using them, I'll be interested to hear and learn :D
edit:
Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the equilateral hyperbola. Hyperbolic functions are also useful because they occur in the solutions of some important linear differential equations, notably that defining the shape of a hanging cable, the catenary, and Laplace's equation (in Cartesian coordinates), which is important in many areas of physics including electromagnetic theory, heat transfer, fluid dynamics, and special relativity.