If I hang a rope from two points that are at the same height above the ground, what is the mathematical function that describes the shape of the rope between the two points? Assuming the mass of the rope is evenly distributed between the two points.
Upon visual inspection, it appears to be parabolic, but looks can be deceiving. I want to be able to calculate how much rope I'll need to span the distance, assuming that I want it to sag by a given amount. If I know the function of the rope's shape, I think I can use an integral to calculate the length of the curve.