Catenary

Do you know " Catenary" ?

This is the catenary equation. cosh is the hyperbolic cosine function. Catenary means chains or electric cords. In fact, that is the equation which indecates a dip of a cord and used when catenary arches are built because catenary forms are very stable. Is it coincidence or necessity ? I don't know.

L = 2Csinh(S/2C)

D = C(cosh(S/2C) - 1)

catenary number, C = T/W

For example, when a electric cord is built, in this case, catenary formularized in this way. (L is the length of the electric cord. sinh is hyperbolic sine function. S is the span. D is the dip. T is the tension of a horizontal component. W is the whight per 1 meter.) It is very mysterious and interesting, isn't it? Math is closely connected with nature.