It can be defined as the locus of the mid-point of the vertical line segment between the curves "e to the x" and "e to the negative x."
Leonard Euler discovered that this curve, the evolute of a tractrix, forms the only minimal surface of revolution when it is revolved about its asymptote. It can be defined as the locus of the mid-point of the vertical line segment between the curves "e to the x" and "e to the negative x." With the general equation of "y equals a times the hyperbolic cosine of the quantity x over a," this curve can be generated as the locus of the focus of a parabola rolling along a straight line. FTP, identify this shape that is formed by a chain suspended by its endpoints and only acted on by gravity.
Leonard Euler discovered that this curve, the evolute of a tractrix, forms the only minimal surface of revolution when it is revolved about its asymptote.
catenary