In 1697, David Gregory wrote a comprehensive treatise on this shape, and a challenge in Acta Erudito
In 1697, David Gregory wrote a comprehensive treatise on this shape, and a challenge in Acta Eruditorum to find its equation prompted solutions from Huygens (HOY-gunz), Leibniz, and Johann Bernoulli. Euler (OY-lur) proved that this shape produces the surface of revolution with minimum area, while a road pitted with a continuous series of these curves will allow a square wheel to roll smoothly. This curve is traced by the focus of a parabola as it rolls along a straight line, and it is asymptotic to graphs of both exponential growth and exponential decay. Because it eliminates shear forces at joints and causes weight to be directed down into the ground rather than at an angle, Robert Hooke determined that this is the optimal shape of an arch. Having general equation y equals a times the hyperbolic cosine of the quantity x over a, name this curve that results when a cable or chain hangs under its own weight.
In 1697, David Gregory wrote a comprehensive treatise on this shape, and a challenge in Acta Eruditorum to find its equation prompted solutions from Huygens (HOY-gunz), Leibniz, and Johann Bernoulli.