Blaise Pascal believed that thoughts of this curve cured his toothache, leading him to publish a prize for those who could find the area, volume, and center of gravity of this curve. To create better chronometers, Christiaan Hyguens developed a pendulum whose pivot was placed inside of this curve and whose bob traced out a path that was also this curve. This curve (-5[1])was the result of a proof by Isaac Newton that was recognized "from his claw mark," of an "indirect (10[1])method" (10[1])devised by Johann Bernoulli that relied on (10[1])Fermat's Principle. (10[2])A track in the shape of this curve (10[1])provides the fastest descent for an object (10[1])frictionlessly sliding down it, so this curve is the solution of the brachistochrone problem. For 10 points, name this curve formed by a point on a rolling circle. ■END■ (0[3])