Chapter+9+-+Conics

=History of Conics= Conic sections are among the oldest curves, and is one of the oldest math subject studied systematically and thoroughly. The conics seems to have been discovered by Menaechmus (a Greek, c.375-325 BC), tutor to Alexander the Great. They were conceived in an attempt to solve the three famous construction problems of **trisecting the angle, doubling the cube, and squaring the circle.** (These problems lingered until early 19th century when it was shown that it's impossible to solve them with the help of only a straightedge and a compass.) The conics were first defined as the intersection of: a right circular cone of varying vertex angle; a plane perpendicular to an element of the cone. Appollonius (c. 262-190 BC) consolidated and extended previous results of conics into a monograph Conic Sections, consisting of eight books with 487 propositions. Appollonius was the first to base the theory of all three conics on sections of one circular cone, right or oblique. He is also the one to give the name ellipse, parabola, and hyperbola. In Renaissance, Kepler's law of planetary motion, Descarte and Fermat's coordinate geometry, and the beginning of projective geometry started by Desargues, La Hire, Pascal pushed conics to a high level. = = =You Tube Videos= Sonic Boom