History of Conic Sections

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Ancient Greeks knew about conics early on. Menaechmus discovered conic sections in about 350 B.C. while struggling to solve the difficult problem of "doubling the cube." He noticed that slicing a cone with a plane not parallel to its base would create curves depending on what angle the plane passes through the cone. Apollonius, a Greek mathematician, wrote an 8 chapter book on conic sections. He showed that the plane did not have to be intersecting the cone to be perpendicular with it. It could instead be an oblique or scalene cone and not just a right cone. He also illustrated that all three conic sections could be shown on the same cone. As a result from his knowledge, he solved the problem of finding the shortest and longest distances between one point and a conic. Many other Greek mathematicians studied conics, including Euclid and Pappus, but unfortunately, conic sections were basically ignored until the sixteenth century. Johannes Kepler discovered that the orbit of Mars made an ellipse with the sun as one of its foci. He soon found out this was the same with all planets and called it Kepler's First Law of Planetary Motion. Kepler also came up with the terms focus and directrix. Ancient Greek and Eqyptian architecture has many conics formed into their buildings. Several temples and other religious buildings contain conics to help support the buildings. These conics can be found on the columns of buildings or numerous other places. Conics can be found in modern architecture as well. Bridges and buildings use conics as support systems. The St. Louis Gateway Arch is an example of a parabola and a Farris wheel represents a circle. The Eiffel Tower was built in the form of a parabola in order to support the wind and make it more stable. Also, roller coasters are parabolic because when falling from the top of a parabola, air resistance is

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