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CONIC SECTIONS

CONIC SECTIONS. Presented By: Angela Wood. History of Conics. Appolonius of Perga, great mathematician, was one of the first to study conic sections. He was the first to show all three curves.

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CONIC SECTIONS

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  1. CONIC SECTIONS Presented By: Angela Wood http://mathinscience.info

  2. History of Conics • Appolonius of Perga, great mathematician, was one of the first to study conic sections. • He was the first to show all three curves. • The early Greek astronomers thought that the planets orbited in a circular motion, however, Johannes Kepler was an astronomer who discovered the orbits of the Earth and other planets are other conic sections (i.e. ellipses). • Newton’s analysis showed that the possible orbits are figures known as conic sections. http://mathinscience.info

  3. Gravitational Orbits • Most planets have elliptical orbits. • Venus, however, has such a small orbit that it appears to be circular. • Comets have either elliptical or parabolic orbits. • Comets with parabolic orbits pass the sun once and leave the Solar System. • When two stars pass each other it results in a hyperbolic shape. hyperbola ellipse circle parabola http://mathinscience.info

  4. Conic Sections can be found all around us. • Structures • Mirrors • Satellite Dishes • Orbit Paths • Etc… • Can you think of any more? http://mathinscience.info

  5. What happened when you cut your cone? First resulting shape: Circle Second resulting shape: Ellipse Third resulting shape: Parabola Fourth resulting shape: Hyperbola http://mathinscience.info

  6. How can we define a circle? Circle: a closed plane curve, every point of which is equidistant from a fixed point within the curve According to Webster http://mathinscience.info

  7. How can we define an ellipse? Ellipse:a closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points is a constant : a plane section of a right circular cone that is a closed curve According to Webster http://mathinscience.info

  8. How can we define a parabola? Parabola: a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line According to Webster http://mathinscience.info

  9. How can we define a hyperbola? Hyperbola:a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant According to Webster http://mathinscience.info

  10. References Conic Lesson Plan http://www.exploremath.com/activities Power Point Background Information http://mathworld.wolfram.com/ConicSection.html http://xahlee.org/SpecialPlaneCurves_dir Historical View of Conic Sections http://www.krellinst.org/UCES/archive/resources/conics/node5.html Occurrence of the Conics http://ccins.camosun.bc.ca/~jbritton/jbconics.html Newtonian Gravitation and the Laws of Keplar http://csep10.phys.utk.edu/astr161/lect/history/newtonkeplar.html Drawing the Paths and Planets http://www.galashiels.org.uk Orbits http://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/BrombacherAarnout/OrbitsLesson/orbits_lesson_series.html http://mathinscience.info

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