Uses of Conics
Date: 05/09/99 at 22:15:21 From: Jim Martin Subject: The uses of conics What are some real life examples of conics?
Date: 05/10/99 at 08:24:55 From: Doctor Jaime Subject: Re: The uses of conics Hello Jim There are many applications for the conic sections parabola, hyperbola and ellipse. Some answers in our archives deal with this: Who works with Ellipses? http://mathforum.org/dr.math/problems/fu12.3.96.html Practical Uses for Computing Parabolas http://mathforum.org/dr.math/problems/indon1.30.96.html Here are some other examples from a recent discussion from the geometry-pre-college list: Hyperbolas in nature http://mathforum.org/kb/message.jspa?messageID=1075958 "If you shine a flashlight against a wall with the axis of the flashlight parallel to the wall, the light will make a hyperbola. "You can generate a hyperbola if you investigate Boyle's Law: PV = constant. "The shock wave generated by the wing of a supersonic plane is well- approximated by a hyperbola. I expect the wake generated by a boat with a not-too-pointed prow is an even better approximation. "[Remember that as soon as you get far enough away from its center, a hyperbola rapidly becomes almost indistinguishable from a pair of straight lines.] "If you charge a thin plane strip of conducting material, then the equipotential surfaces are elliptic cylinders (the focal lines being the edges of the strip), and the lines of force (which are orthogonal to them) will be hyperbolas (with foci on those edges. So a small particle that's attracted or repelled by the strip (according to the sign of its own charge) will travel in a hyperbolic path. "You could do much the same with magnetism instead of electricity. Diffraction of light around a sharp edge also involves hyperbolic curves. (Light only travels in straight lines when looked at on macroscopic scales - for diffraction in this experiment they are really hyperbolas whose curvature is only noticeable at lengths comparable with the wavelength.) "I think it's worth while to point out that the graph of y = 1/x is a hyperbola, and that this crops up in many physical applications." - John Conway Most - if not all - astronomical objects in high-energy (i.e. unbounded) orbits about their primaries have hyperbolic orbits. Only those objects with *precisely* enough energy to escape to infinity have parabolic orbits; such objects must be extremely rare. Those with less energy have elliptic orbits; those with more, hyperbolic. Other sites that deal with applications of conic sections are: Newtonian Gravitation and the Laws of Kepler http://csep10.phys.utk.edu/astr161/lect/history/newtonkepler.html Motion, Gravity and Orbits I http://zebu.uoregon.edu/~js/ast121/lectures/lec04.html Feel free to write us back if this is not enough. - Doctor Jaime, The Math Forum http://mathforum.org/dr.math/
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