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/