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Topic: Hyperbolas in Nature
Replies: 29   Last Post: Mar 24, 2010 6:05 AM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: Hyperbolas in nature
Posted: May 3, 1996 10:58 AM
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On 3 May 1996, Erica Morse wrote:

> I am learning to be a teacher at the University of
> Tasmania(Australia)and am doing an assignment on the hyperbola. I
> have already used some of the articles that appear in your newsgroup
> previously.
> However I need some examples of the hyperbola in nature and there did
> not appear to be any here. I have also looked in other places but to
> no avail. Is there anyone that could give me some examples
> please!!!!!

I take it you know about the shadow of a lampshade on the wall?

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

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