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Applications of Parabolas


Date: 10/24/2000 at 14:57:09
From: Alex Lau
Subject: How parabolas are used in real life.

My question is; how are parabolas used in real life?

I have tried to find this answer through several math sites and books, 
but have not found any satisfactory applications. If you could help me 
on this subject, that would be wonderful. 

Thank you.


Date: 10/24/2000 at 17:09:21
From: Doctor Ian
Subject: Re: How parabolas are used in real life.

Hi Alex, 

Parabolas have some interesting properties. If you put a light at a 
particular point (called the "focus") of a parabolic mirror, particles 
of light start moving away from the light in all directions, but after 
bouncing off the mirror they all move in the same direction, which 
means that you can shine the light on something very far away. This is 
how a headlight on a car works.

This also means that if you have particles of light that are coming 
from very far away, all moving in the same direction - for example, 
coming from a star in the sky - then no matter where those particles 
bounce off of a parabolic mirror, they all end up in the same place - 
at the focus. So you can collect a lot of light from something that 
appears very dim to the eye. This is how a telescope works.

The same principles are used to construct the satellite dishes that 
send and receive television and radio signals.

A microphone at the focus of a parabolic mirror can be used to listen 
to a conversation at a great distance. This is one of the ways that 
sportscasters can listen in on what's being said when the coach pulls 
his players over to the sideline during a time-out.

Basically, whenever you want to transform radial motion (motion to or 
from a central point) into parallel motion or vice versa, a parabolic 
mirror is the tool for the job.

There are certainly all kinds of applications for this kind of 
transformation that haven't even been thought of yet. For example, if 
gravity really is just the exchange of particles (gravitons) that are 
sent out in all directions, then a mirror made from a material that 
would reflect gravitons could be used to channel all the gravitational 
attraction from a lump of mass in a particular direction - which 
would be useful for constructing the kind of "tractor beam" that 
you're always hearing about on Star Trek...

I hope this helps.  

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Basic Algebra
High School Conic Sections/Circles
High School Geometry
High School Practical Geometry

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