What is Geometry For?

Date: 03/01/2002 at 12:23:20
From: Sum1
Subject: Math

What is geometry really for?

Date: 03/01/2002 at 12:53:43
From: Doctor Ian
Subject: Re: Math

Hi,

Geometry is the study of shape. So any time you need to decide what 
shape something should have (like a car, or an MP3 player), that 
involves geometry.  

Materials - like water, or steel, or hair, or proteins, or different 
kinds of rocks - are made of atoms, and different materials have 
different properties largely because of the way their atoms are 
arranged - in other words, the shapes that the atoms form, their 
distances from each other, the angles at which they connect, and so 
on. That involves geometry. 

When you get right down to it, it's hard to think of things that 
_don't_ involve geometry, at least at some level. The famous scientist 
Kepler, who figured out that the planets travel in ellipses around the 
sun, once said that "Where there is matter, there is geometry." He was 
right.

Of course, like all of mathematics, geometry is also a kind of game 
played by mathematicians, as I've described here:

   What is Mathematics?
   http://mathforum.org/dr.math/problems/erum.09.22.00.html   

Another famous scientist, Michael Faraday, was cornered by a woman who 
had just attended one of his lectures on electric and magnetic fields, 
which were just beginning to be understood. She asked him: What is the 
_use_ of these theories about fields? He replied: Madam, what is the 
use of a newborn baby?

Of course, now it's hard to go 5 minutes without taking advantage of 
the products that have been developed as a result of Faraday's 
investigations!  

But when asking what any branch of knowledge is _for_, it's important 
to keep in mind that there is a difference between wanting to _know_, 
and wanting to _do_. A lot of the things that we're now able to _do_, 
we can do only because at some time, someone investigated something - 
which probably seemed pointless to everyone around him - simply 
because he wanted to _know_ about it. 

I hope this helps.  Write back if you'd like to talk more about this, 
or anything else. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/