Geometric Objects

Date: 4/1/96 at 20:58:1
From: Terry Perkins
Subject: geometry assignment

My son's 5th grade math assignment says to name objects in the 
real world that suggest geometric figures including lines and 
planes. The definitions of these two terms indicates infinite 
dimensions. The examples in the text (MacMillan) are the horizon 
for line and the ocean for plane. What are some other real world 
examples? Are we taking the infinite dimensions too literally?  Is 
a desk top a plane?  Even though your answer will not be received 
in time, we are still curious.  Please help.

Date: 4/2/96 at 2:36:53
From: Doctor Jodi
Subject: Re: geometry assignment

Your question is a really good one.  At my college, everyone 
studies Euclid's ELEMENTS - a great, ancient geometry book - in 
the freshman year.  Classes invariably spend at least the first 
class, and sometimes the first WEEK discussing the existence of 
points and lines.

The geometry of mathematics is much different from the "geometry" 
of our experience.  In my opinion, such comparisons must be taken 
with a grain of salt:it is too easy to confuse experience and 
truth.  

For example, would you believe it if I told you that the shortest 
path betwen two objects isn't always a straight line?  Or that 
"straight lines" don't always have to be straight?

Of course, having an IDEA of what we're studying - being able to 
visualize it - is very important.  But if we depend too much upon 
whatwe can see, we may find it difficult to talk about the 
geometry of four or even more dimensions.  (Just for the record, 
visualizing the fourth dimension is a hot topic among research 
mathematicians.)

Thanks for your question.  I wonder what your son's class thinks 
about the similarity and differences between mathematical and 
"real" geometry...

By the way--I'd say that points are one dimensional, lines two- 
dimensional, etc.  I'd also say that they're infinitely small. A 
little bit different from your wording, but I think we mean the 
same thing...

-Doctor Jodi,  The Math Forum