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### Geometric Objects

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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
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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.)

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

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Associated Topics:
Elementary Three-Dimensional Geometry
Elementary Two-Dimensional Geometry

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