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### Geometry Project

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From: Marilyn S. Heath
Subject: Geometry Project
Date: Tue, 1 Nov 1994 22:27:48 -0500 (EST)

Dear Dr. Math,

I am a ninth grader at the Upper Darby High School.  I have been
assigned a Geometry project and there are no restrictions on ways of
this project?

Project:
Geometry In The Real World

"This project consists of thinking of three examples of geometry in the
real world.  One example must be non man-made (found in nature).  Each
example must have a written explanation of how geometry relates to it.
Each example also must be visually displayed."

Dan Heath
```

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From: Dr. Ethan
Subject: Re: Geometry Project
Date: Wed, 2 Nov 1994 01:17:36 -0500 (EST)

Dan, this is a great problem.  I must say that if I were doing it,
I would try to make them all be natural.  I could give you a huge
list but I think you'd have more fun thinking of a lot of them yourself.
So here are some questions to get you going. The first ones start
easier and then they get harder. At the end I will give you some great
examples that are a little tougher.

What things are shaped like circles? (Think Big)
What are some objects that are symmetrical along a line?
(Bugs, for example)
What are some objects symmetrical around a point?
(Flowers)
What do bees build?
(And on the same shape theme think winter)
Think about the faces of gemstones or quartz.

Now to get a little harder.

There are some interesting relations beween Fibonacci numbers
(0,1,1,2,3,5,8,13,21,34,...), rectangles, and the spiraling of
things like conch shells. To help you see this take a sheet of paper
and in the middle draw a square 1cm by 1cm. Then lengthen one side
to 2 cm and draw the new rectangle. Then lengthen the shorter side
to 3 and draw the new rectangle. Then lengthen the new shorter side
to 5 and draw the new rectangle. Keep drawing the new rectangles on
top of each other and a beautiful spiral should appear.

My last two examples are pretty intense geometrical shapes. The first
is the shape that a rope or chain makes when hung from its end points.
It is called a caternary curve and is a really interesting shape.
The St. Louis arch is also made in this shape. You may want to think
about why this is a good shape to build an arch in. I'm sure that you
some ideas of where to look write back and I'll give you some.

The last shape is one that I am just starting to understand. (In fact
I have to do a presentation on it on Friday.)  The shapes are called
minimal surfaces but you can just think of them as soap bubbles. (Which
by the way have great geometrical properties - spheres when by
themselves, but what do they do when they touch?) Anyway when you put
a shape in soap and a bubble forms on it the soap will connect the
edges in the shortest way possible. When the shape is just a ring
it will of course go straight across.

What would happen if the shape were more interesting?  Try bending
a coat hanger, dipping it into soap, and then seeing how the soap
connects all the edges. It can be pretty fascinating.

Hope this gives you some stuff to think about. Write back if you need
more.

Ethan - Doctor On Call
```
Associated Topics:
Middle School Geometry
Middle School Higher-Dimensional Geometry
Middle School Two-Dimensional Geometry

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