Math 341
Modern Geometry
Informal Assignment: Viewing Tubes


Most of us at one time or another have used a cardboard or plastic tube as a telescope.  Although the tube does not actually enlarge what we see, it does help us focus on a narrow field of vision.  In this activity, we are going to try to understand and predict how much of a scene is visible through a viewing tube at a distance.  Your group should have been given a viewing tube and a measuring tape.

1.  First, try to identify all the variables that you think might effect how much of a vertical wall is visible through a viewing tube.  These may be properties of what you're looking at (e.g., how far away is it), or properties of the particular tube that you're using.

2.  Next, gather data with your particular tube.  Since you are using one particular tube, some of your variables will be fixed.  See if you can make a conjecture about how your distance from the wall is related to how much of the wall you can see in your field of vision.

3. After you feel that you understand how your initial viewing tube works, try other sizes of viewing tubes and try to see how this changes the patterns that you find.  See what conjectures you can make.  We'd like to be able to predict the field of vision for any viewing tube.

4.  Once you are confident of your conjectures, see if you can find arguments that would convince a reasonable skeptic that your conjectures are correct.

Write up:  Explain what you did, what you found, the conjectures that you made, and whatever evidence you have that they are correct.  You should try to write your explaination so that it would convince one of your peers that your conclusions are correct.