Study guide for fourth dimension: take 1 and rubber sheet geometry: take 1

fourth dimension: we're just getting started with this one. What I expect you to be able to answer is:

3. #7 is a pretty good example too.

3. #7: a 4D person can take the rope at any of the crossing points, pull a bit of it into the fourth dimension, pull it around, and put it back so that the crossing is reversed. If I did that to the crossing at the bottom right of the first knot it would then be unknotted. If I did that to the top left and the far right crossing of the middle knot it would be unknotted. If I did that to the top left crossing and the far right crossing of the right knot it would be unknotted.

Here are some answers and more specific questions for dimension 4

Rubber sheet geometry: I'm going to ask about some 1-dimensional rubber things. I will expect you to:

 

Be able to tell what you get when you remove a pair of points from something...next time

6. Show/tell how many pieces you could get if you removed a pair of points from this object:

6. Show/tell how many pieces you could get if you removed a pair of points from this object:

 

 

Here are some more specific sample problems for 1-D rubber sheet geometry