Assignment 4B (Due Wed 1/29)

4-3 Cylinder Model

Find a right circular cylinder or build one.  On this cylinder, you should draw 3 pairs of points as described below.  In each case draw accurately a straight line between the points.  Also draw one or more additional lines between the points if such lines exist.

• Draw points A and B on an equatorial circle. 
• Draw points C and D on a generating line.
• Draw points E and F in "general position", i.e., neither on an equatorial circle or a generating line.

Note: The model should be constructed with some level of craft and labeled clearly.  However, it can be untaped to be a flat sheet for transportation purposes.

4-4 Cylinder Questions

Write a paragraph or two answering the following questions.

• What is a straight line on a cylinder?  Why is this a reasonable definition?  What do the lines look like?  Are there special cases, and if so, what are they?
• If two points A and B are on an equatorial circle, tell what are the lines through A and B (and why).
• If two points C and D are on a generating line, tell what are the lines through C and D (and why).
• If two points E and F are in "general position", i.e., neither on an equatorial circle or a generating line, tell what are the lines through E and F (and why).

4-5 Cone Model

Make two models of cones, one with a 180 degree cone angle and one with a 90 degree cone angle.  On each cone, you should draw 3 pairs of points as described below.  In each case draw accurately a straight line between the points.  Also draw one or more additional lines between the points if such lines exist.

• Draw points A and B on an equatorial circle. 
• Draw points C and D on a generating line.
• Draw points E and F in "general position", i.e., neither on an equatorial circle or a generating line.
• Also, in each case, draw a straight line that intersects itself, if such is possible.

Note: The model should be constructed with some level of craft and labeled clearly.  However, it can be untaped to be a flat sheet for transportation purposes.

4-6 Cone Questions

Write a paragraph or two answering the following questions.

• What is a straight line on a cone?  Why is this a reasonable definition?  What do the lines look like?  Are there special cases, and if so, what are they?
• If two points A and B are on an equatorial circle, tell what are the lines through A and B (and why).
• If two points C and D are on a generating line, tell what are the lines through C and D (and why).
• If two points E and F are in "general position", i.e., neither on an equatorial circle or a generating line, tell what are the lines through E and F (and why).