Jan 14, 2015: First Meeting

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For our first meeting, we considered two problems about parameterized curves.

Task 1:

In the diagram below, use \(t\) as a parameter and find a parametric description of the unit circle less the point \( (-1,0)\).

Task 2:

A ribbon of length 10 inches is wrapped around a cylinder of diameter 1 inch. We slowly unwrap the ribbon while keeping it taut.

• a. Where is the end of the ribbon just as it comes free?
• b. What path does the end of ribbon trace as you unwind it?

For Wednesday, January 21:

For next time please do the following:

• Read section 1.1 from Shifrin. This is pages 1-8.
• Read section 1.1 and 1.2 from Struik. This is pages 1-10
• Do Shifrin exercises 1-5 on page 8.

How did I make that image?

I used Sage. This time with the Sage Single Cell Server, which is good for quick work. My code for this plot is:

c = circle((0,0),1)
l1 = line([(1,-1),(1,1)])
l2 = line([(-1,0),(1,2/3)], linestyle="--")
t = text("(1,t)",(1.15,2/3), fontsize=10, color='black')
(c+l1+l2+t).show(figsize=[3,3])