Final Exam Essay

Well I don't think anyone solved the World's Easiest Hardest Geometry Problem. Therefore, your here either because I refered you here to get your essay question for the Final Exam

Note that this essay will be written at home and turned in on Thursday at school. When you show up to take your final exam you will work on a surface area/volume problem for the two hour period.

Your Essay:
Part I
1.) Read pg's 233-237.
2.) In your words describe what Fermat's Discovery is proposing.

Part II
1.) What is a tangent line and describe its development by having secant lines from point M and M' become infinitely close; that is, don't allow M to move and then have M' become closer and closer to M as illustrated in the book's drawing on pg 235.
2.) From 1 above, describe what would be taking place to the slopes of the secant lines from M to M' if M is not allowed to move and M' approaches M.
3.) Finally, explain what slopes from 1 2 above have anything to do with the slope of the tangent line?

Part III
1.) Finally, explain how the approximated surface area of the curve on page 236 is related to the Watje-Kowal Cranium Cracker we did in class.
2.) Instead of using cylindrical shells, draw a 3-dimensional view of a "narrow band", in this case a "narrow shell", that would better approximate the surface area of the spherical cap- i.e. the Watje-Kowal Cranium Cracker

Here's the additional information that will help illustrate the process that is being explained in questions 1-3 in Part II. Pay attention to Figure 1 (b); the rest is for your reading and enjoyment.

If you have questions you need to see me after school- let's say during the tutoring session 2:45-3:45 or if catch me before then.

The essay is due on Thursday before school ends.

Best,

Mr. K