Project Page
This semester's project is on the fastest curve, the Brachistochrone.
Details and due on Tuesday 23 November
at 4pm.
There is a lot of information on the web about the Brachistochrone. It is
a simple example of an advance topic. The advance topic is call calculus
of variations and it is usually a senior level class. On the otherhand
the example is simple enough one can do the problem with just calculus
3 and a little help. One of my high school buddies went to UCLA and
I visited his first day of Calculus 3 and the instructor talked about
the Brachistochrone.
Your project is to write several pages on the Brachistochrone and it should
cover the material you understand and not attempt to copy something you
don't understand. We need a list requirements here.
More advanced teams might attempt showing that the cycloid is a weak
solution.
Here are some ideas. How the cycloid is defined and properties of
the cycloid. How the travel time is computed, how the physics works.
Comparing travel time for several curves,
like the straight line, circle, cycloid, a bent line. In calculus we
optimized functions but setting a number of partial derivatives to
zero, in this best curve case, we get a differential equation instead.
You could solve the DE to get the cycloid. Deriving the DE itself isn't
easy for calculus students, but you did solve some DE's in calculus 2.
Some links: