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Gerald Stuhrberg
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Almost a month ago I was tagged by +Refurio Anachro     to do a post about a mathematician, Richard Courant. Well I had only heard of Courant in passing, and wasn't familiar with his work. So I got out my trusty set of "The World of Mathematics" [ISBN 0486432688] books and got to work.  If someone finds something here that is inaccurate please let me know in the comments with a reference. 

Richard Courant's most famous popular work was done in the book "What is Mathematics"  written with Herbert Robbins. Through this book they discuss various mathematical ideas from number theory to calculus to topology. Courant was also known for his work in function theory ( http://en.wikipedia.org/wiki/Geometric_function_theory )  and working with soap-films over various shapes.

Let me talk a little bit about that for a moment, and then I want to talk about my favorite problem developed by Courant.

So in the 1800s there was a Belgium scientist named Joseph Plateau. Plateau worked on this problem of stable soap-film surfaces where he came up with the laws which govern in what shapes soap films remain "stable". The 4 laws deal the the curvature and angle at which soap-film will remain stable.

Courant took this problem to one more topological level (pun sort of intended) and devised a way for a soap film to form a Mobius Strip, a one sided three dimensional object, http://mathworld.wolfram.com/MoebiusStrip.html.

Which makes me think of a small observation: "If you lived on a Mobius Strip, you'd always be on your way home"

Courant took away the small limitations of Plateau's laws and found a shape for wire, that when soaked in soap bounded an infinite number of soap films!

My favorite Courant problem though has very little to do with soap. Courant came up with something called "The Lever of Mahomet"

First we imagine a train.

We take it as granted that we know the full motion of the train and that full motion can be tracked as a function:
f(t)=x

The Train is moving between two stations A and B however neither it's acceleration or velocity needs to remain constant.

In one of the train carriages there is a rod pivoted in the center so that it may move without friction either forward or backward until it touches the floor. (See Figure 1)

If the rod happens to touch the floor, it does not bounce. This is not a physical fact, but one we are using in the constraints of the following problem so as to make things less complex.

Now the big question:

Is it possible for there to be a position where the lever stands without any other force other than gravity and the motion of the train moving between points A and B?

There is no need for kinematic equations to find the answer to this problem, and the proof is actually quite small. I will leave it to the reader if you'd like to know the answer, I will post it at a later time.


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Autodidact. A lover of math and science. Ignorant of almost everything in the universe.

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  • University of Michigan-Dearborn
    Physics, 2011 - present
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