Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In one month I'll be giving a talk to motivated high schools students on a topic of my choice from dynamical systems and/or ergodic theory.

I'm having trouble coming up with a topic compelling enough to keep their interest, yet elementary enough to be comprehensible. In particular I need to keep clear of concepts of measure and multivariate calculus, unless I can somehow compartmentalize the necessary measure concepts in some neat way (e.g. Lebesgue measure on a manifold is probably okay).

I have some inclination towards giving a talk on dynamical billiards on polygons (very easy in terms of prerequisites), but I thought I would ask anyway to hear some different ideas. For instance, can anybody think of a high-school friendly topic in celestial mechanics?

share|improve this question

5 Answers 5

up vote 2 down vote accepted

I would look at the following items.

Books:

  • "A First Course In Chaotic Dynamical Systems: Theory And Experiment (Studies in Nonlinearity)" by Robert L. Devaney

  • National Academy of Sciences: Science At The Frontier

  • Nonlinear Dynamics and Chaos by Strogatz has a few dynamical systems on Celestial Dynamics (see problems 6.5.7 through 6.5.10), but I am not sure they are appropriate.

  • It would be great if you can build an electronic circuit, analyze it with mathematics and then measure stuff with DMMs and O'scopes and the like. maybe the Van Der Pol Oscillator or a Harmonic Oscillator.

Web Sites:

share|improve this answer
    
Amzoti, the "reference" reference! +1 –  amWhy Apr 19 '13 at 0:30

Talking about celestial mechanics, please see this pedagogical blurb: http://www.whydomath.org/node/space/index.html

I would be hard pressed to find a more spectacular success of the dynamical systems theory in the real-world.

share|improve this answer
    
That's some compelling stuff. Thanks! –  A Blumenthal Mar 20 '13 at 18:37

I'd talk about the chaos game for generating images of IFS fractals or Julia sets. See the books Fractals Everywhere and Fractals for the Classroom for instance.

share|improve this answer

If you're happy to just show some fun stuff (rather than really explaining the deep mathematics), then you could show movies of $n$-body choreographies:

http://melusine.eu.org/syracuse/swf/1-nbody/

Or talk about solutions to the $n$-body problem which go to infinity in finite time:

http://www.ams.org/notices/199505/saari-2.pdf

share|improve this answer

You can also talk about cellular automata. The game of Life is a dynamical system.

share|improve this answer
1  
Welcome to MSE! I realize you do not yet enough reputation, but this is probably best left as a comment. Maybe you can add more details to improve it as an answer with details, links, .... Just a friendly note. Regards –  Amzoti Jun 12 '13 at 18:14

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.