A Graph-theoretic Treatment of the
Amitsur-Levitzki Identity

Bharat Dravid

I like to ask my undergraduate students the following question: Consider a planet in a perfectly circular orbit around the Sun. Now take a celestial hammer and give it a slight radial knock. What happens? The answer, of course, is that the planet oscillates radially as it goes around the Sun. Radial oscillation combines with circular motion to give a plausible planetary orbit. So long as the eccentricity of the orbit is small, the radial motion is harmonic and determining the orbit is simpler than solving the general problem of planetary orbits. This approach is perhaps more insightful: it allows us to understand intuitively why a planetary orbit is closed, and why it is stable, and, with a little generalization, to determine the effect on a planetary orbit of the oblateness of the Sun and of corrections due to the general theory of relativity.

Address for Correspondence

Bharat Dravid
Fourth Year Integrated
M Sc. Student
Department of Mathematics
Indian Institute of Technology
Kharagpur 721302, India.
Email:bharat_dravid@yahoo.com