Re: Spheres vs. Triodes

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: Paul Nicholson <paul-at-abelian.demon.co.uk> 

Hi Godfrey, All,

 > elliptic curve theory is one of the most beautiful
 > chapters in mathematics.

Beauty and depth, absolutely!   If you fancy a good feast
on modular functions and modern physics, have a read about
"Monstrous Moonshine" - spine tinglingly nice stuff.  One
day I want to write about this subject.

 > Your interest in elliptic curve theory must stem from
 > cryptography.

No, definately not!   I love the books by Silverman, Knapp,
and Cassels.  But you can keep the crypto stuff - that's when
it gets dull!

Elliptic integrals do seem to crop up a lot in our discussions
don't they!  This is because we often want to know the field
(E or B) at some test point due to a circular ring of charge or
current.  When viewed from the test point, the source ring
looks like an ellipse.  Thus we end up doing lots of integrals
around ellipses.  Not that elliptic integrals have a great deal
to do with elliptic curves, beyond the fact that the latter was
invented when somebody wanted to compute distance along an
ellipse, but I couldn't resist mentioning it because it is such
a very, very nice subject.
--
Paul Nicholson
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