Beauty in Mathematics – Muntz’s Theorem

(For: C.)

[To be finished]

A year or so ago I decided to try to explain why I find some mathematics beautiful, and to use Muntz’s Theorem as a base for the post. A few months ago I mentioned Muntz’s Theorem in a email, and recently received a reply asking for more information on it, which prompted me to actually write the post. So I can now genuinely say this post is a response to a request.

notes for post

* the result is both surprising and (sort of) not-surprising

* mathematics understanding needed is probably quadratic and cubic equation graphs – maybe a bit more?

* how to explain Weierstrauss Approximation Theorem, and how and why Muntz’s Theorem is a beautiful refinement of it

Links: need sophisticated mathematical knowledge

http://en.wikipedia.org/wiki/Müntz–Szász_theorem
http://mathworld.wolfram.com/MuentzsTheorem.html

http://en.wikipedia.org/wiki/Weierstrass_theorem_on_polynomial_approximation

http://en.wikipedia.org/wiki/Mergelyan’s_theorem

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About Colin Bartlett

I'm interested in arts, mathematics, science. Suliram is a partial conflation of the names of three good actors: Ira Aldridge, Anna May Wong, and another. My intention is to use a personal experience of arts to make some points, but without being too "me me me" about it. And to follow Strunk's Elements of Style. Except that I won't always "be definite": I prefer Niels Bohr's precept that you shouldn't write clearer than you think.
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