i agree with David Epstein that you can embed Arnold's problem in a collection of problems which will make it easier for the studk it, and more
enjoyable to work on it.
But i believe it is better for the students if we can give them problems in which the constellation of associated questions unrolls before the students as they work on the initial problem, instead of handing them the constellation at the beginning or feeding it to them in steps.
learning to see the constellation is as important as solving the problem you started with.
A proof of the theorem (ascribed to Artin) that a positve valued polynomial is a sum of squares can be found in lang's algebra book in the section on Real Zeros and homomorphisms p279 in the '65 edition. Of course, this is a key result in trying to move results in algebraic geometry from C to R.
best, Terry Gaffney
This is an unmoderated distribution list discussing post-calculus teaching and learning of mathematics. Please keep postings thoughtful and productive. No cute one-liners please----David.Epstein@warwick.ac.uk
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