UT Math Club Problem of the Month
November 11, 2009
Problem I (Maximal Polygons) Let S 1 = {(x, y)|x2 + y 2 = 1} ⊂ R2 denote the
circle of radius 1, centered at the origin in the Euclidean plane. Let n
be a fixed positive integer. Of all the n-gons (polygons with n edges and
n vertices) that can be inscribed inside of S 1 , which have the largest
possible area? Make sure to carefully justify your claim.
Problem II (A Functional Equation) Find all functions f : R → R such that
f [x2 + f (y)] = y + [f (x)]2 for all x, y ∈ R
Submission Deadline: Wednesday, December 2 by 11:59 PM
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