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Sufficient Condition to be a Polynomial?
Appropriate Level: Real analysis. The Question: Suppose is infinitely differentiable and that for each there is some for which the th derivative of at equals 0. Must be a polynomial?
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Cyclotomic Polynomials
Appropriate Level: Abstract Algebra The Question: Recall that the cyclotomic polynomials are defined for so that . Is it true that every coefficient of every cyclotomic polynomial is either 0, 1, or 1?
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Watching the Sunrise (and figuring the radius of the earth)
Appropriate Level: Trigonometry The Story: I spent a summer in Chicago and early one morning I watched the sun rise over Lake Michigan (the lake is large enough that you cannot see across it, at least from Chicago). I stood … Continue reading
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Cutting a Triangle from a Square
Appropriate Level: Calculus (1 or 2, depending on how your courses are divided). The Question: You start with a unit square (say a piece of paper). Choose two adjacent sides of the square and randomly pick a point on each. … Continue reading
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