Category Archives: Uncategorized

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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