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Classroom Capsules and Notes

Classroom Capsules and Notes brings together the best of over one hundred years of the short classroom materials from the MAA print publications.

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Investigating Possible Boundaries Between Convergence and Divergence Once students master the Integral Test, it is useful to show that there cannot be a series on the boundary between convergence and divergence.		The Cantor Set An elementary proof to convince skeptics that 1/4 is in the Cantor set
When Is \(n^2\) a Sum of \(k\) Squares? A wide-ranging discussion of the question in the title of the paper is presented.		Heron's Formula via Proofs without Words Proofs without words used to obtain proof of Heron's formula
A Counterexample to Integration by Parts The authors exhibit two differentiable functions for which the integration by parts formula does not apply.		Cable-Laying and Intuition A familiar problem concerning cable-laying across a river may yield non-intuitive results.