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Classroom Capsules and Notes

Classroom Capsules and Notes brings together the best of 112 years of the short classroom materials from the MAA print publications.

Using Tangent Lines to Define Means The authors define and discuss a wide variety of means. One of the authors was an undergraduate student.		A Dynamical Systems Proof of Fermat's Little Theorem An interesting unusual visual and rigorous proof of Fermat`s Little Theorem, with unusual generalizations
Power Distribution in Four-Player Weighted Voting Systems Interesting example of 5 possible power distributions in a 4-player veto-proof voting system.		A Graph of Primes The graph obtained by constructing an edge between each pair of primes with difference a power of 2 is not connected.
The Square Roots of 2x2 Matrices The Cayley-Hamilton theorem may be used to determine explicit formulae for all the square roots of 2 X 2 matrices.		A Surprising Application of the Integral of 1 - F(x) to Revenue Projection The author describes an integral that represents the proportion of wages covered by Social Security and exposed to taxation.