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Browse Classroom Capsules and Notes

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The authors show that the locus of the focus of a parabola rolling on the \(x\)-axis is a catenary.

The authors provide a condition for a function to have nested \(n\)-th degree Taylor polynomials with varying centers, which can approximate the function visually.

The author characterizes the positive integers that are the products of two pairs of factors such that the sum of one pair equals the difference of the other.

This is a student research project on zero-divisor graphs of commutative rings, using results from recent professional publications.

Inspired by the Pascal triangle, three young "rascals" from three different countries devise a number triangle based on a diamond recurrence formula.

The author proves visually the double angle formulas for sine and cosine.

How a Saari representation triangle determines the winner of a three-party election for several voting methods is illustrated.

The authors prove a necessary and sufficient condition for the existence of the limits of a class of multivariable rational functions commonly seen in textbooks.

The author uses the Lambert W function to express the equilibrium solutions of the SIR epidemic model.

Following his senior seminars, the author discusses Fermat's last theorem for rational and irrational exponents, in which the rational solutions are characterized.

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