# Browse Classroom Capsules and Notes

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Displaying 1181 - 1190 of 1211

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.

The author provides a characterization of $n$-dimensional quadratic functions in terms of tangent planes.

A mysterious pattern when $\tan x$ tends to infinity is found and explained in terms of L'Hospital's rule.

It is shown that Euler-Cauchy equations with certain types of nonhomogeneous terms can be solved by the method of undetermined coefficients.