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Browse Classroom Capsules and Notes

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Use area to describe the second derivative of a function

Analytic proofs for the generation of conic sections

This paper offers a visual illustration of the fact that every octagonal number is the difference of two squares.

The author shows that two ostensibly different generalizations of the Fundamental Theorem of Algebra are equivalent.

By providing increasingly simpler test functions, this note places in context a primality test developed by Dennis P. Walsh ("A curious test for primes," this Magazine 80(4), October...

The creation of 'extriangles' based on a given triangle is iterated, giving rise to four quadrilaterals each with area five times the area of the original triangle.

The author states a "Master Theorem" from which, exploiting concavity, he deduces several classical inequalities.

The author investigates the graph of a quartic polynomial with inflection points and finds many regularities, some involving the Golden Ratio.

An example is given where Newton's method converges but the limit does not satisfy the equation.

Two trigonometric sums are viewed pictorially.