Browse Classroom Capsules and Notes

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Mercator's Rhumb Lines: A Multivariable Application of Arc Length

Rhumb lines on a sphere correspond to straight lines on a Mercator projection. The authors parameterize the rhumb line on a sphere and finds its length.

A Note on the Ratio of Arc Length to Chordal Length

The article illustrates a gap in some not-so-rigorous methods used by authors to use arc length to show the derivative of the sine function is the cosine function.

Unifying a Family of Extrema Problems

Lagrange multipliers are used to solve a problem that unifies common extrema problems of calculus.

Tying Up Loose Ends with Probability

The author describes an in-class experiment with strings being tied to form loops. The probability of the possible number of loops is examined.

Counterexamples to a Weakened Version of the 2-Variable 2nd Derivative Test

Two counter examples are given for the way the second derivative tests are stated in calculus books.

Doughnut Slicing

Investigates the intersection of a plane through the midpoint of a torus and tangent to the surface.

A Discover-\(e\)

The author uses differentiation to find the point of tangency for exponential functions for all bases and shows they lie on a horizontal line.

Forward Homework - A Motivational Tool

Forward homework could be a good way of teaching math.