Browse Classroom Capsules and Notes

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Some Sums of Some Significance

The authors discuss certain sums and series that arise in combinatorics and their connections to Sterling numbers.

A Rose is a Rose is a Rose...

Plots families of curves in the shape of a roses using parametric and polar plots

Area and Perimeter, Volume and Surface Area

Using derivatives, the author shows the relationship in space between the volume and the surface area and in the plane between area and the perimeter.

Cylinder and Cone Cutting

The author finds the equations for the conic sections by rotating the cone and keeping the plane fixed.

Fibonacci Powers and a Fascinating Triangle

A modified Fibonacci triangle is created by squaring Fibonacci numbers. Interesting numbers such as Lucas numbers appear.

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.

A Concurrency Theorem and Geometer's Sketchpad

The author draws a triangle inside a circle and extends the sides to meet the circle. Then he joins the resulting points and proves that the resulting lines are concurrent.

Some Extensions of a Ubiquitous Geometric Limit Problem

Computing a certain limit for areas of a sector. Note that the first displayed limit is as \(\theta \rightarrow 0\), not as \(\theta \rightarrow \infty\) .

A Nod to Bertrand Russell

The author investigates claims by Russell in Religion and Science about the probability of getting a large number of heads in a row when a coin is repeatedly tossed.

Maximizing the Arclength in the Cannonball Problem

The article shows how to maximize the arclength of the trajectory of a cannonball.