# Browse Classroom Capsules and Notes

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Two of Euler's familiar identities, the sum of reciprocals of squares of integers and the infinite product expression of the sine function, are proved again. This article originally...

Every standard calculus textbook contains the derivations for the definite integral of $x$ and $x^2$ using Riemann sums $\ldots$

The classical Buffon needle problem is to find the probability that a needle of length $n$ when dropped on a floor made of boards of width $b$ will cross a crack between the boards.

Geometrical notions are abundant in calculus, where one learns how problems involving them can be addressed via the derivative or integral.

There are few random processes more avidly watched than the state lottery drawings in which six numbered balls are chosen from a set of forty-four.

"Imagine a fuel tank in the shape of a horizontal cylinder, with length $l$ and circular cross section with diameter $d \ldots$"

Most calculus students take it for granted that the shell and disk methods for computing the volume of a solid of revolution must always give the same result.

In this capsule, proofs of the equivalence of the two definitions of the Fibonacci numbers are discussed. This helps the undergraduate view mathematics as a unified whole with a variety of...

A study of the sensitivity of the volume of cans to the radius of the base

"This problem also fits quite nicely in the area of convex geometry, from which we draw the following proof..."