# Browse Classroom Capsules and Notes

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Displaying 81 - 90 of 1209

"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..."

The following is a short, simple, but not well-known proof of the well-known trigonometric identify $$\sin(a+b) = \sin a \cos b + \cos a \sin b$$.

The range of validity of the inequality for various values of $$n$$

In his work On the Sphere and the Cylinder, Archimedes showed that the volume of the sphere is exactly two thirds of the volume of the circumscribed cylinder. This article explores...

The importance of round-off errors, ill-conditioned systems, and interval analysis in the context of baseball statistics

Calculation of the minimum distance from a point to a curve