# Browse Classroom Capsules and Notes

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Displaying 71 - 80 of 1212

Consider the sum of $n$ random real numbers, uniformly distributed in the unit interval. Although the expected value of this sum is $n/2$, the value of $n$ for which...

This article takes another look at the sliding ladder problem that students meet in the study of related rates in calculus.  Three variations of the problem are analyzed using elementary...

In Sam Loyd's classical Courier Problem, a courier goes around an army while both travel at constant speeds. If the army travels its length during the time the courier makes his trip, how...

The formula $\theta = \arctan(y/x)$ gives the angle associated with a point $(x,y)$ in the plane, valid for $\mid \theta \mid < \pi/2$.  This capsule presents a formula...

The result is illustrated for ratio 1/9, via an approach that is readily generalized.  In particular, the result $\frac{1}{n} + \frac{1}{n^2} + \frac{1}{n^3} + \cdots = \frac{1}{n... In this article a classroom "trick" involving square arrangements of natural numbers is used to motivate a discussion of a special class of matrices. In particular, a basis is... In this note, the Cauchy-Schwarz inequality is derived from Pearson's inequality. It follows that the two are equivalent. This note is on the digital (floating-point) representation in various arithmetic bases of the reciprocal of an integer \( m$. An algorithm is given to change the representation of \( 1/m...

The authors describe how to generate many pairs of smooth functions having the property that slices of the two corresponding surfaces of revolution have equal surface areas.

Some results in plane geometry can be proved easily using 3-dimensional vectors. This article explores several such examples.