Using a simple trigonometric limit, the author provides an intuitive geometric proof of the Singular Value Decomposition of an arbitrary matrix.

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*Motivated by the observation that the derivatives of \(e^x\) are all positive and the derivatives of \(e^{-x}\) alternate sign, the author asks what kinds of ``sign patterns" are possible...*

*The author provides a simple context and some history in which actuarial computations take place.*

*In a classic pouring problem, given two jugs with capacities \(m\) and \(n\) pints, where \(m\) and \(n\) are relatively prime integers, and an...*

*Fay and Sam go for a walk. Sam walks along the left side of the street while Fay, who walks faster, starts with Sam but walks to a point on the right side of the street and then returns to...*

*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 \( \frac{1}{n} + \frac{1}{n^2} + \frac{1}{n^3} + \cdots = \frac{1}{n-1} \) is illustrated for \( n = 9 \) and the remark is made that a similar construction shows the result...*