(Archive Question of the Week) Students commonly expect that textbooks all say the same thing (in fact, some think they can ask us about “Theorem 6.2” and we’ll know what they’re talking about!). The reality is that they can even give conflicting definitions, depending on the perspective from which they approach a topic. Here, I …
(Archive Question of the Week) We have had a number of questions over the years about inverse trig functions and their ranges. For today’s question, I have chosen one from 2011, which will link to a number of others that I will not quote in detail.
(Archive Question of the Week) We occasionally got questions about Probability Distribution Functions (PDFs) from students who lacked a full picture of what they are; when I searched for references to give them, I never found one that explained the whole concept as I wanted to. When the following question came in, I took it …
From Histograms to Probability Distribution FunctionsRead More »
(Archive Question of the Week) An interesting question that has been referred to many times since it was written in 1999 deals with averaging angles. At first the question seems trivial; then almost impossible; and then we end up with a rather simple formula that is totally unlike what we started with. And further applications …
(Archive Question of the Week) Fractions are a frequent source of questions from elementary students. I plan to devote several posts to various aspects of this, from using a common denominator to add fractions, to flipping and multiplying to divide fractions, to converting between improper fractions and mixed numbers. Here, I want to look at …
(Archive Question of the Week) One of my favorite questions, from 2001, asked about how to convince a skeptical friend, when a clear mathematical result goes against their intuition. Why should they believe the math? It led me into thoughts about the relationship of intuition to math, whether (and when) math can be trusted, and …
(Archive Question of the Week) We often receive questions saying something like, “My wife has the same birthday as my son-in-law, whose dog has the same name as my wife’s brother, … ,” and asking us to calculate how likely it is that this would happen. Sometimes it is simply impossible to answer (without, say, looking up …
(Archive Question of the Week) Although high school and up probably constitute the majority of our questions, I always enjoy answering younger children. For today’s look at the archives, I thought I’d look at two such questions, both from 1999, and very memorable. The first is almost certainly the youngest “patient” we’ve ever had, and …
(Archive Question of the Week) Having recently discussed a couple different issues that touched on the relationship of math to reality, I was reminded of this old favorite – a question that is not asked often enough, and reveals some of the “dirty little secrets” behind math. Math is not reality; it is often used …
(Archive Question of the Week) Recently I discussed the definition of the median of a data set, pointing out how it needs refinements that are not often discussed. In searching for questions in our archive on that topic, I ran across a discussion of an opposite issue: the breadth of the general term “average”, which …