(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 …
Recall that the domain of a function is the set of all valid input values (x), and the range is the set of all possible output values (y). It is reasonably easy to find the domain: look for what could make it impossible to evaluate, such as dividing by zero or taking the square root …
(New Question of the Week) I like working with a student who is willing to take chances, and also willing to be corrected. As I have often explained, just like a medical doctor, a Math Doctor wants you to “show me where it hurts” in order to diagnose the problem; so showing detailed work is …
(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 …
How to Convert a Fraction to a Decimal – and Why Read More »
We get many questions about classifying shapes, from both elementary and high school students (or their parents or teachers). They often have trouble with the very idea of classifying items by applying definitions, and also with the fact that definitions can vary, both between everyday and technical usages, and from one textbook to another.
(New Question of the Week) One of the strengths of the Math Doctors is the breadth of knowledge represented by our volunteers; we are all different. I have tended here to show the topics that I myself deal with, because those are what I can say most about; but whereas I focus mostly on elementary …
(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 …
Questions about geometric proofs have often been handicapped by the inability to show us the associated figure (until we made that easier to do on this new site). In principle, that should not be a problem, because the statement to be proved should contain all the necessary information. It should never be necessary to refer …
(New Question of the Week) From time to time a student will ask for help understanding what he reads in his textbook. This often requires some back-and-forth as we try to understand both what the textbook is saying in its context (without having a copy of it to look at), and how the student is …
(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 …