(An archive question of the week) A recent question asked about a well-known problem about stacking books (or cards, or dominoes) so that the top one extends beyond the base, giving a link to one of many explanations of it – but one, like many, that doesn’t quite fill in all the details. Doctor Rick …
(An archive question of the week) In preparing the last couple posts, on recurrence relations, I ran across an answer to a much harder question, that illustrates what it can take to solve one that doesn’t fit the convenient forms. It’s linear, but the coefficients are not constant as they have been in all our …
A Challenging Homogeneous Second-Order Recurrence Read More »
(An archive question of the week) In gathering information on how to count the diagonals of a polygon, I found this long discussion about a similar-sounding issue, which is hardly more difficult, yet far more complex. It was interesting to explore what the question means, and take it in different directions, on the way to …
(An archive question of the week) We’ve looked at the scalar (dot) product and the vector (cross) product; but there is one answer in the Ask Dr. Math archives that was too long to fit in either post. Here we’ll see again where the two familiar products come from, while looking deeper into the math …
(An archive question of the week) Last time we ended with questions about writing (or ignoring) zeros at the end of a decimal. I didn’t have room for one more question, so I’ll put it here. Zeros at the start This question comes from 2000: Zero Before the Decimal Point? A fellow instructional designer and …
(An archive question of the week) Here’s a little problem with some big lessons for problem solving. Not enough equations? This question is from Kenanga in 2017, not long before the Ask Dr. Math service stopped taking questions: Insufficient Information In Question Given A + B + C = 1 B + C + D …
(An archive question of the week) When I heard Thursday that the great mathematician John Conway had died (see the New York Times obituary here), I recalled not only his books I have read, but his involvement in Ask Dr. Math‘s early days. In addition to a couple dozen quotes from him, there were several …
(An archive question of the week) I’m in the middle of discussing the Law of Sines and the Law of Cosines, and in searching for questions about them, I ran across one that stands by itself. A student asks his teacher why his method without trig doesn’t work, and gets three answers from us. They …
(An archive question of the week) While gathering answers to questions about volume and surface area formulas, I ran across this question that applies to all of them: Given all the approximations and assumptions we make in the derivations we show (without calculus), how can we claim that the resulting formula is exact? Or can …
(An archive question of the week) Last week we looked at a recent question that touched on the idea of the derivative as a rate of change. Let’s look at a long discussion from a few years ago digging into what that means within calculus. Instantaneous rate, or rate per inch? Here’s the question, from …