(A new question of the week) It can be an interesting challenge to be presented with a formula and asked how it was derived. This becomes a bigger challenge when the formula is only approximate, so we have to figure out how to arrive at this particular approximation. But it is impressive when several different …
Distances to an Arc: Exact and Approximate Formulas Read More »
Having just talked about definition issues in geometry, I thought a recent, short question related to a definition would be of interest. We know what the Greatest Common Divisor (GCD, also called the Greatest Common Factor, GCF, or the Highest Common Factor, HCF) of two numbers is; or do we?
(A new question of the week) A recent question asked about one of our explanations of the limit of x2 (which we have discussed at least five times). This led to a deeper examination of what was said; and as I have looked through this and other pages, I have realized that it would be …
(An archive question of the week) One of the discussions we looked at last time involved rolling three dice and getting at least one six. I didn’t go into detail on the calculation there; but I found another place where we discussed it at length. We’ll look at that here. A wrong way and a …
(An archive question of the week) Last time we looked at various 2- and 3-set Venn diagram problems (and alternative methods). One discussion I found while collecting them deserved to be set aside for special examination, if only because it would scare the beginner. A mixture of tools will make the work easier. Here it …
Puzzles involving two or three properties of people or objects, commonly solved by Venn diagrams, are popular with teachers, and perhaps not so popular with students! Several have asked about them recently, leading me to catalog our past answers about them, to find the most useful examples to point to. Some of these are very …
(A new question of the week) In many areas of math, an answer can come in several forms, which can make it hard to know if you are right when you compare your answer to the answer in the back of the book. Even worse is when the problem is multiple-choice, and your answer has …
Last time we looked at the question of why we have to have postulates, which are not proved, rather than being able to prove everything. Often, this question is mixed together with a different question: Why do different texts give different lists of postulates, so that what one calls a postulate, another calls a theorem? …
(A new question of the week) In Monday’s post about fallacies in calculus, one of them used the definition of the derivative (or rather, misused it). Today we’ll look at a short question about applying that same definition, that came in last month.
(An archive question of the week) In searching for answers to include in Monday’s post on calculus fallacies, I ran across a long discussion that illustrates some important aspects of methods of integration. In particular, there are often multiple ways to find an integral (the best not necessarily being the one taught in your textbook); …
Integration: More Than One Way, More Than One Answer Read More »