We have seen a number of questions recently about combinatorics: the study of methods for counting possibilities. These topics are studied at all levels of mathematical education, from elementary (where they might just be called counting) to high school (where they are often learned along with probability) to college (where they are part of “discrete …
(A new question of the week) Looking through recent answers we’ve given, I realized that one shares several features with my last post, as both involved proving facts using modular arithmetic and the pigeonhole principle. I need to do posts specifically about both of those concepts soon. For now, you can use the references I …
(An archive problem of the week) While gathering sequence/pattern questions for my last post, I ran across a very different problem. Here we are told what the pattern is (a good example of one that you would probably never discover on your own), and asked some questions about later terms. It can be understood either …
Back in May, I wrote about pattern and sequence puzzles, and didn’t have the space to cover all that I would have liked. It’s time to revisit the topic, looking at a couple different types of sequences, and then the “input/output” or “function” puzzles that add an extra twist to the idea.
(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 written about issues of wording with regard to percentages, we should look at another wording issue that touches on percentages and several other matters of wording. What does “three times larger” mean? How about “300% more”? We’ll focus on one discussion that involved several of us, and referred back to other answers we’ve …
A recent discussion with a student I was tutoring face to face, about an ambiguously worded problem, led me to gather a few answers we’ve given related to the words we use associated with percentages.
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?
(An archive question of the week) Having looked at the matter of faces, edges, and vertices from several different perspectives, I want to look at one more question and answer, to tie it all together.
Having discussed how to count faces, edges, and vertices of polyhedra, and then looked at Euler’s formula that relates them (not only in polyhedra but in graphs on planes and other surfaces), we need to consider a question we have received at least 100 times: Are these terms even defined (or defined correctly) for cylinders, …
Do Curved Surfaces Have Faces, Edges, and Vertices? Read More »