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 »
(A new problem of the week) Having discussed counting earlier this week, let’s take a look at a different kind of counting. The subject of combinatorics (the study of counting) arises in many guises: probability, sets, geometry. Here, we look at a relatively basic type of problem that involves the same sort of organized thinking …
Last time we looked at how to count the parts of a polyhedron, and a mention was made of Euler’s Formula (also called the Descartes-Euler Polyhedral Formula), which says that for any polyhedron, with V vertices, E edges, and F faces, V – E + F = 2. We should take a close look at that simple, yet amazing, …
More on Faces, Edges, and Vertices: The Euler Polyhedral Formula Read More »
Over the years, we have had many questions, often from young students, asking how to count the parts (faces, edges, vertices) of a polyhedron (cube, prism, pyramid, etc.). The task requires understanding of terms, visualization of three-dimensional objects, and organizing the parts for accurate counting — all important skills. How can we help with this?
(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) Many calculus courses start out with a chapter on limits; or they may be introduced in a “precalculus” course. But too often the concept is not sufficiently motivated. What good are limits? Why did they have to be invented? Are they as simple as they seem? Why is an epsilon-delta …