Words

Three Times Larger: Idiom or Error?

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 …

Three Times Larger: Idiom or Error? Read More »

Talking About Percentages

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.

Counting Faces, Edges, and Vertices

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?

Necessary and Sufficient Conditions: If, or Only If?

Sometimes in math, we trip over words, especially when they are used in ways that differ from everyday usage, or when the associated grammar is complicated. This set of three answers from our archive, each of which is referred to by the next one, look at relationships among the ideas of “necessary and sufficient conditions”, …

Necessary and Sufficient Conditions: If, or Only If? Read More »