Algebra

Why Isn’t Slope Run Over Rise?

Definitions are interesting in several ways. Sometimes they are essentially arbitrary; other times there is a very good reason for them, and understanding that reason can be helpful in understanding and using them. But they are usually taught just as something to memorize. Let’s think about why slope is defined as it is, and not …

Why Isn’t Slope Run Over Rise?Read More »

Fun with a Quartic Equation

(New Question of the Week) Sometimes a problem leads to a very interesting discussion that brings out many good ideas – but then turns out to be something entirely different, which brings out even more (and simpler) ideas. This polynomial equation problem we helped with last week was like that. I will not be quoting …

Fun with a Quartic EquationRead More »

Why Must the Number of Variables Equal the Number of Equations?

(New question of the week) Now that we are receiving questions at the new site, we will be periodically posting some of those questions and answers, in addition to going back to particularly interesting questions from the old archive. This question (which I have slightly edited) came to The Math Doctors earlier this month, from …

Why Must the Number of Variables Equal the Number of Equations?Read More »