Impossible? Try anyway!
(An archive question of the week) Here’s a little problem with some big lessons for problem solving.
Algebra
John Conway on Thinking and Teaching
(An archive question of the week) When I heard Thursday that the great mathematician John Conway had died (see the New York Times obituary here), I recalled not only his books I have read, but his involvement in Ask Dr. Math‘s early days. In addition to a couple dozen quotes from him, there were several …
Reading Pandemic Graphs
(A new question of the week) Having just discussed several mathematical topics that lie behind the various graphs we have seen in the news lately, I want to depart from our usual style and answer my own current questions. We’ll look at several graphs of COVID-19’s growth and think about what we can learn from …
Logarithmic Graphing
We’ve been looking at the math underlying some of the graphs associated with the COVID-19 pandemic, starting with exponential growth, and then logistic growth. I want to look in more detail at a feature I mentioned in the first post, viewing a graph logarithmically. This is a powerful technique that goes far beyond a button …
Logistic Growth
Last time we looked at the meaning of exponential growth, a term commonly used in describing the initial spread of a virus such as the current SARS2 (which causes COVID-19). But exponential growth can’t continue forever, as it would soon exceed the total population. A slightly more complicated model for growth that takes into account …
Exponential Growth
The term “exponential” has gone viral, so to speak. Do we all know what it means? In the next few posts I’ll look at answers we’ve given to questions about exponential growth and related concepts, some of them about the spread of diseases or rumors. (Disclaimer: I will be writing about the basic math, not …
Trig Functions Meet Polynomials
(A new question of the week) A recent series of questions from one student involved interesting combinations of trigonometric identities and solutions of polynomials. At one time using trig to solve equations was far better known than it is today, and these presumably are meant in part as an introduction to those ideas. Some were …
Using Algebra for a Ratio Problem
(A new question of the week) Some kinds of problems can be solved at various levels; in particular, when we get a problem about ratios, we often can’t be sure whether the student knows only arithmetic, or can use algebra, which usually makes the problem easier. This is one reason we ask for a category …
Supply, Demand, and Proportion
(A new question of the week) Since we looked at a question about economics last week, let’s examine another, which is very different, relating the supply and demand curves to the concept of variation or proportion. We are not economists, so we can’t go deeply into that subject, but it makes us think about some …
Intercepts of a Sideways Quadratic
(A new question of the week) Sometimes a topic you think you know looks entirely different in an unfamiliar context. Here, a returning student faces a quadratic equation where x and y are reversed, making the quadratic formula seem foreign! But this is when real learning happens, when you are forced to think through the …