On Monday, January 18, my son turned 1 week old. We have a cute little sign to mark his age, but the sign is in months, not weeks. So, the question was, “What is 1 week in months?” It is a fraction, but it is not one quarter. If every month was 4 weeks, then … Continue reading 3/13 Months Old
Traveling around the world tends to shift my perspective. If for only a moment, I remember our planet is round, not flat. I know it is round, sure, but I often live as if the world is flat. For example, I tend to think of streets as parallel and perpendicular lines. (Surprising, since I live … Continue reading Let digons be bigons.
Jedi love the advice: “Use the force.” They mean something a little different than the product of mass and acceleration, but somehow the language of force, work, and power fits for any display of force, even on Dagobah. In Earthly physics, force equals mass times acceleration, where m is the mass of an object and … Continue reading Force. Work. Power.
Then your teacher said, “Let x be the number of goats….” He started writing stuff on the board with numbers and plus signs and x‘s, and you just kept thinking, “x is a letter, not a number.” In graduate school, I had the opposite experience. I was in a course on special functions, such as … Continue reading Unknown
There is so much to say about nothing. Choosing nothing breaks false dilemmas. This or that? None for me, thanks. Some of my favorite books about math, such as Seife’s Zero: The Biography of a Dangerous Idea, were written with zero as the main topic. Earlier this year, Amir Aczel published an account of his search for the earliest … Continue reading The Power of Zero
We like reversible processes. If I earn 5 dollars, I want to be able to spend 5 dollars. Subtraction undoes addition. It is the inverse process. All is well, until you subtract 5 dollars from your account that only has 3 dollars in it. You might have some negative feelings about that. Multiplication has an inverse process … Continue reading What to the what?
A student asked me recently what it means when we multiply a negative by a negative. Specifically, she was asking: “Why is a negative times a negative a positive?” Negatives are strange, sometimes counterintuitive. If all you remember about negative numbers is a disconnected set of rules, those rules may have ended up in a bit of a knot. Students … Continue reading Negative Numbers
I have been working with some middle and high school students this fall. It has only been a few short years since they were learning the basics. They retain some of those basics as disembodied rules, rules with no meaning or purpose. The situation seems to hinder them from experiencing the beauty and wonder that is high … Continue reading Repeated Operations
Abraham de Moivre was born in France in 1667, a year after the Great Fire in London. de Moivre arrived in London in the late 1680s. Leading up to his emigration, life in France for Huguenots, i.e. French Protestants, was growing ever more uncomfortable. As Louis XIV consolidated power, he grew to see religious tolerance as a … Continue reading de Moivre’s Shortcut
To square a complex number, square the length, and double the angle. A vector is a directed line segment, an arrow if you will. Think of a complex number, z = a + bi, as a vector from the origin (0,0) to the point (a,b). In polar form, z can be written in terms of r, the distance from the … Continue reading Square of a Complex Number
Footpath Math: Chalk it up to a math geek 