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
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?
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
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
You may have met the complex numbers. Gauss named them in 1831, but our knowledge of complex numbers was born in the first half of the 16th century in northern Italy with attempts to solve cubic equations. Leveraging knowledge from Tartaglia, Girolama Cardano published his findings in his book Ars Magna in 1545. Complex numbers have a real part and an … Continue reading Polar Form of Complex Numbers