# Mathematics

## Is Zero a Factor of Zero?

Generally speaking, if $$a \times b = c$$, then $$a$$ and $$b$$ are factors of $$c$$. This concept appears at the secondary level in two contexts: The factors of positive integers, and the factors of a polynomial. If we limit…

## Pascal, Pacioli, Probability, and Problem-Based Learning

I’m currently reading Howard Eves’s Great Moments in Mathematics After 1650 (1983, Mathematical Association of America), a chronological collection of lectures. The first lecture in this volume (the second of two) is on the development of probability as a formal field of…

## The Fourth Dimension (Thoughts)

I’ve had two recent thoughts about the fourth dimension. The first relates to Euler’s Formula, which says that the difference between the sum of the vertices and faces of a convex polyhedron and its edges is always 2 (that is,…

## Writing Rationals with the Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic says that all integers greater than one can be written uniquely as the product of prime numbers. Another way of stating this is that, if $$P = (p_1, p_2, p_3, …)$$ is the (infinite) set…

## A trio of math limericks

Inspired by Math with Bad Drawings, here a trio of my own limerick creations: Two circles surrounding a square Was more than the poor thing could bear. It made itself fetal ‘Til planar was hedral. Cylindrical nets are a snare!…

## Multiplication Table Slide Rule

Using Publisher, I’ve created a slide rule for multiplication tables (up to 10×10). To use it: — Print it out and cut along the dotted line. — Move the 1 on the bottom part to any single digit on the…

## Town Squares problem

A friend of mine, a father, recently posted this item on his Facebook feed. It’s from Pearson, and he was struggling figuring it out. I also had to read it several times to figure it out. This is a large…

## The Geometric Proof of Infinite Primes

I was recently wondering why Euclid, the geometer, published a proof that there is an infinite number of primes. I should have known that his proof is geometric. It is: “Let A, B, and C be distinct lengths that cannot be…

## Some Thoughts on Complex Numbers

The first shoe: Multiplying Adding complex numbers is a straightforward task. Given two numbers, $$a + bi$$ and $$c + di$$, the sum is the sum of the real portion and the sum of the imaginary portion: \((a + c)…