# Author Archive: Paul Hartzer

## Sums of Consecutive Positive Integers

Edit: The bit about the larger prime numbers was due to an error in my VBA programming, but it lead to a better understanding of the problem. Don’t take this article as “final”, is the point. This week’s puzzle in…

Mathematics

## The Difference of Squares

In our Mathematical Reasoning class tonight, we discussed this problem: Can your age in years be written in terms of the difference of two square numbers? If so, what two numbers? There are at least three mathematical problems contained here:…

## Logarithmic notation: Mathematics vs. computer programming

One of my concerns as an educator is the way in which peccadilloes of mathematical notation can get in the way of understanding. In the case of logarithms, this has become more troublesome as general education about numeric bases at…

## Minimal Eulero

Eulero is a grid-based logic puzzle. Like Sudoku, it involves Latin squares; however, while Sudoku relies on a single Latin square, Eulero consists of two overlaid squares, one of numerals and one of letters. An additional constraint is that each…

## Trigonometry as the Study of Circles

I recently read John Derbyshire’s book, Unknown Quantity: A Real and Imaginary History of Algebra (Plume 2007 edition). I recommend it overall, although the second half becomes increasingly inaccessible to the layperson. One bit that particular stuck in my head, because…

## The Prefix Dia-

A good teacher is always aware that there are things they can learn. One of the ways in which I encourage students to connect mathematics to other topics is by showing how words and morphemes used in mathematics are used…

## PEMDAS and negative numbers

By standard mathematical convention, $$-1^2=-1$$. At the same time, students are taught to refer to $$-1$$ as a negative number. A friend recently led me to realize that these two conventions are at logical odds with each other, as discussed…

## Well… is algebra necessary?

Except for the final grades, I’ve just wrapped up teaching six weeks of credit recovery for Freshman Algebra. It’s tough enough packing nine months’ of material into six weeks, but consider these are the students who didn’t do well enough…

## Trick question memes

From time to time, a mathematical question of some sort will make its rounds on Facebook and other social media platforms. For instance, the one making the rounds most recently in my portion of the blogosphere was: \[5 + 5…

## Introduction and purpose

As of this summer, the summer of 2012, I am qualified to teach mathematics at the high school level in the state of Michigan. I am expecting to be doing so full-time this fall. I am also qualified to teach English,…