## Introducing the Spry

Some time ago, the discussion on π being the incorrect number for calculations in trigonometry, in favor of τ (2π), led me to muse about creating a unit to replace the degree, called the wedge and being equal to nearly two degrees (100W…

## Polygon Sets: Doing the Math

In my previous post, I created sets of regular polygons in GeoGebra by setting a parameter of the polygons equal to a constant. In this post, I will show the mathematics for determining the side length given a particular parameter….

## Polygon Sets

I recently found myself creating a set of regular polygons for a worksheet. I used GeoGebra to create them, and then free-handed the zoom in order to get them consistently sized. This led me to wonder what “consistently sized” would…

## Reflections on Fractions

I was reading an article on fractions, waiting for students to show up for after-school tutoring. One of them asked me what I was reading, so I told him. He groaned. I asked him what his least favorite topic in…

Education

## Three Card Monty Hall

Imagine we are playing a game of cards. In this game, there are only three cards in the deck: An Ace and two Kings. I will deal you one card, and I will keep the other two. You win if,…

Mathematics

An adult friend is getting tested to see if she has a formal neurological problem that would account for her struggles with mathematics. She asked how it could be that she might make it all the way through public education…

Education

## Forms of the Quadratic: Terminology

Because mathematical terminology developed piecemeal over time, there are many inconsistencies which prove to be a challenge to students. One of the more obvious examples is what is called the “standard form” of the quadratic. A quadratic equation has three…

## Slide rules and calculators

Several of my math teacher colleagues are of the opinion that calculators have destroyed math sense. I am not convinced that this is directly true: Calculators are a tool, nothing more. A few months ago, I saw a video by…

## MEYL: Q. 1194

This is my translation of Meyl’s 1878 proof that a triangular pyramid of balls will only have a square number of balls if the base side is two or forty-eight. “Solutions to questions posed in The New Annals: Question 1194.”…

## Lucas: Q. 1180

This is my translation of Lucas’s 1877 proof that a square pyramid of balls will only have a square number of balls if the base side is twenty-four. “Solutions to questions posed in The New Annals: Question 1180.” M. Édouard…

## Gerono: Q. 1177

This is my translation of Gerono’s 1877 proof listing all the possible solutions (x, y) for the equation $$y^2 = x^3 + x^2 + x + 1$$. “Solutions to questions posed in The New Annals: Question 1177.” MM. Gerono, Nouvelles…

## Pyramids and Squares

I have been spending my free time the last few days on the task of working backwards through three proofs in a 19th century French language mathematics journal. This started with a simple question in the G+ Mathematics community, posted…