# Mathematics

## 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…

## 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

## 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…

## SSA Congruence: Constraints

In my last post, I pointed out that SSA is in fact sufficient for determining all three sides and angles under certain conditions. In this post, I will specify those conditions, with illustrations. Given two noncollinear segments $$\overline{S_1}$$ and $$\overline{S_2}$$…

## Fibs Our Geometry Teachers Told Us: SSA

There is a standard litany of theorems involving proving triangle congruence that has remained largely unchanged since my high school days. I was told that, to prove that two triangles are congruent, we need three pieces of information. The abbreviations…

Mathematics

## The Pizza Party

In this post, I’d like to reflect on story problems and the purpose of mathematics education. Consider this problem: Every week, Julie invites some friends over for pizza. Last week, she had four friends over and they ate one whole…

## Object-Oriented Geometry

In an earlier post, I reflected on the relationship between mathematics, language, and computer programming. One detail of that has been on my mind quite a bit lately, as I’ve been teaching geometry. While early computer programming was heavily reliant…