## Modeling in GeoGebra

Introduction In this entry, I’m going to demonstrate the use of GeoGebra to estimate a value for a fairly tricky trigonometry problem, then illustrate how...

## Angles and Congruence

Congruence As I discussed in an earlier post, there are two basic definitions of geometric congruence that are presented to students. The first is based on meas...

## Programming, Mathematics, and Language

I’ve been struggling for a while now to find a way to frame and articulate the answer to what seems like a simple question: “What is mathematics?...

## The Golden Ratio and Generalizing Quadratics

A poster on the Google Plus Mathematics community commented that one feature of the Golden Ratio ϕ is that adding one to ϕ yields the same value as squaring ϕ d...

## Negative Bases

And now, for something silly. In general, number bases are expected to be positive integers greater than one. The most widely used are decimal (because we have ...

## What Do Digits Mean, Anyway?

Puzzle I found this puzzle in the G+ Mathematics community, courtesy of Paul Cooper. Solve the final addition: 50 + 60 + 90 = 380 30 + 40 + 60 = 330 90 + 60 + 7...

## A pair of probability problems

I’ve recently come upon two probability problems with counterintuitive solutions. One I’d seen before and dismissed because I didn’t understan...

## All Lines are Congruent

A standard high school geometry textbook talks about congruence in terms of three types of objects: Line segments, angles, and polygons. Congruence is then defi...