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...