Mathematical diagrams

There’s no excuse for any authors to be satisfied with less than perfection in their diagrams – for simple diagrams at least. Software, both commercial and open-source, can now produce diagrams of extraordinarily high quality. But I keep coming across published books where the excellence of the exposition is let down by the [...]

3D visualization

Most mathematical software will allow you to create elegant graphs and objects in 3D; often you can then move your graph around with the mouse, finding the position at which it looks best. For complicated shapes like minimal surfaces, finding the parameters and position which produce the best view can be more time-consuming than [...]

Australian-American educational terms

At an educational conference I went to recently, I attended a workshop, during much of which I was hopelessly confused. It turned out that my confusion was caused by educational terms in America have different meanings in Australia.
Here then is a little table showing some of the different terms:

American
Australian

Program
Course

Course
Subject

Assessment
Evaluation

Grading
Assessment

As you see, there’s plenty of [...]

Teaching mathematics: programming or CAS?

I’ve got a few books which aim to teach (discrete) mathematics through the use of a programming language: one book uses Haskell; the other Python. Now I like both these languages – I find them elegant, fun to program in (at my elementary level, anyway), and as languages for teaching programming I think they [...]

Mathematics and origami

For those of us who are, or were, avid paper-folders, there’s a flourishing field of mathematically-inspired origami. This goes in two directions: using origami to illustrate mathematical principles or theorems, and discovering new mathematical and algorithmic aspects to origami.
Just to whet your appetite, here are two examples. The first is dividing a square [...]

The RSA Theorem

Let and be distinct primes, and let satisfy . Then for any , .
For some reason, even in published works, this important cryptographic result is often only half proved. Here is a full proof.
Proof: We consider two cases: (i) is relatively prime to both and (and hence [...]

Bravo, Julia Gillard

The current state of Australia’s maths education has been described as being in crisis. Low student enrolments at university, lowering of interest at schools, retiring of experienced maths teachers who aren’t being replaced, teachers at schools forced to teach beyond their knowledge level… the system is indeed in a dire state. The [...]

Van Aubel’s theorem

This theorem can be stated:
Start with any planar quadrilateral. Draw squares outwards from each edge, and draw lines between the centres of opposite squares. The two lines thus drawn will be equal in length, and perpendicular.
Here are some illustrations (from answers.com):

As you see, one of the pleasant things about this theorem is its [...]