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Quadrilateral family tree
I have always loved the naming of quadrilaterals, right from when I first heard about it in high school. I'm not entirely sure why, but some of it has to do with the nested nature of the definitions – I like that a square is a kind of rectangle and a rectangle is a kind of parallelogram.
One reason I'll still use pi
Every so often, someone brings up the thing with tau (τ) versus pi (π) as the fundamental circle constant. In general I find the discussion wearisome because it usually focuses on telling people they are stupid or wrong for choosing to use one constant or the other. There are more productive uses of your time, I think.
All dogs have tails
In maths, or at least university maths, there are a lot of statements that go like this: "If ...., then ..." or "Every ..., has ...." or "Every ..., is ...". For example, "Every rectangle has opposite sides parallel", "If two numbers are even, then their sum is even", "Every subspace contains the zero vector", "If a matrix has all distinct eigenvalues, then it is diagonalisable". Many students when faced with statements like these automatically and unconsciously assume that it works both ways, especially when the subject matter is new to them. This post is about a way of helping students see the problem.
Where the complex points are
When you first learn complex numbers, you find out that they give you ways to solve equations that were previously unsolvable. The classic example is the equation equation x^2 + 1 = 0, which if you're only using real numbers has no solutions, but with complex numbers has the solutions x=i and x=-i.
Brackets
I had a meeting with an international student in the MLC on Friday who has having a whole lot of language issues in her maths class.
TMC16 reflections from someone who wasn't there
This post is about my response to TMC16. For the uninitiated, TMC is short for Twitter Math Camp. This is a conference designed by teachers for teachers with teacher speakers, organised through the collective efforts of the Math Twitter Blog-o-Sphere (MTBoS) – a group of people who blog and tweet about their experiences teaching math(s). That description is not the best description of the MTBoS, but I'll get to that later.
[Read more about TMC16 reflections from someone who wasn't there]
David Butler and the Prisoner of Alhazen
Once upon a time, I did a PhD in projective geometry. It was all about objects called quadrals (a word I made up) - ovals, ovoids, conics, quadrics and their cones - and the lines associated with them - tangents, secants, external lines, generator lines. During the first two years, I did talks about my PhD research, which I could not resist calling "David Butler and the Philosopher's Cone" and "David Butler and the Chamber of Secants".
Mansplaining
A few months ago, I learned a new word: "mansplaining". You may have heard it before, but I never had until this year.
The line at infinity
I foolishly said this on Twitter about a month ago:
A Day of Maths
Last Monday, I was invited into my daughter's Year 7 classroom to do a full day of maths with the students. It was the Best Day Ever. I had so much fun giving the students things to think about, and watching and helping the students think and talk about them.
