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Category: Isn’t maths cool?
Anything about maths concepts or processes that I think is really cool.
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 […]
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The line at infinity: conics
The story so far
I promised Tina on Twitter that I would write about how the line at infinity relates to conics, and I’ve been doing it in the last two blog posts.
First, I talked about what the line at infinity is. We noticed that a set of parallel lines all share a slope, so we […]
The line at infinity: coordinates
The story so far
I made a promise to someone on Twitter to talk about how conics relate to the line at infinity, but when I came to do that, I realised it’s a can of worms that will take a few blog posts to untangle. Last time, I talked about how I construct and think […]
The line at infinity
Why I’m doing this
I foolishly said this on Twitter about a month ago:
@DavidKButlerUoA @MathguyArt on the line at infinity? Tell me about those!
— Tina Cardone (@crstn85) June 14, 2016
At the time I declared this was a bit of a can of worms and I promised to write something and post it later. Well, here it […]
A Day of Maths 5: Looking at Maths Art
This is the fifth in a series of posts coming from my Maths Day in a Year 7 classroom. So far I’ve talked about the following:
how awesome the day was
how I implemented Quarter the Cross
the unexpected things that happened with Zero Zeros
how I implemented Spotless Dice
You may be thinking by this stage, “David, how much […]
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Quarter the Cross
At the end of last year, the MTBoS (Math(s) Twitter Blog-o-Sphere) introduced me to this very interesting task: you have a cross made of four equal squares, and you are supposed to colour in exactly 1/4 of the cross and justify why you know it’s a quarter. I call it “Quarter the Cross”.
(The teachers who […]
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The crossed trapezium
Recently I started thinking about the properties of the following shape, which I like to call the “Crossed Trapezium”. It has two parallel edges, which are joined by two crossing lines.
Because of Quarter the Cross, I’ve also been interested in areas recently, so of course I had a desire to know more about the area […]
The trig functions are about multiplication
When I was taught trigonometry for the first time, I learned it as ratios of sides of right-angled triangles. Like this:
Most students coming into a Science degree at the University of Adelaide are at least vaguely familiar with this, and it’s their first instinct when using trigonometry. However, the lecturers in Physics and Engineering don’t […]
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A story instead of stars and bars
In a recent post (Counting the Story), I talked about how if you look closely at most solutions of combinatorics problems, you’ll see that they actually count the story of constructing the object rather than the object itself.
One exception to this is a problem like this:
“The balloon man has a huge collection of balloons in […]
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