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Category: Isn’t maths cool?
Anything about maths concepts or processes that I think is really cool.
The Sausage-Stacking Theorem
It’s no secret that the powers of two are some of my favourite numbers. There are so many interesting things to say about them that often I don’t know where to begin! (In case you’re not au fait with the terminology, the powers of two are the numbers you can make by starting with 1 […]
The square root of two
In first year maths, they briefly study the five families of number: the natural numbers N, the integers Z, the rational numbers Q, the real numbers R, and the complex numbers C. In particular, they focus on the distinction between the rational numbers and the real numbers. A classic proof they are given at this […]
The advent calendar function
In a previous post I discussed how we need ways to think about functions that are not curves on an x-y-plane. Well I have a seasonally-appropriate one for you: the Advent Calendar.
The advent calendar I have in mind is the kind where there is a little cardboard door for each day in December up to […]
Splitting logs
In our bridging course (and indeed in Maths 1M and Maths 1A and several other courses) there is a section on differentiating logarithmic functions. One of the classic questions that we ask in such a section is to differentiate the log of some horrifying function, with the intention that the students use the log laws […]
Archimedes’s Integrals
One of my staff (thanks Fergus) told me ages ago about Archimedes’ proof that the volume of a sphere is 4/3 π R3 (where R is the radius of the sphere). It is a very very cool proof and it’s high time I shared it! One of the reasons it is so cool is that […]
Where’s the t?
Once upon a time, I lectured Maths 1A calculus, and when I got to teaching hyperbolic trig functions I put a great deal of effort into making sure they were well-connected to other ideas the students knew. So I listed the properties of ordinary trig functions and alongside I listed the matching properties of hyperbolic […]
Two wrongs make a right
Students make a lot of mistakes when doing their maths, but sometimes they will make two mistakes in such a way that their final answer is still correct. This happened last week with one student quite spectacularly, because his doubly wrong method of doing a particular problem always produces the correct answer.
Let me explain: the […]
Maths is not Science
Let me say it again a little more emphatically: Maths is NOT Science. The major difference I want to focus on here is the concept of truth. Things are true in Maths, but they are not in Science.
Let me explain. As far as I can tell, Science is about coming up with models that explain […]
Quadric Cameo
As I said recently, quadrics hold a special place in my heart and I get excited every time the topic comes around in Maths 1B. Quadrics have so many cool things you can say about them, and are such a great opportunity to talk about the deep connection between algebra and geometry. I personally could […]
My conic likes to hide in boxes
Conics (or conic sections if you like) are very close to my heart. My PhD thesis was about conics and their higher-dimensional relatives, and way back in high school they were one of the bits I particularly loved. So it’s no surprise that I get excited each semester when the Maths 1B students study them.
The […]