TAG: proofs


A recent video from Howie Hua showed how if you split a collection of numbers into equal-sized groups, then find the mean of each group, then find the mean of those means, it turns out this final answer is the same as the mean of the original collection. He was careful to say it usually […]

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Why mathematical induction is hard

Students find mathematical induction hard, and there is a complex interplay of reasons why. Some years ago I wrote an answer on the Maths Education Stack Exchange describing these and it’s still something I come back to regularly. I’ve decided to post it here too.
Some reasons why students find mathematical induction difficult.
These come from a […]

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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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Pretending not to know

Yesterday the Maths 1M students handed in an assignment question that asked them to prove a property of triangles using a vector-based argument. It’s not my job to help students do their assignment questions per se, but it is my job to help them learn skills to solve any future problem. This kind of problem, […]

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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 […]

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