# Category: Isn’t maths cool?

Anything about maths concepts or processes that I think is really cool.

#### Gerry-mean-dering

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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#### Introducing Digit Disguises with a small game

Because [reasons], my game Digit Disguises has been on my mind recently, and reading the original blog post from 2019, I suddenly realised I had never shared my ideas on how to introduce the game to a whole class at once. This blog post fixes that. To keep in the spirit of it, I have […]

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#### The line joining two complex points using i-arrows

Nearly two weeks ago, I first wrote about the i-arrow visualisation of the points in the complex plane. Here’s a reminder of how they work:
Every point with complex coordinates is represented as an arrow (which I call an “i-arrow”) from one place to another on top of the Cartesian plane.

Real points are dots […]

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#### The complex points on unreal circles using i-arrows

Introduction
This is the last (for now) post in a series about about i-arrows, which are a way I have created of visualising the complex points on graphs in the real plane. As I’ve done for every other post since the first one, I will repeat the description here.
Every point with complex coordinates is represented as […]

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#### The complex points on real circles using i-arrows

Introduction
This is the second last (it was going to be the last, but it got too big so I made it a separate one) in a series of blog posts about i-arrows: a way I have created of visualising complex points on real graphs. The first blog post described how they work, and I repeat […]

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#### The complex points on a line in finite geometry using i-arrows

Why I want a finite plane
In the previous several blog posts (in particular this one), I have been investigating a new representation of complex points called i-arrows. The idea is that every complex point is represented as an arrow from one point to another on top of the Cartesian plane. In particular, the complex point (p+si,q+ti) […]

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#### UPDATES on the complex points on a line using i-arrows

On 27th July 2022, I wrote a blog post about using i-arrows to make sense of the complex points on both real and unreal lines. And at the end I mentioned how there were still some things mysterious to me. But of course I kept thinking about them and now I know more things.
I’ll keep […]

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#### The complex points on a line using i-arrows

Introduction
The Cartesian plane is pretty cool. You think up an equation like y=x²+1 and find all the points (x,y) whose coordinates satisfy it, and you get a shape (in this case a parabola). Different kinds of shapes have different kinds of equations, and finding the places where shapes meet becomes solving equations simultaneously. Geometry becomes […]

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#### Where the complex points are: i-arrows

Problems with i-planes
Once upon a time in 2016, I created the idea of iplanes, which I consider to be one of my biggest maths ideas of all time. It was a way of me visualising where the complex points are on the graph of a real function while still being able to see the original […]

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#### My first Maths Teacher Circle

Last week I participated in my first Maths Teacher Circle. I just want to do a quick blog post here to record for posterity that I did it and it was excellent. I choose to take the practical approach of just relating what happened.
I had been interested in somehow going to one since I heard […]

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