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# Monthly Archives: July 2022

#### 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 […]

#### 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 […]

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

Introduction

In an earlier post in this same series, I presented the following introduction, and I think it’s good enough to just repeat here…

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). […]

#### 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) […]

#### 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 […]

#### 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 […]

#### 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 […]