I don’t know about you, but right now maths is serving as a happy distraction from what’s going on outside. (You are *inside*, aren’t you?)

If there wasn’t currently a pandemic on, right now I’d be starting to think about how this year’s Big Internet Math-Off would run. Instead, I’ve had an idea: let’s have fun talking about interesting bits of maths *now*.

So, I’ve had an idea: the **Big Lock-Down Math-Off**. It’ll run like this:

- Anyone who wants to take part, can.
- Send in your pitch for a bit of fun maths.
- I put all the pitches I receive in a pile
- Each day, I pick two pitches off the pile, put them on the site and pit them against each other.
- Everyone votes on the bit of maths that made them go ‘Aha!’ the most.
- This continues until I run out of pitches, or we’re allowed outside again.
- At the end, everyone wins.

I’ve already been in touch with some past Math-Off contenders, and it seems there’s some appetite for distracting ourselves with mathematical enthusiasm. I’d been low-key worrying about how to run this year’s tournament and who to invite, so I think I’ve solved a couple of problems here.

For this to work, I need two kinds of people:

## Contenders

If you’ve got the time and mental bandwidth to make a pitch for a bit of maths that you enjoy, please do!

Your entry should be a pitch for the topic you’re proposing. It can include text, pictures, a video, links to resources, anything that can go in a blog post. You can include stuff that you haven’t made, or stuff that you’ve already put out on the internet; if you just add a sentence saying why you think the thing is cool, that’s fine. Enlisting the help of others to make your pitch is fine. I don’t want a lecture, or a wall of introductory lemmas – handwaving, and linking to deeper explanations, will make it more approachable.

Once you’ve made your pitch, send it in to upload.aperiodical.com. You can upload whatever files you like there, and I’ll see them. Please include whatever identifying information you’re willing to give. Anonymity is fine: I’ll make sure pitches by anonymous entrants only go up against other anonymous pitches.

You can submit more than one pitch, and there’s no deadline: we’ll keep adding pitches to the queue after the Math-Off has started.

If you make a video, *please don’t upload it to us!* Instead, put it on your own YouTube account (or whatever service you prefer) and send in a document with the link to the video.

For text, a Word document is fine, as is LaTeX.

## Helpers

After last year’s tournament, a few people offered to help with admin for the next round. This year, I can use your help!

I’ll need people to help with transferring pitches from the drop-box to the Aperiodical’s editor, and setting up the polls.

If you’d like to help, please email root@aperiodical.com and I’ll give further instructions. Helpers can still make pitches – I’m planning on making a pitch or two myself.

The Big Lock-Down Math-Off will begin once I’ve got about 10 pitches. So get cracking!

Um tópico de matemática de considerável relevância é sobre a prova da inexistência de funções de caminho único. Uma sugestão para uma possível solução da questão está descrita a seguir: dada uma função genérica qualquer que seja, por exemplo, f(x): R—>R, então um método geral proposto para encontrarmos a sua função inversa de f(x)’: R—R, é que poderemos aplicar os conceitos e definições de análise matemática e utilizando os cálculos de integrais sucessivas, descobrirmos a função primordial mais primitiva e trivial correspondente a função inicial f(x), qual seria f(x)*: R—>R. Inferindo-se que f(x)* é naturalmente inversível, calculamos f(x)*’: R—>R, deduzindo-se daí a prova de que toda e qualquer função matemática possui inversa, respectivamente.

Take a rectangle $ABCD$ and bisect it with a diagonal $BD$. In the triangle $BCD$ inscribe a circle centre $E$. Construct through $E$ lines parallel to $AB$ and $BC$ to intersect $AB$ and $AD$ at $F$ and $G$. Prove that the area of rectangle $AFEG$ is exactly half the area of $ABCD$.