Written and performed by TRM intern Siddiq Islam. Siddiq is a second year maths student at the University of Oxford. FULL LYRICS BELOW.

The show was first performed at IF Oxford – the Oxford Science and Ideas Festival. With thanks to the London Mathematical Society (LMS) for financial support for the event.

I’m in a love triangle
I wish polygons existed that only had two sides
It’s not viable
Between two points in Euclidean space you can only draw one line

I’m in a love isosceles
And this is quite possibly the worst I’ve ever felt
Is there something wrong with me
For wishing polygons existed that only had two sides?

Well, hold on just one second! Maybe they do
Just make a zero angle between me and you
We’d have overlapping edges in our unusual polygon
And if you disapprove of what you hear
I could plot the sides as great arcs on a sphere
So the edges are distinct and now it’s clear what’s going on…

I’m in a love biangle
Totally in love and there’s no one else in sight
It’s so magical
Knowing polygons exist that only have two sides

I’m in a love digon
Nobody else to rely on, it’s just you and me
In our own atmosphere
We’re just two corners on a happy sphere with two great smiles between

Well hold on just one second as I cause a scene
If biangles are shapes then doesn’t that mean
That from the very start I could have been not two but one?
A single vertex on a sphere all alone
A single edge that runs from me to my own
I think this is the loneliest shape ever known to anyone…

I’m in a love monagon
No, there’s nobody on this Earth in love with me
What’s going on?
This could never have existed in Euclidean 2-D

A love monagonal dihedron
Nobody to lean on ‘cos it’s only me
In this sad town
That’s cut in two by a sad frown running in between

Well hold on just a second just one more time
If I were to continue on this downward climb
Remove the last vertex, Could there be a zero-gon?
No vertices with no edges in between
Now, what the hemisphere does that even mean?
I think that I was better off just being stuck with
Standard definitions of a shape
If ‘polygon’ means ‘many angles’, how could one or zero ever count?
Maybe I was destined to be in a

Love triangle 
Everything is fine, one line going in between each guy
It’s so reliable
Knowing polygons exist only if they have at least three sides…