(This song is about the solution in March 2023 of the Einstein Problem. The solution is tessera which became known as The Hat. To the tune of the Mexican Hat Dance as arranged by Alan Sherman)
Einstein’s Problem is hard mathematics,
It’s been gathering dust up in attics,
It’s a puzzle, that’s most enigmatic,
And the answer looks just like a hat.
It’s a polygon, almost deltaïc,
Fits together as in a mosaïc,
Its appearance is rather prosaïc,
‘Cause it looks very much like a hat.
You can cover the plane with triàngles,
You can cover the plane just with squares,
You can do it with oodles
Of Penrose’s doodles
But he only makes them in pairs.
They do more! They explore!
Four great mathematicians
Worked out the positions
And threw lots of hats on the floor.
It was drawn by a man on a mission,
It forms patterns without repetition,
And the man was no academician,
But an artist who liked drawing hats.
So he published a paper in ’Nature,’
And so far it’s not been peer-reviewed,
We shall wait for the comments
And see if it’s nonsense
Or whether they think it’s been proved.
Time will show, We don’t know,
Any Tom, Dick or Harry,
Or mad adversàry,
Can write in and say it’s not so!
If your bathroom’s in need of new tiling,
Something beautiful, new and beguiling,
That will leave you delighted and smiling,
There’s a shape just for you,
It’s not in B and Q,
It’s a damned sight more posh than a mat,
It’s a floor-tile that looks like a hat. Olé!