# Pi Representation Project

For Pi Day 2023 we ran a π representation project/competition.

We can now announce the winners! Please find the results here.

See the Pi art ideas below for future inspiration!

## Pi art ideas

### Giant Pi-skylines

This is a very simple idea where the digits of π are represented by bars of varying height in a picture made to look like a city-scape, with clouds or the night sky in the background and the bars as the cities’ towers. We found the Pi-skylines idea here.

Perhaps maths and art departments could join forces to encourage students to make a Pi-skyline? Or perhaps you could even make a whole school giant Pi-skyline happen! Could students take n digits each and contribute to a Pi-skyline long enough to cover a whole corridor, or the perimeter of a hall? Or could you cover all the school walls with striped π-wallpaper? The thickness and colour of the stripes could represent the digits of π.

### Martin Krzywinski’s Data Visualisation Art

Martin Krzywinski is a scientist who works on data visualisation applied to cancer research and genome analysis, but also uses his data visualisation skills to create artwork based on the digits of π. Perhaps students could take inspiration from his work.

Martin’s π artwork, featured here on his website, is both beautiful and informative. For example, in this piece from Pi Day 2013, the Feynman point (where the digit 9 appears six times consecutively) can be spotted in the bottom right hand corner (the colour of the outer ring of the nth circle represents the nth digit of π and the colour of its inner circle represents the (n+1)th digit). This piece of Martin’s artwork was used to make this interactive that enables key metrics in the artwork (for example the number of digits represented or the radius of the circles) to be varied by the user.

In his work, Martin uses many different characteristics besides colour to denote the different digits. For example, in this piece from Pi Day 2015 he uses a method called ‘tree mapping’ that splits areas into the number of pieces given by each digit. Read more about his method here

And our favourite piece represents π as a path that connects its successive digits. The circumference of a circle is split into 10 equal-length different-coloured arcs, with each arc representing a digit from 0 to 9. The path goes between these arcs, visiting each digit in order. The position on the arc where it and the path meet varies based on which digit of π (from the 1st to nth) is being represented. A layered effect is created, where no two lines sit entirely on top of each other.

Martin’s work was featured by James Grime in a Numberphile video ‘Pi is Beautiful‘ (below).

### Other Data Visualisation Artwork

In this artwork, as in Martin’s work, π has been represented by a path between successive digits, but here the digits are not arcs but single points equally spaced around the circumference of a circle.

π could also be represented using a ‘random walk’, a technique invented by mathematician John Venn where digits are represented by a direction. Venn represented 8 different digits in his ‘random walk’, but by adding two more directions we can represent the digits of π, as shown here by Jeffrey Thompson.

### Mile of π

If you’d prefer to not create something yourself, we created this resource a few years ago to help schools celebrate π. Our Mile of π resource is a printable version of the decimal expansion of π which can be used to decorate walls, floor and ceiling with up to a mile (1.6km) of transcendental goodness.