Visualizing Pi

There are many ways to visualize pi, the number which describes circles and symbolizes completeness. As pi is irrational, it is an infinite and irregular chain of digits. It begins with 3.1415… and the first one who could constrain pi was Archimedes in the ancient Greece. Many people try to calculate pi more precisely (in August 2013, 12.1 Trillion digits were known), but it is also possible to visualize pi in a spiral.

Pi in a circle

We can use a colour palette, where every number from 0 to 9 is mapped to a colour:

Colour palette

As pi is used to describe a circle, we can use a circle to visualize pi. For this, we can divide a circle in 10 sections, where 1 section represents one number in the range of 0 to 9. We can also the segments with a line. Starting at the number 3, we draw a line to number 1, and from 1 to 4, from 4 back to 1, and so on, as pi starts with 3.141. Using this method, we get the following circle for the first 10 digits:

Pi Circle with 10 digits

And the circle for 20,000 digits:

Pi Circle with 20,000 digits

Pi in a spiral

We can roll this sequence of circles up to an Archimedian spiral:

Archimedian spiral for pi

If we use this procedure to represent the first 3000 digits of pi, we get a large spiral:

Archimedian spiral for pi of 3000 digits

In this spiral, we can highlight sequences of numbers, for example all sequences where at least two neighboured digits are equal. Then the spiral takes a new shape:

Archimedian spiral for pi with sequences

Squaring of pi

We can also visualize pi in a square of 30 x 30. In the first row, the first 30 digits are represented, in the second row the second 30 digits, etc. The result of the procedure Looks like this:

Pi in a square

In this grid, we can connect adjacent circles of the same colour:

Pi in a square with adjacent circles connected

If we remove all the circles, we get a set of forms:

Pi in a square with forms