# Why π Is Special

How a circle's edge, a rolling wheel, waves and dropped needles all lead to the same number, π, from the ratio of a circle's length to its width\.

By Sasori Murasaki

Topic: Maths

[Open the interactive Jig](https://ask.jig.com/j/1wjE0ReC5IOW)

## Transcript

### 1. Why π Is Special

Every circle hides the same number\. Measure around a circle, measure straight across, and the long way is always just over three times the short way\. That number is π, said "pie"\. Drag anywhere to look around the workbench\.

π is about 3\.14159, and its digits never end\.

### 2. Roll the wheel

Roll the wheel exactly one turn\. The red tyre leaves a stripe as long as the edge of the wheel\. Each mark on the ruler is one wheel width, and the stripe ends a little past three: at π\.

You can also drag the wheel along the ruler yourself\.

### 3. Big or small, same π

Make the wheel bigger or smaller\. The ruler marks change with it, because they count wheel widths\. One turn always ends at π\. That is how a bike computer or a surveyor's measuring wheel turns spins into distance\.

This never changes: every circle in the universe gives the same π\.

### 4. Squeezing a circle

Around 250 BCE, Archimedes trapped π with shapes\. He fitted shapes with straight sides inside a circle and kept doubling the number of sides\. The more sides, the closer the shape hugs the circle, and the closer its edge gets to π widths\.

With 96 sides, inside and outside the circle, he showed π is between 3\.1408 and 3\.1429\.

### 5. Turning makes waves

Watch the dot go round the ring and follow its height on the board\. One full turn draws one wave\. Sound, light, swings and the electricity in your walls all repeat like this, so π turns up whenever things wiggle or spin\.

Spin faster and the waves pack closer together, like a higher note\.

### 6. Drop needles, catch π

Drop needles as long as the gap between the lines\. Count the needles and how many land across a line\. Twice the number of needles divided by the crossings creeps toward π\. Chance hides a circle, because each needle can point any way round\.

Georges\-Louis Leclerc, Comte de Buffon, described this puzzle in 1777\. It is slow: thousands of drops give only about two good decimals\.

### 7. How many digits do we need?

The digits of π, carved round the table edge, never end and never repeat\. In 2025 computers worked out 314 trillion of them\. Yet NASA steers spacecraft with just the gold ones: 15 decimal places\.

With 15 decimals, a circle 40 billion miles across comes out wrong by only about half an inch\.