# What Makes π Special

How π links every circle's diameter to its circumference, from Archimedes' polygon trick to the waves and orbits that rely on it\.

By Thierry Lefebvre

Topic: Maths

[Open the interactive Jig](https://ask.jig.com/j/nwNioYA39Mmf)

## Transcript

### 1. Meet π

π \(say “pie”\) is a number that belongs to every circle\. Its first digits are 3\.14159, and the glowing counter shows more\. Let's find out where it comes from, and where it turns up in real life\.

Drag any empty part of the scene to turn the table and look around\.

### 2. Roll out a circle

The line straight across a wheel, through its middle, is its diameter: the blue bar\. Roll the wheel exactly one turn and its red paint dot marks out the distance around it, the circumference\. Then line up blue sticks, each as long as the diameter\.

You can also tap the wheel to roll it\.

### 3. Every circle agrees

Make the wheel bigger or smaller\. The red trail always fits three diameters and a little extra yellow piece: about 3\.14 diameters\. That is true for a coin, a bike wheel or a whole planet\.

A bike computer uses this: every turn of the wheel carries you π times its diameter\.

### 4. Digits that never end

The digits of π go on forever and never settle into a repeating pattern\. That means no simple fraction is exactly π: 22/7 is close, but not quite\. Watch the counter run through the digits\.

By late 2025, computers had worked out more than 300 trillion digits of π\.

### 5. Archimedes' clever trick

About 2,250 years ago, Archimedes trapped π using shapes with straight sides\. Add more sides and the blue shape hugs the red circle, so the distance around it gets closer to π diameters\. The counter shows the sides and that distance\.

With 96 sides he proved π lies between 3\.1408 and 3\.1429\.

### 6. π makes waves

Watch the white peg as the wheel spins\. Its up\-and\-down motion draws a wave, and each wave is exactly as long as one trip around the wheel\. Sound, music, radio and Wi‑Fi are all built from waves like this\.

Whenever something repeats in cycles, engineers reach for π\.

### 7. π steers spacecraft

A probe circling a planet follows a curved path, and π helps plan every orbit\. NASA's navigators use π to just 15 decimal places\. That is plenty for journeys across the whole Solar System\.

With 15 decimals, a circle as wide as Voyager 1's journey would come out wrong by only a few centimetres\.

### 8. π is all around you

Pizzas, cans, wheels, waves and orbits all hide π\. Next time you see a circle, remember: the way around is always a little more than three times the way across\. Celebrate Pi Day every March 14, written 3\-14\.

Drag to look around the workshop, or revisit any step with the dots\.