# What Makes Pi Special

How a circle's edge, width and waves all connect through π, shown with a rolling wheel, Archimedes' squeezed circle and the endless digits of π\.

By gentle\-fox\-147918bc

Topic: Maths

[Open the interactive Jig](https://ask.jig.com/j/Oo0lSoMMtKPw)

## Transcript

### 1. Meet π, the circle number

Every circle hides the same number\. Measure around its edge, then straight across its middle\. The trip around is always a little more than three times the trip across\. That ratio is called pi, written π, and it is about 3\.14\.

Drag the red wheel along its track to roll it\. Drag anywhere else to turn the table\.

### 2. Roll out the edge

Roll the wheel exactly one full turn\. Its rim paints a ribbon as long as the wheel's edge\. The blue bar across the wheel is its width, called the diameter\. Three diameters fit along the ribbon, plus a small gold piece\.

That gold piece is about 0\.14 of a diameter\. Three and a bit makes 3\.14\.

### 3. Any size, same π

Swap in a smaller or bigger wheel\. The ribbon shrinks or grows, yet it always holds the same 3\.14 diameters\. That is how a bike computer turns wheel spins into distance: each turn rolls you π times the wheel's width\.

A bike wheel 70 centimetres across rolls about 2\.2 metres every turn\.

### 4. Squeeze the circle

More than 2,000 years ago, Archimedes trapped π between two straight\-sided shapes, one inside a circle and one outside\. More sides hug the circle more tightly\. Slide to add sides and watch the gap close\.

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

### 5. Digits that never end

π's digits go on forever and never settle into a repeating pattern\. No fraction can ever equal it exactly, so mathematicians call it irrational\. Each bead on this spiral is one digit, coloured by its value\.

Computers have now worked out more than 300 trillion digits of π\.

### 6. Circles make waves

Spin the wheel and follow the yellow dot on its rim: up, down and up again\. Trace its height as it turns and you draw a wave\. Sound, light, ocean swells and radio all travel as waves, so π appears wherever things repeat\.

One whole wave here is exactly as long as the wheel's edge: π diameters\.

### 7. Steering through space

Space navigators use π to plan curved paths around the Sun and planets\. Plan this loop with π as just 3 and the probe misses home by a wide gap\. With 3\.14 it nearly closes, and with 15 decimals it lands right on target\.

NASA's most precise navigation uses about 15 decimals of π\. More would change almost nothing\.

### 8. π is everywhere

Wheels, waves, pizzas and planets: wherever there is a circle, a curve or a rhythm, π is quietly at work\. People celebrate it every year on Pi Day, March 14, written 3/14\. Drag the wheel to roll it once more\.

A pizza twice as wide holds four times as much, because circle areas use π too\.