# What Makes π Special

A playful workbench where a rolling wheel, Archimedes' polygons, falling matches, waves and orbits reveal the number π and where it is used

By brave\-moon\-9303e0a0

Topic: Maths

[Open the interactive Jig](https://ask.jig.com/j/x369BcVhbraN)

## Transcript

### 1. What makes π special?

Measure around any circle, then measure straight across it\. The distance around is always a little more than three times the distance across\. That number is called pi, written π\. Drag the workbench to look around\.

π starts 3\.14159 and its digits go on forever\.

### 2. Roll the wheel

Roll the wheel exactly one turn and let it paint its path\. Then lay rods as long as the wheel is wide beside the stripe\. Three rods fit, with a little bit left over\. Three and a bit: that is π\.

The distance around a circle is its circumference\. The distance across is its diameter\.

### 3. Any size, same π

Make the wheel tiny or huge\. The stripe grows and shrinks with it, yet it always holds three rods and the same little bit\. A coin, a pizza and a Ferris wheel all share this one number\.

Around ÷ across = 3\.14159… for every circle ever drawn\.

### 4. Squeeze the circle

More than 2,000 years ago, Archimedes trapped the circle between shapes with straight sides\. Add more sides and the shape hugs the circle tighter, so its distance around creeps closer to π\. With six sides it gives exactly 3\.

Archimedes went up to 96 sides and showed π is between 3\.1408 and 3\.1429\.

### 5. Digits without end

No fraction is exactly π, so its digits never stop and never fall into a repeating pattern\. Mathematicians call a number like this irrational\. Watch the ribbon of digits keep unrolling\.

In 2025 computers worked out 314 trillion digits of π\. 22/7 is a handy guess, but it is a little too big\.

### 6. Drop matches, find π

Here is a surprise\. Drop matches on lined paper, where each match is as long as the gap between lines\. Count the drops, count the matches that cross a line, and two times drops divided by crossings lands near π\.

Georges\-Louis de Buffon described this puzzle in 1777\. The more matches you drop, the closer it tends to get\.

### 7. π at work

Anything that turns or repeats uses π\. A wheel travels π times its width in one turn\. A point going round a circle draws a wave, like sound and radio\. Spacecraft paths around planets are worked out with π too\.

NASA navigators use π to 15 decimal places\. Over tens of billions of kilometres, that is off by only a few centimetres\.

### 8. Happy π Day

One simple question about circles leads to a number that never ends and turns up everywhere\. People celebrate it every year on March 14, written 3/14\. Keep exploring, and look for π in every circle you meet\.

Only 38 digits of π are needed to measure the whole visible universe to the width of a hydrogen atom\.