Pi approximation

Archimedes trapped π between the perimeters of polygons drawn inside and outside a circle of diameter 1. More sides squeeze the bounds together. Aryabhata gave π ≈ 3.1416.

π ≈ 3.14Pi approximation

📐 Formula

n sin(π/n) < π < n tan(π/n)

✏️ Worked example

Hexagons: 3 < π < 3.46. With 96 sides: 3.1410 < π < 3.1427.

🌍 Where it is used

How π was calculated before computers.

❓ Quick check

Which is closest to π?

🏋️ Practice

EasyAryabhata's value: 62832/20000 = ?

Answer: 3.1416

MediumIs 22/7 exactly π?

Answer: No (22/7 ≈ 3.1429)

ChallengeDo the bounds get closer with more sides?

Answer: Yes