Pi Experiments
Animations show the properties of pi and how to calculate it.
Rolling circle
Roll the circle once without slipping. The distance traveled is its circumference; divide it by the diameter to get pi.
- Distance
- 0.000000
- Diameter
- 1
Regular polygon approximation
Approximate the circle’s circumference with polygon perimeters, then divide by its diameter to estimate pi.
- Inscribed
- 3.000000 ÷ 1 ≈ 3.000000
- Circumscribed
- 3.464102 ÷ 1 ≈ 3.464102
How it works
A regular polygon’s perimeter is its side length times its number of sides. As you add sides, its perimeter approaches the circle’s circumference. Dividing by the circle’s diameter gives an approximation of pi. Inscribed polygons give smaller values and circumscribed polygons give larger ones, so you can also check the approximation’s accuracy. Archimedes used this approach. Displayed bounds are rounded outward to keep pi inside the interval.
n × sin(π / n) < π < n × tan(π / n)
Monte Carlo method
Estimate pi from the share of random points inside the circle.
The diagram displays up to the first 20,000 points.
- Total dots (N)
- 0
- Inside the circle (M)
- 0
Circle area
Cut the circle into sectors and rearrange them without changing its area. Finer cuts bring the shape closer to a rectangle.