Best Approximations

Why 355/113 is so good

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Truncating a continued fraction gives convergents, the best rational approximations.
• Large terms make the preceding convergent exceptionally accurate (355/113 for π).
• Convergents obey a simple recurrence.

Steps

1. Convergents
2. A string pulled tight
3. Record breakers
4. How good is 22/7?
5. The big jump
6. Close call
7. Next convergent