Bisection

Trap the root and halve

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• If a continuous function changes sign on an interval, a root lies inside.
• Bisection halves the interval each step; it always works but is slow.
• After $n$ steps the width is $2^{-n}$ of the original.

Steps

1. Squeeze it
2. Halving the interval
3. How many steps?
4. When bisection can’t start
5. Three midpoints
6. Six decimal places