Squares in Rectangles

Euclid’s algorithm, drawn

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

• A continued fraction repeatedly splits off whole parts and flips the remainder.
• Its terms come from Euclid’s algorithm, or from cutting squares off a rectangle.
• Rational numbers give finite continued fractions; irrational numbers infinite ones.

Steps

1. One over, one over…
2. Cutting off squares
3. Count the squares
4. Your turn
5. Back to a fraction
6. All ones