The Broken Stick

Will the pieces make a triangle?

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

• Three lengths summing to 1 form a triangle when each is less than ½.
• Representing the two breaks as a point in a square turns probability into area.
• The probability is 1/4.

Steps

1. Two random breaks
2. The space of breaks
3. The answer
4. One long piece
5. The shortest piece
6. A single break