Unit 19
Patterns and chance.
Optional enrichment: chaos in a double pendulum, fractals and their dimension, and the prisoner's dilemma.
Before this unit
The unit, lesson by lesson
Lessons
3 lessons · 16 practice questions · about an hour
Chaos
Two almost identical double pendulums: motion fixed completely by its start that still cannot be predicted, a tiny gap that grows by multiplying, and why more precision buys very little time.
Fractals
Shapes whose every part is a small copy of the whole: how many parts each step makes, a perimeter that grows without end round a finite area, and a dimension that is not a whole number.
Game theory
The prisoner's dilemma: why betrayal pays in a single round even when cooperation is better for both, what happens when strategies compete over generations, and why a long game rewards tit for tat.