Unit Overview
Introductory Student Activities
The Sierpinski Triangle
Paper Folding the Dragon
Iteration: Order in Chaos
A Million Grains of Rice
Sensitive Dependence on Initial Conditions
Simple Model for a Complex System
The Evolution of a "Gizmo"
Web Resources
Ideas for Field Trips
Extension Activities
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There are two overarching objectives of this unit. Students will understand that:
- chaos theory is used to understand complex, dynamic, physical systems in a new way.
- randomness can occur in apparently normal data calculations and conversely, patterns can be found
in apparently random data.
For centuries scientists believed that mathematics could be used to accurately predict long-range outcomes,
as long as the starting conditions were well understood and the variables were accurately measured (cause and effect).
This view of the world, based on Newton's Laws, is linear and deterministic. It is now understood that measurements
cannot be made with infinite accuracy and that mathematics yields accurate predictions only in the short-term.
Dynamic systems are non-linear and indeterminate.
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