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Chaos Theory and Mathematics
Transcript of Chaos Theory and Mathematics
By: Kate and Isaac Henri Poincaré Three Body Problem Jacques Hadamard Three-Body Problem there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point http://upload.wikimedia.org/wikipedia/commons/4/45/Double-compound-pendulum.gif http://www.crossgroup.caltech.edu/chaos_new/Lorenz.html What is chaos? 1) sensitive to initial conditions
2) topologically mixing
3) dense periodic orbits the system will evolve over time so that any given region or open set of its phase space will eventually overlap with any other given region every point in the space is approached arbitrarily closely by periodic orbits What is NoT Chaos Theory? http://www.southparkstudios.com/clips/153995/chaos-theory And now to answer the TOK Question: In what sense might chaos (non-linear dynamical system) theory
suggest a limit to the applicability of mathematics to the real world? Weather Now we know what chaos is...
What is Chaos THEORY? • Uses applications from applied mathematics, physics, economics, biology, and philosophy
• Studies the behavior and results of systems that are highly sensitive to initial conditions (ex. Rounding errors)
• There is no way to predict these systems, thus it is known as deterministic chaos
• Also referred to as the butterfly effect Solar System Predictions Environmental Predictions Molecular Predictions Works cited:
WE DON'T How do we know
what we know?? WE DON'T