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What are everyday ``nonlinear" examples?
Hello!
Is there a simple way to identify a nonlinear equation or physical system by looking at it?
I have sifted through material about unpredictability, chaos, fractals, and the other buzzwords encompassing ``nonlinear systems", and have glossed over mathematical explanations covered in Wiki articles, but do not seem to understand how to identify an algebraic nonlinear example other than ``variable cannot be separated", ``superimposed," is "non-homogenous". I am seeking a basic explanation for rather young kids in a gifted physics program.
For example, is an exponential, logarithm, root, or quadratic nonlinear as they do not conform to ``lines"? (Notwithstanding that I can just plot it against two logs to get a line.) And also, the above examples are ``predictable," no? Are they still nonlinear?
Does nonlinearity imply that despite knowing the initial conditions the outcome cannot be predicted?
(I solved the intersection of a quadratic and a linear equation, found two points, and am concluding the system is ``nonlinear" because the ``nonlinear" shape of x^2 (parabolic) causes the equation to be a ``system" of solutions (more than one point satisfies the bounds).
I am seeking an elementary school explanation and basic examples.
Thanks,
-E
Hello!
Is there a simple way to identify a nonlinear equation or physical system by looking at it?
I have sifted through material about unpredictability, chaos, fractals, and the other buzzwords encompassing ``nonlinear systems", and have glossed over mathematical explanations covered in Wiki articles, but do not seem to understand how to identify an algebraic nonlinear example other than ``variable cannot be separated", ``superimposed," is "non-homogenous". I am seeking a basic explanation for rather young kids in a gifted physics program.
For example, is an exponential, logarithm, root, or quadratic nonlinear as they do not conform to ``lines"? (Notwithstanding that I can just plot it against two logs to get a line.) And also, the above examples are ``predictable," no? Are they still nonlinear?
Does nonlinearity imply that despite knowing the initial conditions the outcome cannot be predicted?
(I solved the intersection of a quadratic and a linear equation, found two points, and am concluding the system is ``nonlinear" because the ``nonlinear" shape of x^2 (parabolic) causes the equation to be a ``system" of solutions (more than one point satisfies the bounds).
I am seeking an elementary school explanation and basic examples.
Thanks,
-E