"Nonlinear" doesn't mean "curved." It means "everything else left after you take out the linear". That's a huge inifinity of possibilities.
for example, people don't realize that linearity implies f(0)=0. If it's a const and you can't move origin, linearity breaks.
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OK - I'd have said that linear or not refers to functions and that in that domain, if d2/dx2 NE 0 was a definition.
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Jerky lines clearly meet the criteria as do irregular curves. I'll need to think about your dean of linearity.
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