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[–] 1 point2 points  (0 children)

Might the winding number be useful here?

[–] 0 points1 point  (1 child)

The "graph" transform (which may be a thing, but I'm just making up) G(f(t)) is that the image of f(t) satisfies:

(f(t), t % 2pi) for f(t) > 0

(f(t), (t+pi) % 2pi) for f(t) < 0

(0,0) for f(t) = 0

So find the minimal a such that G(f(t+a)) = G(f(t)) for all t.

So given some f(t), you'd want to write G(f(t+a) = G(f(t)), resolve it over the nine cases, and solve for the minimal a.

[–] 0 points1 point  (0 children)

This won't necessarily work. You are finding the period of f, but f may not be periodic. For instance, imagine a function that traces out two unit circles which meet at the origin and whose tangent line is the y axis. When theta is between 2kπ and 2(k+1)π, it traces out the right hand circle if k is prime, and the left hand circle otherwise. There is no period, but you only need to go around 4π if you pick, say [6π, 10π]
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