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Antipodal points

Posted on: September 6th, 2015 by
2

Let f(t) be a continuous periodic function with period T, i.e.
  1. f(t) is continuous over reals.
  2. f(t+T) = f(t) for all real t.
Show that there always exists some time instant t_0 for which f(t_0) = f(t_0+T/2).

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