For p, q ∈ S^1, the unit circle in the plane, let d_a(p, q) = min{|angle(p)...

For p, q ∈ S^1, the unit circle in the plane, let
d_a(p, q) = min{|angle(p) − angle(q)| , 2π − |angle(p) − angle(q)|}
where angle(z) ∈ [0, 2π) refers to the angle that z makes with the positive x-axis.
Use your geometric talent to prove that d_a is a metric on S^1.

Expert Solution

Colby Messinger answered 2 years ago

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