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"Consider now an angular sector A(x, r, θ, v) inside a small disk B(x, r) of small angular aperture θ (measured in radians) centred around some direction v (a unit vector) emanating from x; this sector is well-defined, basically because the Riemannian metric gives us the notions of distance and angle."

I have googled and not found any reference to angular sector but have found references to circular sector. is there a difference and if there is what is an angular sector?

Thanks in advance.