= Ideal centre of a horocycle
= Ideal centres of horocycles
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= Horocycle centre
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The ideal centre of a <horocycle> is its point of tangency to the boundary at infinity; a horizontal <horocycle> in the <upper half-plane model> has centre infinity. Sending the centre to infinity by an <isometry> makes the <horocycle> horizontal. Orthogonal <hyperbolic lines> then become vertical, proving that a <hyperbolic line> meets a <horocycle> orthogonally exactly when it has the centre as an <ideal endpoint>.
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