Cayley–Klein metric
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In mathematics, a Cayley–Klein metric is a metric on the complement of a fixed quadric in a projective space which is defined using a cross-ratio. The construction originated with Arthur Cayley's essay "On the theory of distance"[1] where he calls the quadric the absolute. The construction was developed in further detail by Felix Klein in papers in 1871 and 1873, and subsequent books and papers.[2][3][4][5][6][7][8][9] The Cayley–Klein metrics are a unifying idea in geometry since the method is used to provide metrics in hyperbolic geometry, elliptic geometry, and Euclidean geometry. The field of non-Euclidean geometry rests largely on the footing provided by Cayley–Klein metrics.