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Laguerre geometries and some connections to generalized quadrangles
2007
Journal of the Australian Mathematical Society
A Laguerre plane is a geometry of points, lines and circles where three pairwise non-collinear points lie on a unique circle, any line and circle meet uniquely and finally, given a circle C and a point Q not on it for each point P on C there is a unique circle on Q and touching C at P. We generalise to a Laguerre geometry where three pairwise non-collinear points lie on a constant number of circles. Examples and conditions on the parameters of a Laguerre geometry are given. A generalized
doi:10.1017/s1446788700037964
fatcat:xlti5hpcjrfsnovjq7owa5lzma