Summary
In this paper the Miquel-Clifford configuration is studied both from the standpoint of the projective geometry of the plane and of Mobius Geometry —the inversive geometry of the plane. By combining both view-points conditions are obtained for the Clifford Circle of 2t+1 lines to be (i) a straight line, (ii) a circle of given radius. It is also shown that at each of the points of multiple intersection of the configuration the concurrent circles cut at the same angles as at any other of these points.
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Literatur
W. K. Clifford, “Synthetic Proof of Miquel’s Theorem”,Mathematical Papers, p. 38.
Grace, “Circles, Spheres and Linear Complexes”,Trans. Camb. Phil. Soc., 1898,16, 31.
Neville, “The Inverse of the Miquel-Clifford Configuration,”Jour. Ind. Math. Soc., 1926, p. 241.
A. Narasinga Rao, “On certain Cremona-Transformations in Circle-Space connected with the Miquel-Clifford Configuration,”Proc. Camb. Phil. Soc., 1937,33, § 31.
V. Ramaswami Aiyar, “Note on a Class of Curves,”The Mathematics Student, 1936,4, p. 106.
Both here and throughout this paper the order of the letters in a bracket is a matter of indifference. The notation is that of my paper onCremona Transformations, etc.
Vide A. Narasinga Rao, “The Miquel-Clifford Configuration in the Geometries of Mobius and Laguerre,”Annamalai University Jour., VII, 1937.
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Rao, A.N. On the Miquel-Clifford configuration. Proc. Indian Acad. Sci. (Math. Sci.) 7, 68–74 (1938). https://doi.org/10.1007/BF03045381
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DOI: https://doi.org/10.1007/BF03045381