Lie Geometry The Lie Quadric figure Courses at UCSD, LaJolla, California, USA - Fillmore and Springer Jay P. Fillmore - University of California at San Diego Arthur Springer - San Diego State University Twenty two-hour lectures Spring 1988 - hand-written notes by Fillmore Spring 1990 - typed notes by Fillmore and Springer Spring 1992 - additions to Spring 1990 course Two important references are in: The geometric vein, The Coxeter Festschrift, C. Davis, B. Grünbaum, and F.A. Sherk, eds., Springer, New York, 1981. * J.F. Rigby, The geometry of cycles and generalized Laguerre inversion, pp. 355-378. Mathematical Reviews (MathSciNet): MR661792 Zentralblatt MATH: 0499.51003 * I.M. Yaglom, On the circular transformations of Möbius, Laguerre and Lie, pp. 345-353. Mathematical Reviews (MathSciNet): MR661791 Seminars 1988 Fillmore Seminar on Lie Geometry Universidad Central de Venezuela notes 1993 Fillmore and Springer Informal Seminar on Lie Geometry University of California, San Diego notes Talks 1977 Fillmore On Lie's Higher Sphere Geometry Colloquiun talk University of Minnesota, Minneapolis, Minnesota notes 1991 Fillmore and Springer (both are speakers) Old and New Euclidean Theorems from Lie Geometry. I and II. AMS San Francisco, January 16 transparencies 1994 Fillmore (speaker); Arthur Springer The Generalized Apollonius Contact Problem AMS Minneaolis, Minnesota, August transparencies - additional transparencies Papers 1979 Fillmore On Lie's higher sphere geometry. Enseign. Math. (2) 25 (1979), no. 1-2, 77--114. MR0543553 (81f:53041) article - seals - Swiss Electronic Acacdemic Library Service 1995 --------; Arthur Springer; Planar sections of the quadric of Lie cycles and their Euclidean interpretations. Geom. Dedicata 55 (1995), no. 2, 175--193. MR1334212 (96j:51005) Articles 2000 Fillmore and Springer Determining circles and spheres satifing conditions which generalize tangency article earlier Fillmore and Springer version An algorithm for determining circles and spheres satisfying conditions which generalize tangency article