Abstract
When Bolyai János was forty years old, Philip Beecroft discovered that any tetrad of mutually tangent circles determines a complementary tetrad such that each circle of either tetrad intersects three circles of the other tetrad orthogonally. By careful examination of a new proof of this theorem, one can see that it is absolute in Bolyai’s sense. Beecroft’s double-four of circles is seen to resemble Schläfli’s double-six of lines.
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Coxeter, H. (2006). An Absolute Property of Four Mutually Tangent Circles. In: Prékopa, A., Molnár, E. (eds) Non-Euclidean Geometries. Mathematics and Its Applications, vol 581. Springer, Boston, MA. https://doi.org/10.1007/0-387-29555-0_5
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DOI: https://doi.org/10.1007/0-387-29555-0_5
Publisher Name: Springer, Boston, MA
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