Octagrammum mysticum and the golden cross-ratio

Abstract

When the authors met at a geometry conference at Easter 1999, they found that each had discovered and investigated an elegant result (Theorem 2.1) about an octagon inscribed in a conic, Larry Evans algebraically and John Rigby synmetically. This turned out to be a rediscovery, as the result had been discussed by E. H. Lockwood in the Gazette in 1967, in an article that complements the present article. Also, almost a century earlier in 1872, the result had been posed somewhat imprecisely by T. T. Wilkinson as a problem in the Educational Times. There is a surprising connection between a special case of the octagon theorem and the golden cross-ratio.