1854/12/31 by Arthur Cayley · 1 citation
Mathematics · #History and Theory of Mathematics #Mathematics and Applications #Extension (predicate logic) #Mathematics #Order (exchange) #Combinatorics #Memoir #Surface (topology) #Steiner tree problem #Calculus (dental) #Mathematical economics #Computer science #Geometry #Art history #Art
paper · doi:10.1098/rspl.1850.0072
openalex publication_date 1854/12/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/14
Abstract The problem, in a triangle to describe three circles each of them touching the two others and also two sides of the triangle, has been termed after the Italian geometer, by whom it was proposed and solved, Malfatti’s Problem. The problem to which the author refers as Steiner’s extension of Malfatti’s Problem, is as follows: “To determine three sections of a surface of the second order, each of them touching the two others, and also two of three given sections of the surface of the second order,” a problem proposed in Steiner’s memoir ‘Einige Geometrische Betrachtungen’, Crelle, t. i. The geometrical construction of the problem in question is readily deduced from that given in the memoir just mentioned for a somewhat less general problem, viz. that in which the surface of the second order is replaced by a sphere; it is for the sake of the analytical developments to which the problem gives rise that the author proposes to resume here the discussion of the problem.