Original title: Projective Geometry and the Law of Mass Action
Authors: Gottvald, Aleš
Document type: Papers
Conference/Event: Mendel 2009 - International Conference on Soft Computing /15./, Brno (CZ), 2009-06-24 / 2009-06-26
Year: 2009
Language: eng
Abstract: A new law of nature asserts that chemical equilibria and chemical kinetics are governed by fundamental principles of projective geometry. The equilibrium constans of chemical reactions are the invariants of projective geometry in disguise. Chemical reactions may geometrically be represented by incidence structures, which are preserved under projective transformations. Theorems of Ceva, Menelaus, and Carnot for triangles and n-gons represent the chemical equilibria, while Routh's theorem represents non-equilibria. Intrinsically projective Riccati's differential equation, being also generic to many other equations of mathematical physics, governs parametric dependence of the equilibrium constants. The theory offers tangible geometrizations and generalizations to the Law of Mass Action, including a new projective-geometric approach to soft computing of very complex problems.
Keywords: Camot's theorem; Ceva's theorem; chemical equilibrium; cross-ratio; cyclic products; incidence structure; law of mass action; Menelaus' theorem; projective geometry; Riccati's equation; Routh's theorem
Project no.: CEZ:AV0Z20650511 (CEP)
Host item entry: Mendel 2009 - 15th International Conference on Soft Computing, ISBN 978-80-214-3884-2

Institution: Institute of Scientific Instruments AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0179666

Permalink: http://www.nusl.cz/ntk/nusl-40958


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