Projective Geometry and the Law of Mass Action

0335097 - ÚPT 2010 RIV CZ eng C - Conference Paper (international conference)
Gottvald, Aleš
Projective Geometry and the Law of Mass Action.
Mendel 2009 - 15th International Conference on Soft Computing. Brno: Brno University of Technology, 2009, s. 259-268. ISBN 978-80-214-3884-2.
[Mendel 2009 - International Conference on Soft Computing /15./. Brno (CZ), 24.06.2009-26.06.2009]
Institutional research plan: CEZ:AV0Z20650511
Keywords : projective geometry * chemical equilibrium * law of mass action * cross-ratio * incidence structure * Ceva's theorem * Menelaus' theorem * Routh's theorem * Camot's theorem * cyclic products * Riccati's equation
Subject RIV: BA - General Mathematics

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.
Permanent Link: http://hdl.handle.net/11104/0179666