Search results
Results from the WOW.Com Content Network
An interesting example is the modular group = (): it acts on the tree given by the 1-skeleton of the associated tessellation of the hyperbolic plane and it has a finite index free subgroup (on two generators) of index 6 (for example the set of matrices in which reduce to the identity modulo 2 is such a group).
The proof was completed by Werner Ballmann about 50 years later. Littlewood–Richardson rule. Robinson published an incomplete proof in 1938, though the gaps were not noticed for many years. The first complete proofs were given by Marcel-Paul Schützenberger in 1977 and Thomas in 1974. Class numbers of imaginary quadratic fields.
P. Oxy. 29, one of the oldest surviving fragments of Euclid's Elements, a textbook used for millennia to teach proof-writing techniques. The diagram accompanies Book II, Proposition 5. [1] A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the
Abraham, R.; Marsden, J. E. (2008). Foundations of Mechanics: A Mathematical Exposition of Classical Mechanics with an Introduction to the Qualitative Theory of Dynamical Systems (2nd ed.).
Unlike most other books on mechanics, this one elaborates upon the virial theorem. The discussion of canonical and contact transformations, the Hamilton-Jacobi theory, and action-angle coordinates is followed by a presentation of geometric optics and wave mechanics. Eskergian believed this book serves as a bridge to modern physics. [7]
Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.
Antecedent of Playfair's axiom: a line and a point not on the line Consequent of Playfair's axiom: a second line, parallel to the first, passing through the point. In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate):
This was, in considerable part, influenced by the example Hilbert set in the Grundlagen. A 2003 effort (Meikle and Fleuriot) to formalize the Grundlagen with a computer, though, found that some of Hilbert's proofs appear to rely on diagrams and geometric intuition, and as such revealed some potential ambiguities and omissions in his definitions ...