DescriptionHyperbolic geometry can be understood as a geometry of negatively curved surfaces. Many of its properties coincide with the properties of Euclidean geometry, but many others are different. For example, given a line and a point not on the line, in hyperbolic geometry one can find infinitely many lines passing through the point and disjoint from the line.It turns out that a mathematical object (such as a surface or a manifold) more likely admits hyperbolic structure than Euclidean one. This makes hyperbolic geometry one of the central subjects in modern mathematics. PrerequisitesWe will use some tools from linear algebra, algebra, and complex analysis. A willingness to learn geometry is also essential.ResourcesThe main source will be the book Hyperbolic Geometry by James W Anderson.Another very good reference is the book Hyperbolic Geometry by Caroline Series. You can also look at the wikipedia article on hyperbolic geometry. Some more references (including hyperbolic geometry based online fun) can be found here. |
email: Pavel Tumarkin