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In mathematics, a generalized conic is a geometrical object defined by a property which is a generalization of some defining property of the classical conic.For example, in elementary geometry, an ellipse can be defined as the locus of a point which moves in a plane such that the sum of its distances from two fixed points – the foci – in the plane is a constant.
AlphaGeometry is an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry.It was developed by DeepMind, a subsidiary of Google.The program solved 25 geometry problems out of 30 from the International Mathematical Olympiad (IMO) under competition time limits—a performance almost as good as the average human gold medallist.
Chapter 7 (by Milnor) describes the Lobachevsky function and its applications to computing volumes of hyperbolic 3-manifolds. Chapter 8 on Kleinian groups introduces Thurston's work on train track and pleated manifolds. Chapter 9 covers convergence of Kleinian groups and hyperbolic manifolds. Chapter 10 does not exist.
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points , lines , planes , circles , spheres , polygons , and so forth.
Whoopi Goldberg admits she'd leave “The View” if she had more money, says she's having 'a hard time' like many Americans
The suspense was centered on how far Ohio State, ranked No. 2 last week, would fall after its loss to Michigan and whether Miami, ranked No. 6 last week, would see its at-large hopes damaged after ...
In geometry, focuses or foci (/ ˈ f oʊ k aɪ /; sg.: focus) are special points with reference to which any of a variety of curves is constructed. For example, one or two foci can be used in defining conic sections , the four types of which are the circle , ellipse , parabola , and hyperbola .
Business leaders say they are relieved President-elect Donald Trump made a safe choice to lead the Department of Treasury after more unconventional selections to other cabinet posts.
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