The definition: A spherical neighborhood of a point is itself open-a-Euclidean Space in one dimension is a finite interval-Euclidean in two dimensions is a circle and Euclidean in 3-Dimensions and spheres- The blog looks the sphere in Euclidean-Geometry, non-Euclidean geometry, like sphere in a sphere or hyperbole for example, using differential geometry, topology and algebraic topology
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Saturday, December 15, 2012
Saturday, November 3, 2012
Hyperbolic Geometry in Solid Geometry
Lobatschewsky-Bolyai Geometry in Euclidean Geometry can be extend into by solid geometry by:
Space = Region of points inside a sphere.
Point = Point inside of a Sphere
Strait Line = Chord in the Sphere (i.e. Volume Cap is Pi*h^2*(3r-h)/3 and the spherical cap is 2*Pi*r*h)
Plane = Points of a plane section which are inside of the Sphe
Displacements = Projective transformation in the space (i.e. dot products, cross product and linear mapping), which change the region of the point inside the sphere itself
Space = Region of points inside a sphere.
Point = Point inside of a Sphere
Strait Line = Chord in the Sphere (i.e. Volume Cap is Pi*h^2*(3r-h)/3 and the spherical cap is 2*Pi*r*h)
Plane = Points of a plane section which are inside of the Sphe
Displacements = Projective transformation in the space (i.e. dot products, cross product and linear mapping), which change the region of the point inside the sphere itself
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