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Although Euclidean geometry, in which every line has exactly one parallel through any point, is most familiar to us, many other geometries are possible. Particularly important is hyperbolic geometry, in which infinitely many parallels to a line can go through the same point.
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www.ics.uci.edu/~eppstein/junkyard/hyper.html
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Hyperbolic geometry is similar to euclidean geometry in many respects. It has concepts of distance and angle, and there are many theorems common to both. But there are also striking differences - for example, the sum of angles of a hyperbolic triangle is always less than π.
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www.maths.gla.ac.uk/~wws/cabripages/hyperbolic/hyperbol...
www.maths.gla.ac.uk/~wws/cabripages/hyperbolic/hyperbolic0.html
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Cabri constructions for the demonstration of the basic concepts of hyperbolic geometry in the Poincare disc model. ... Hyperbolic Geometry using Cabri...
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mcs.open.ac.uk/tcl2/nonE/nonE.html
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Hyperbolic geometry is also known as Non-Euclidean geometry. The latter name reflects the fact that it was originally discovered by mathematicians seeking a geometry which failed to satisfy Euclid's parallel postulate.
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geom.math.uiuc.edu/docs/education/institute91/handouts/...
geom.math.uiuc.edu/docs/education/institute91/handouts/node37.html
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NonEuclid is Java Software for Interactively Creating Ruler and Compass Constructions in both the Poincaré Disk and the Upper Half-Plane Models of Hyperbolic Geometry for use in High School and Undergraduate Education. ... Aside from being interesting in itself, a study of Hyperbolic geometry can, through its novelty,
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cs.unm.edu/~joel/NonEuclid/NonEuclid.html
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Models of Hyperbolic Geometry ... Hyperbolic Analytic Geometry ... Coordinate Geometry in the Hyperbolic Plane...
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www.math.uncc.edu/~droyster/math3181/notes/hyprgeom/hyp...
www.math.uncc.edu/~droyster/math3181/notes/hyprgeom/hyprgeom.html
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From Hyperbolic Geometry you can also connect to the Patterns and Space Filling theme ... The non-Euclidean geometry developed independently by Nikolai Lobachevski and Farkas Bolyai in the 19th century is known as hyperbolic geometry. It differs from both Euclidean geometry and spherical geometry.
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www.btinternet.com/~connectionsinspace/Higher_Dimension...
www.btinternet.com/~connectionsinspace/Higher_Dimensions/Hyperbolic_Geometry_/body_hyperbolic_geometry_.html
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Welcome to the exciting world of hyperbolic geometry! Hyperbolic geometry is one of the most important examples of a "non-Euclidean" geometry, with far reaching applications in math and science, including special relativity.
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www.geom.uiuc.edu/~crobles/hyperbolic/
www.geom.uiuc.edu/~crobles/hyperbolic/
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One of the most surprising facts in hyperbolic geometry is that there is an upper limit to the possible area a triangle can have, even though there is not an upper limit to the lengths of the sides of the triangle.
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www.geom.uiuc.edu/~asr/java/TriangleArea/
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