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Download Notes on the hyperbolic plane.
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Transcript
Hyperbolic Geometry properties: Lines: In Hyperbolic Geometry, if you use a crocheted model, how can you find a straight line? In hyperbolic geometry, two distinct lines intersect in… In hyperbolic Geometry, if you have a line and a point P that is not on it, then there is/are ______ line(s) through the point P that do(es) not intersect line . Congruent triangles: Does SAS work? Does ASA work? Does SSS work? Angles in a triangle and similar triangles: In Hyperbolic Geometry, if you measure the angles in a triangle and add them up, you get… In Hyperbolic Geometry, if you make two triangles ABC and DEF and A D and B E but AB DE , are the angles C and F congruent, and if not which is larger? Transformations: Tell whether each of the following is possible on a hyperbolic plane. If it is possible, describe what it’s like. If it’s not possible explain why not. Is it possible to reflect across a hyperbolic line? Is it possible to rotate around a point on the hyperbolic plane? Is it possible to translate on a hyperbolic plane?
