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Euclidean, Spherical, and Hyperbolic Shadows
The College Mathematics Journal
Vol. 44, No. 2 (March 2013), pp. 126-134
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/college.math.j.44.2.126
Page Count: 9
You can always find the topics here!Topics: Geometry, Geometric planes, Spheres, Mathematical functions, Mathematical problems, Euclidean space, Unit vectors, Feet, Hyperbolic geometry
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Summary Many classical problems in elementary calculus use Euclidean geometry. This article takes such a problem and solves it in hyperbolic and in spherical geometry instead. The solution requires only the ability to compute distances and intersections of points in these geometries. The dramatically different results we obtain illustrate the effect curvature has on basic geometric objects.
Copyright the Mathematical Association of America 2013