Spherical geometry - Wikipedia, the free encyclopedia
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Spherical geometry is the geometry of the two-dimensional surface of a sphere. It is an example of a non-Euclidean geometry. Two practical applications of the principles of spherical geometry are to ...
en.wikipedia.org/wiki/Spherical_geometry
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Exercise: Comparison with plane geometry ... Spherical distance and isometries ... We are interested here in the geometry of an ordinary sphere. In plane geometry we study points, lines, triangles, polygons, etc. On the sphere we have points, but there are no straight lines --- at least not in the usual sense.
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math.rice.edu/~pcmi/sphere/
math.rice.edu/~pcmi/sphere/
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Planar geometry is sometimes called flat or Euclidean geometry. The geometry on a sphere is an example of a spherical or elliptic geometry. Another kind of non-Euclidean geometry is hyperbolic geometry. Spherical and hyperbolic geometries do not satify the parallel postulate.
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www.math.hmc.edu/funfacts/ffiles/20001.2.shtml
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Spherical geometry and trigonometry used to be important topics in a technical education because they were essential for navigation. During that time an important element of their presentation was the matter of making accurate computations.
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www.sjsu.edu/faculty/watkins/sphere.htm
www.sjsu.edu/faculty/watkins/sphere.htm
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Below are some suggestions for using the applet. Note that there are three modes for what the mouse does: drag arrow, rotate sphere, and draw triangle. The menu lets you ... Spherical Geometry Demo ... This applet demonstrates certain features of spherical geometry, in particular, the parallel transport of tangent vectors.
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torus.math.uiuc.edu/jms/java/dragsphere/
torus.math.uiuc.edu/jms/java/dragsphere/
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How big is the sphere from which a cap was cut? (Spherical geometry) ... This section is supposed to be for "spherical and hyperbolic convexity" but it appears to be the only geometric area focusing on things spherical! So we use it to hold a few posts on spherical geometry.
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www.math.niu.edu/~rusin/known-math/index/52A55.html
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Such polygons do not even exist in Euclidean geometry! The sides of a lune are both half lines with common endpoints. Recall that "lines" on a sphere are great circles. You can picture the area of a lune as the area between two lines of longitude on a ... What do you notice about the angle sum of a spherical triangle?
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www.uwosh.edu/faculty_staff/szydliks/elliptic/elliptic....
www.uwosh.edu/faculty_staff/szydliks/elliptic/elliptic.htm
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Spherical geometry is based on the surface of a sphere, not a plane. The first four basic axioms are still true in spherical geometry. ... However, in spherical geometry, a straight line is a great circle. The shortest distance between two points always lies on a great circle. Longitude lines are great circles.
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math.youngzones.org/Non-Egeometry/spherical.html
math.youngzones.org/Non-Egeometry/spherical.html
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Note: You rarely fly a true great circle, even on long trips. Why? Two factors: 1) Winds. If flying an extra 400 miles puts you into a favorable jet stream (or gets you out of an unfavorable one), then it is more than worth doing so, in terms of time ... it's just spherical geometry... March 10, 2005 1:21 PM Subscribe...
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www.metafilter.com/40339/its-just-spherical-geometry
www.metafilter.com/40339/its-just-spherical-geometry
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