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The Geometry of the Sphere is an interactive mind map based on:
The Geometry of the Sphere
by John C. Polking, Rice University.
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
navigation and astronomy.
In plane geometry the basic concepts are points and line. On the sphere, points are defined in the usual sense. The equivalents of lines are not defined in the usual sense of "straight line" but in the sense of "the shortest paths between points" which is called a geodesic. On the sphere the geodesics are the great circles, so the other geometric concepts are defined like in plane geometry but with lines replaced by great circles. Thus, in spherical geometry angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects (for example, the sum of the interior angles of a triangle exceeds 180 degrees).
Mindmap Instructions:
To see a note, hover over a note button
 above.
To scroll the mindmap
above, click and drag the map's background and move it around , or click on
background and use the arrow keys.
To
link to another page, click a link button
above.
To
Fold/Unfold a node, click the node
or right click a Node and select Fold/Unfold all from Node.
Buttons above:
 Search,
 Go to,
 Zoom in
or CTRL '+',
 Zoom
out or CTRL '-',  Reset
(center),
Shadow  On/
 Off,
 FreeMind,
 BG
color.
Last updated:
October 2, 2008
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