<map version="0.8.0">
<!-- To view this file, download free mind mapping software FreeMind from http://freemind.sourceforge.net -->
<node CREATED="1222918027324" ID="Freemind_Link_900505806" MODIFIED="1222969662119" TEXT="&lt;html&gt;&lt;img src=&quot;sphere_geometry_17.jpg&quot;&gt;">
<edge WIDTH="2"/>
<node BACKGROUND_COLOR="#ffff00" CREATED="1178901393578" ID="Freemind_Link_607705999" MODIFIED="1222997131339" POSITION="right" STYLE="bubble" TEXT="Help: use your mouse to interact&#xa;To Pan: click and drag the map canvas&#xa;To Fold/Unfold: click a branch&#xa;To Link: click a red arrow&#xa;To see a note: Hover over a note button">
<edge COLOR="#cccc00"/>
<font NAME="SansSerif" SIZE="10"/>
<icon BUILTIN="ksmiletris"/>
<hook NAME="accessories/plugins/NodeNote.properties">
<text>To see the notes!</text>
</hook>
</node>
<node CREATED="1222918030784" ID="Freemind_Link_17332083" LINK="http://math.rice.edu/%7Epcmi/sphere/gos4.html#1" MODIFIED="1222976428055" POSITION="left" TEXT="The area of a spherical triangle.&#xa;Girard&apos;s Theorem">
<edge COLOR="#009999"/>
<icon BUILTIN="full-4"/>
<hook NAME="accessories/plugins/NodeNote.properties">
<text>Albert Girard (1595&#x2013;1632) showed how the area of a spherical triangle depends on its interior angles. The result is called Girard&apos;s Theorem.</text>
</hook>
</node>
<node CREATED="1222918030786" ID="Freemind_Link_1158116562" LINK="http://math.rice.edu/%7Epcmi/sphere/gos5.html#1" MODIFIED="1222920423298" POSITION="left" TEXT="Consequences of&#xa;Girard&apos;s Theorem&#xa;Exercises">
<edge COLOR="#000066"/>
<icon BUILTIN="full-5"/>
<node CREATED="1222918030788" ID="Freemind_Link_1092722307" LINK="http://math.rice.edu/%7Epcmi/sphere/gos5.html#3" MODIFIED="1222920432911" TEXT="Distortion in maps">
<hook NAME="accessories/plugins/NodeNote.properties">
<text>Everyone knows that a map from even a small portion of the sphere to the plane must involve some distortion.</text>
</hook>
</node>
<node CREATED="1222918030793" ID="Freemind_Link_448905078" LINK="http://math.rice.edu/%7Epcmi/sphere/gos5.html#5" MODIFIED="1222920441156" TEXT="Similarity"/>
<node CREATED="1222918030794" ID="Freemind_Link_1914181354" LINK="http://math.rice.edu/%7Epcmi/sphere/gos5.html#7" MODIFIED="1222920449533" TEXT="Congruence theorems"/>
<node CREATED="1222918030796" ID="Freemind_Link_955920112" LINK="http://math.rice.edu/%7Epcmi/sphere/gos5.html#9" MODIFIED="1222920500946" TEXT="Small triangles&#xa;on large spheres"/>
<node CREATED="1222918030799" ID="Freemind_Link_1259671079" LINK="http://math.rice.edu/%7Epcmi/sphere/gos5.html#11" MODIFIED="1222920477375" TEXT="Spherical polygons"/>
</node>
<node CREATED="1222918030801" ID="Freemind_Link_415846368" LINK="http://math.rice.edu/%7Epcmi/sphere/gos6.html" MODIFIED="1222977123728" POSITION="left" TEXT="A Proof of Euler&apos;s formula">
<edge COLOR="#990000"/>
<icon BUILTIN="full-6"/>
<hook NAME="accessories/plugins/NodeNote.properties">
<text>Let P be a convex polyhedron with V vertices, E edges, and F faces. then&#xa;               V - E + F = 2.</text>
</hook>
</node>
<node CREATED="1222918030756" ID="Freemind_Link_1924606509" LINK="http://math.rice.edu/%7Epcmi/sphere/#intro" MODIFIED="1222920008387" POSITION="right" TEXT="Introduction">
<edge COLOR="#ff0033"/>
<icon BUILTIN="full-1"/>
<hook NAME="accessories/plugins/NodeNote.properties">
<text>The Geometry of the Sphere&#xa;by John C. Polking&#xa;Rice University </text>
</hook>
</node>
<node CREATED="1222918030758" ID="Freemind_Link_1906950827" LINK="http://math.rice.edu/%7Epcmi/sphere/sphere.html#basic" MODIFIED="1222920115352" POSITION="right" TEXT="Basic information&#xa;about spheres">
<edge COLOR="#0000cc"/>
<icon BUILTIN="full-2"/>
<hook NAME="accessories/plugins/NodeNote.properties">
<text>A sphere is a set of points in three dimensional space equidistant from a point called the center of the sphere. The distance from the center to the points on the sphere is called the radius of the sphere. </text>
</hook>
<node CREATED="1222918030760" LINK="http://math.rice.edu/%7Epcmi/sphere/sphere.html#1" MODIFIED="1222918030760" TEXT="Lines and spheres"/>
<node CREATED="1222918030762" FOLDED="true" ID="Freemind_Link_1496169618" LINK="http://math.rice.edu/%7Epcmi/sphere/sphere.html#2" MODIFIED="1222919652580" TEXT="Planes, spheres, circles,&#xa;and great circles:">
<node CREATED="1222918030763" ID="Freemind_Link_670971031" LINK="http://math.rice.edu/%7Epcmi/sphere/sphere.html#3" MODIFIED="1222918030763" TEXT="Exercise: Comparison with plane geometry"/>
</node>
<node CREATED="1222918030765" ID="Freemind_Link_1536370725" LINK="http://math.rice.edu/%7Epcmi/sphere/gos2.html#1" MODIFIED="1222918030765" TEXT="Incidence Relations on a Sphere"/>
<node CREATED="1222918030767" ID="Freemind_Link_540618652" LINK="http://math.rice.edu/%7Epcmi/sphere/gos2.html#2" MODIFIED="1222918030767" TEXT="Spherical distance and isometries"/>
<node CREATED="1222918030769" ID="Freemind_Link_945430411" LINK="http://math.rice.edu/%7Epcmi/sphere/gos2.html#3" MODIFIED="1222918030769" TEXT="Lunes"/>
<node CREATED="1222918030771" ID="Freemind_Link_98379978" LINK="http://math.rice.edu/%7Epcmi/sphere/gos2.html#angles" MODIFIED="1222918030771" TEXT="Angles on the sphere"/>
</node>
<node CREATED="1222918030773" ID="Freemind_Link_1951300567" LINK="http://math.rice.edu/%7Epcmi/sphere/gos3.html#area" MODIFIED="1222977273585" POSITION="right" TEXT="Area on the sphere">
<edge COLOR="#339900"/>
<icon BUILTIN="full-3"/>
<hook NAME="accessories/plugins/NodeNote.properties">
<text>The area of a sphere of radius R is 4.PI.R**2</text>
</hook>
<node CREATED="1222918030774" LINK="http://math.rice.edu/%7Epcmi/sphere/gos3.html#1" MODIFIED="1222918030774" TEXT="The area of a lune"/>
<node CREATED="1222918030776" FOLDED="true" ID="Freemind_Link_1395921453" LINK="http://math.rice.edu/%7Epcmi/sphere/gos3.html#2" MODIFIED="1222920198833" TEXT="Spherical triangles">
<hook NAME="accessories/plugins/NodeNote.properties">
<text>A spherical triangle is defined just like a planar triangle. It consists of three points called vertices, the arcs of great circles that join the vertices, called the sides, and the area that is inclosed therein.</text>
</hook>
<node CREATED="1222918030780" ID="Freemind_Link_1336414055" LINK="http://math.rice.edu/%7Epcmi/sphere/gos3.html#3" MODIFIED="1222918030780" TEXT="Exercise: Experimenting with spherical triangles"/>
<node CREATED="1222918030782" ID="Freemind_Link_1917030615" LINK="http://math.rice.edu/%7Epcmi/sphere/gos3.html#3" MODIFIED="1222918030782" TEXT="Exercise: The area of a spherical triangle"/>
</node>
</node>
<node CREATED="1222918030717" ID="Freemind_Link_782110220" MODIFIED="1222920536127" POSITION="left" TEXT="Appendices">
<edge COLOR="#666600"/>
<icon BUILTIN="full-7"/>
<node CREATED="1222918030802" ID="Freemind_Link_1565097936" LINK="http://math.rice.edu/%7Epcmi/sphere/linincidence.html#1" MODIFIED="1222920555829" TEXT="Incidence relations in the&#xa;plane and in space"/>
<node CREATED="1222918030804" ID="Freemind_Link_996861863" LINK="http://math.rice.edu/%7Epcmi/sphere/drg_txt.html" MODIFIED="1222918030804" TEXT="Degrees and radians"/>
<node CREATED="1222918030807" LINK="http://math.rice.edu/%7Epcmi/sphere/ruler.html" MODIFIED="1222918030807" TEXT="Making a &quot;spherical straightedge&quot;"/>
</node>
</node>
</map>
