Section 7.6 Spherical Geometry II
¶The standard model for double elliptic geometry is the sphere. So points are all Euclidean points on the surface of the sphere, lines are great circles, and angles are Euclidean.
You can explore constructions in spherical geometry using the new tools shown in Figure 7.6.1, or on the standalone page at handouts/spherical.html. 1 Do not confuse these new tools (in the right-most menu) with their Euclidean analogs, even though their icons are the same! 2
If the sphere is not rotating smoothly, try selecting "Zoom to fit" from the right-click menu. If (parts of) objects seem to disappear, try scrolling out.
The new tools are a spherical circle tool, a spherical distance function, a spherical compass, spherical angle measurement, and tools for drawing spherical lines and line segments, labeled respectively with the (Euclidean!) icons below:
Use each of these tools as you would their Euclidean counterparts: to measure disance or draw lines or line segments, select two points; to measure angles, select three points, with the vertex second; to construct a circle, select the center point and a point on the circle; to use the compass, select two points to set the distance, then the new center. Unlike their Euclidean analogs, however, these tools require that the points to be selected already exist. Construct them on the sphere using the (Euclidean) point-on-object tool (the second item in the point menu).