C.a.R. > Applications > Non-Euclidean Geometry > Elliptic Geometry

Elliptic Geometry

With this applet you can construct in the geometry on the sphere (elliptic geometry). To represent the sphere in the plane, the sphere is projected from the north pole to a plane tangent to the south pole. The green circle is the image of the southern hemisphere, its boundary is the image of the equator. This projection keeps the angles and maps circles to circles. The great circles are mapped to circles through opposing points on the equator circle. Note that the centers of the circles are not mapped to the centers of their images!

The constructions are realized with macros. Click some empty space with the right mouse button to see all macros of the elliptic geometry.

Some hints: the macro point creates a point that cannot be moved off the southern hemisphere. The macro "intersection" chooses the intersection in the southern hemisphere.

Technical Information

The basic green circle is a parameter to all macros, of course. However, it is a fixed parameter, and needs not be selected.

I have explained the ideas behind the macros of both geometries in an article (written for CarZine).