Spherical

In this geometry, any pair of non-antipodal points can be connected with a unique line segment; this is not the case for antipodal points like the N and S poles (Euclid's Postulate 1). Straight lines can still be extended indefinitely (Postulate 2). However, this does not mean that they are infinitely long, as Euclid probably intended: they eventually wrap back atop themselves. In addition, there are no such things as parallel lines in spherical geometry (Postulate 5).

Constructions Included:

04-hedron:

A spherical tetrahedron; the 4 points are connected to tile the sphere with 4 regular 3-gons.

06-hedron:

A spherical cube; the 8 points are connected to tile the sphere with 6 regular 4-gons.

08-hedron:

A spherical octahedron.

12-hedron:

A spherical dodecahedron.

20-hedron:

A spherical icosahedron.

inCircle:

The foundation is a moveable triangle from which is constructed the incircle.

inExCircles:

The foundation is a moveable triangle from which is constructed the incircle and three excircles.

circumCircle:

The foundation is a moveable triangle from which is constructed the circumcircle.

earth:

A rough outline of the main continents on Earth. It is especially interesting to view, and move about, in the Mercator projection.

diameterTriangle:

A circle with three points on it; those points form vertices of a triangle for which one of the sides is a diameter.

rightTriangle:

A moveable right triangle from which the spherical Pythagorean Theorem can be investigated. The constant pi is also included for calculations.

PolTriTheorem:

quadMPquad: