Spherical
The Spherical Postulates are:
- Any two points (.) can be connected with a line segment (s).
- Non-antipodal points are connected with a unique line
- Antipodal points (e.g. N and S poles) can have infinite lines
- Any straight line segment can be extended indefinitely in a straight line (l).
- These lines are not indefinitely long. Their length is constrained by the maximum circumference of the sphere.
- Given any straight line segment, a circle can be drawn having the segment as the radius and one point as the center (c).
- All Right Angles are congruent.
- Given any straight line and a point not on it, there exists no straight line that passes through that point and is parallel (q) to the first line.
A spherical tetrahedron; the 4 points are connected to tile the sphere with 4 regular 3-gons.
A spherical cube; the 8 points are connected to tile the sphere with 6 regular 4-gons.
A spherical octahedron.
A spherical dodecahedron.
A spherical icosahedron.
The foundation is a moveable triangle from which is constructed the incircle.
The foundation is a moveable triangle from which is constructed the incircle and three excircles.
The foundation is a moveable triangle from which is constructed the circumcircle.
A rough outline of the main continents on Earth. It is especially interesting to view, and move about, in the Mercator projection.
A circle with three points on it; those points form vertices of a triangle for which one of the sides is a diameter.
A moveable right triangle from which the spherical Pythagorean Theorem can be investigated. The constant pi is also included for calculations.