Hyperbolic

Hyperbolic Geometry

The Hyperbolic Postulates are:

1. Any two points (.) can be connected with a unique line segment (s).
2. Any straight line segment can be extended indefinitely in a straight line (l).
3. Given any straight line segment, a circle can be drawn having the segment as the radius and one point as the center (c).
4. All Right Angles are congruent.
5. Given any straight line and a point not on it, there exists an infinite number of lines that pass through that point and is parallel (q) to the first line.

Constructions Included:

inCircle

The foundation of this construction is a moveable triangle, from which is constructed the incircle.

inExCircles

The foundation of this construction is a moveable triangle, from which is constructed the incircle and three excircles, when they exist.

circumCircle

The foundation of this construction is a moveable triangle, from which is constructed the circumcircle, when it exists.

rightTriangle

This construction is a moveable right triangle. It is used for student experimentation with the hyperbolic Pythagorean Theorem. The constant pi is included for use in that exploration.

diameterTriangle

This is a construction of a circle with three points on it forming vertices of a triangle, one of whose sides is a diameter.

Unannotated Constructions:

quadMPquad