Euclidean

Euclidean Geometry

The Pure Euclidean Postulates are:

1. Any two points (.) can be connected with a straight 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 one and only one straight line that passes through that point and is parallel (q) to the first line.

Constructions Included:

The following constructions are available in the github repository:

stereo0

This construction is a demonstration of one of the two standard stereographic projections.

stereo1

This construction is a demonstration of one of the two standard stereographic projections.

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.

circumCircle

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

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 the three excircles.

parabola

A standard construction of a parabola from a focus and directrix.

9PtCircle

The foundation of this construction is a moveable triangle, from which is constructed the 9-point circle.

diameterTriangle

This construction is a circle with a triangle constructed with vertices on it, so that one of the sides of the triangle is a diameter of the circle.

Unannotated Constructions:

quadMPquad, 05-gon, secantSlope, 06-gon, 07-gon, hyperbolicRipples, latticePts, sohCahToa