NonEuclid allows the curious explorer to
gain experience in Hyperbolic Geometry and to
empirically investigate questions such as:
"Does the Euclidean geometry method for constructing
an equilateral triangle work in Hyperbolic geometry?" or
"In Hyperbolic Geometry,
are the base angles of an isosceles triangle congruent?"
Authors:
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Polar Coordinates: |
The above new Javascript version is still under development. The older Java version is:
NonEuclid.jar To run this, download, and either double-click or use the command:
java" -jar NonEuclid.jar
3) Activities: - Exploring properties in Hyperbolic Geometry of Adjacent Angles, General Triangles, Isosceles Triangles, Equilateral Triangle, Right Triangles, Congruent Triangles, Rectangles, Squares, Parallelograms, Rhombuses, Polygons, Circles, and Tessellations of the Plane. | |
4) The Shape of Space: - Curved Space, Flatland, Ourland, and Mercury's Orbit. | |
6) Axioms and Theorems: - Euclid's Postulates, Hyperbolic Parallel Postulate, SAS Postulate, Hyperbolic Geometry Proofs. | |
8) X-Y Coordinate System: - A description of how an x-y coordinate system can be set up in Hyperbolic Geometry. | |
9) Disk and Upper Half-Plane Models: - An informal development of these two models of Hyperbolic Geometry. |
For The Teacher: Why is it Important for Students to Study Hyperbolic Geometry? | |
References & Further Reading. | |
Wikipedia: Euclidian Compass-and-straightedge Construction. | |
Hyperbolic Geometry Art by Clifford Singer Back when NonEuclid and the Internet were young, some of the young Clifford Singer's art was hosted on this website. Here you will find the original scans form the early 1990s as well as links to Clifford's newer works in mathematically inspired art. |