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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?"



Aside from being interesting in itself, a study of hyperbolic geometry can, through its novelty, be helpful to high school geometry students. For example, when asked to prove that the opposite sides of a rectangle have the same length, many beginning geometry students will be confused about what to do. Students sometimes think: "Why I am being told to prove what I learned in kindergarten is just part of the definition of what it means for a figure to be a rectangle." The strangeness of hyperbolic geometry helps such students think about and understand the difference between what is part of an object's definition and what is a theorem about an object.



Hyperbolic Geometry also has practical aspects such as orbit prediction of objects within intense gravitational fields. Hyperbolic Geometry is used in Einstein's General Theory of Relativity and Curved Hyperspace.



