1. A great deal of Euclidean geometry carries over directly to elliptic geometry . 2. Other applications are in statistics, and another is in elliptic geometry . 3. This description gives the standard model of elliptic geometry . 4. This results in a surface possessing elliptic geometry . 5. Riemann's elliptic geometry emerges as the most natural geometry satisfying this axiom. 6. This universe is actually the real projective plane with a metric : elliptic geometry . 7. The Pythagorean theorem fails in elliptic geometry . 8. The geometry that results is called ( plane ) " Elliptic geometry ". 9. Elliptic geometry has a variety of properties that differ from those of classical Euclidean plane geometry.10. These early attempts did, however, provide some early properties of the hyperbolic and elliptic geometries .
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