Non-Euclidean Geometry Crossword

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Across
  1. 3. Type of Geometry done on a convex surface
  2. 6. In Hyperbolic Geometry, parallel lines are not ____________ throughout
  3. 9. Shape that forms on a sphere when all angles are 90 degrees
  4. 11. Discoverer of Spherical Geometry
  5. 13. Discoverer of Hyperbolic Geometry
  6. 14. Lobachevsky was trying to prove Euclid's _________ postulate with his other postulates
  7. 15. In Hyperbolic Geometry, angles of a triangle sum up to ____ than 180 degrees
Down
  1. 1. Type of Geometry done on a concave surface
  2. 2. In Spherical Geometry, angles of a triangle sum up to ____ than 180 degrees
  3. 4. In Spherical Geometry, all (boundless) straight lines are of ______________
  4. 5. Riemann was trying to define n-___________ space
  5. 7. Shape that forms on a hyperbolic plane when all angles are 90 degrees
  6. 8. In both types of non-Euclidean geometry, Euclid's _____postulate is rejected
  7. 10. In Spherical Geometry, parallel lines always _______
  8. 12. In Hyperbolic Geometry, ________ parallel lines exist for a given line