Non-Euclidean Geometries – Riemann & Lobachevsky

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Across
  1. 3. In __________ geometry triangle angle sums here are less than 180 degrees.
  2. 5. Mathematicians began questioning _____’s postulates.
  3. 6. Euclidean, spherical, and hyperbolic each have unique rules, especially about ____ Lines
  4. 8. Euclidean, spherical, and hyperbolic each have unique rules,about Triangle ____ as well.
Down
  1. 1. In _______ geometry parallel lines don’t exist, and triangle angle sums are greater than 180 degrees.
  2. 2. ____________geometries emerged in the 1800s.
  3. 4. Instead of assuming a flat space, they explored ________ surfaces.
  4. 7. In __________ geometry the sum of the angles is exactly 180 degrees.