Which of the following statements is/are not true about non-Euclidean geometries? I. In Lobachevskian geometry, there are no parallel geodesics.  II. In Riemannian geometry, at least 2 lines are parallel to a given line. III. In non-Euclidean geometry, there exists exactly one line parallel to a given line.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 2E: Does a right circular cone such as a wizards cap have a symmetry with respect to at least one plane?...
icon
Related questions
Question

Which of the following statements is/are not true about non-Euclidean geometries?

I. In Lobachevskian geometry, there are no parallel geodesics. 

II. In Riemannian geometry, at least 2 lines are parallel to a given line.

III. In non-Euclidean geometry, there exists exactly one line parallel to a given line.

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage