Which of the following statements is/are true about non-Euclidean geometries? I. In non-Euclidean geometry, there exists exactly one line parallel to a given line. II. In Lobachevskian geometry, there are no parallel geodesics. III. In Riemannian geometry, at least 2 lines are parallel to a given line. O Statements I and III only None of the statements Statements II and III only O Statement II only O Statement Ill only Statements I, II, and III Statements I and II only O Statement I only
Which of the following statements is/are true about non-Euclidean geometries? I. In non-Euclidean geometry, there exists exactly one line parallel to a given line. II. In Lobachevskian geometry, there are no parallel geodesics. III. In Riemannian geometry, at least 2 lines are parallel to a given line. O Statements I and III only None of the statements Statements II and III only O Statement II only O Statement Ill only Statements I, II, and III Statements I and II only O Statement I only
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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
Transcribed Image Text:Which of the following statements is/are true about non-Euclidean
geometries?
I. In non-Euclidean geometry, there exists exactly one line parallel to
a given line.
II. In Lobachevskian geometry, there are no parallel geodesics.
III. In Riemannian geometry, at least 2 lines are parallel to a given
line.
O Statements I and III only
None of the statements
Statements II and III only
O Statement II only
O Statement Ill only
Statements I, II, and III
O Statement I only
O Statements I and II only
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