“Angle of Parallelism”的概念、定义、习题解题方法及翻译-数学辞典

单词

Angle of Parallelism

释义

Angle of Parallelism

Given a point and a Line , draw the Perpendicular through and call it . Let be any other line from which meets in . In a Hyperbolic Geometry, as moves off to infinityalong , then the line approaches the limiting line , which is said to be parallel to at .The angle which makes with is then called the angle of parallelism for perpendicular distance , and is given by

This is known as Lobachevsky's Formula.

See also Hyperbolic Geometry, Lobachevsky's Formula

References

Manning, H. P. Introductory Non-Euclidean Geometry. New York: Dover, pp. 31-32 and 58, 1963.

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