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Spherical Geometries and Multigroups

Published online by Cambridge University Press:  20 November 2018

Walter Prenowitz
Walter Prenowitz*
Affiliation:
Brooklyn College
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1. Introduction. The notion spherical geometry is suggested by the familiar geometry of the Euclidean 2-sphere in which the role of path is played by “arc of great circle”. The first postulational treatment of the subject seems to be that of Halsted [10] for the two-dimensional case. Kline [11] under the name double elliptic geometry, gave a greatly simplified foundation for the three-dimensional case based on the primitive notions point and order. Halsted and Kline study not merely descriptive (that is positional, non-metrical) properties of figures but also introduce metrical notions by postulating or defining congruence. Kline includes a continuity postulate designed to yield real spherical geometry.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 2 , 1950 , pp. 100 - 119
Copyright
Copyright © Canadian Mathematical Society 1950

References

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