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Brushes and Cycles

  • George E. Martin
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

In Euclidean geometry the set of all lines passing through a point is called a pencil. (The term comes from the former use of the word for an artist’s paintbrush.) The set of all lines parallel to a given line in the Euclidean plane is called a parallel pencil. To be useful this second idea must be refined for the Bolyai — Lobachevsky plane where we have two distinct types of parallelism.

Keywords

Distinct Point Euclidean Geometry Euclidean Plane Unique Line Perpendicular Bisector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1975

Authors and Affiliations

  • George E. Martin
    • 1
  1. 1.Department of Mathematics and StatisticsState University of New York at AlbanyAlbanyUSA

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