Brushes and Cycles

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


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.


Distinct Point Euclidean Geometry Euclidean Plane Unique Line Perpendicular Bisector 
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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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