Brushes and Cycles
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.
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