pencil

A pencil is a set of geometric objects, usually either congruent orsimilar to each other, that share a common incidence property. Below are some of the most commonly encountered pencils:

1.
A pencil of lines usually means a set of straight lines that are incident with one point. If the lines all lie in the same plane, the pencil is sometimes called a flat pencil.
2.
In some cases, a pencil of lines denotes a set of parallel lines in a plane. If a point of infinity is added to the plane, then we are back to the previous example.
3.
A pencil of circles can mean that either these circles all intersect at exactly one point (or share the same tangent line)
4.
A pencil of circles can also mean that the circles have two common points of intersection.

References

1 E. Artin, Geometric Algebra, Wiley-Interscience, Reprint (1988).
2 H. S. M. Coxeter, Projective Geometry, Springer-Verlag, 2nd Edition (2003).

单词	Pencil
释义	pencil A pencil is a set of geometric objects, usually either congruent orsimilar to each other, that share a common incidence property. Below are some of the most commonly encountered pencils: 1. A pencil of lines usually means a set of straight lines that are incident with one point. If the lines all lie in the same plane, the pencil is sometimes called a flat pencil. 2. In some cases, a pencil of lines denotes a set of parallel lines in a plane. If a point of infinity is added to the plane, then we are back to the previous example. 3. A pencil of circles can mean that either these circles all intersect at exactly one point (or share the same tangent line) 4. A pencil of circles can also mean that the circles have two common points of intersection. References 1 E. Artin, Geometric Algebra, Wiley-Interscience, Reprint (1988). 2 H. S. M. Coxeter, Projective Geometry, Springer-Verlag, 2nd Edition (2003).
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