![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/6/67/Lines.svg/640px-Lines.svg.png&w=640&q=50)
Pencil (geometry)
Family of geometric objects with a common property / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Pencil of planes?
Summarize this article for a 10 year old
In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a plane, or the set of circles that pass through two given points in a plane.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/6/67/Lines.svg/320px-Lines.svg.png)
Although the definition of a pencil is rather vague, the common characteristic is that the pencil is completely determined by any two of its members. Analogously, a set of geometric objects that are determined by any three of its members is called a bundle.[1] Thus, the set of all lines through a point in three-space is a bundle of lines, any two of which determine a pencil of lines. To emphasize the two-dimensional nature of such a pencil, it is sometimes referred to as a flat pencil.[2]
Any geometric object can be used in a pencil. The common ones are lines, planes, circles, conics, spheres, and general curves. Even points can be used. A pencil of points is the set of all points on a given line.[1] A more common term for this set is a range of points.