The set of all lines through a point. The term was first used by Desargues (Cremona 1960, p. x). The six angles of any pencils of four rays are connected by the relation

and the lengths satisfy

(Lachlan 1893).

Woods (1961) uses the term pencil as a synonym for line segment range, and Altshiller-Court (1979, p. 12) uses the term to mean sheaf of planes.

Altshiller-Court, N. Modern Pure Solid Geometry. New York: Chelsea, 1979.

Cremona, L. Elements of Projective Geometry, 3rd ed. New York: Dover, 1960.

Lachlan, R. "Relations Connecting the Angles of a Pencil." §29 in An Elementary Treatise on Modern Pure Geometry. London: Macmillian, pp. 16-18, 1893.

Graustein, W. C. Introduction to Higher Geometry. New York: Macmillan, p. 36, 1930.

Woods, F. S. Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry. New York: Dover, pp. 8 and 11-12, 1961.

CITE THIS AS:

Weisstein, Eric W. "Pencil." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Pencil.html