Locus (mathematics)

For other uses, see Locus (disambiguation).
Each curve in this example is a locus defined as the conchoid of the point P and the line l. In this example, P is 8 cm from l.

In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.[1][2]

The set of the points that satisfy some property is often called the locus of a point satisfying this property. The use of the singular in this formulation is a witness that, until the end of the 19th century, mathematicians did not consider infinite sets. Instead of viewing lines and curves as sets of points, they viewed them as places where a point may be located or may move.

  1. ^ James, Robert Clarke; James, Glenn (1992), Mathematics Dictionary, Springer, p. 255, ISBN 978-0-412-99041-0.
  2. ^ Whitehead, Alfred North (1911), An Introduction to Mathematics, H. Holt, p. 121, ISBN 978-1-103-19784-2.