Editing Locus (mathematics) (section)

{{short description|Set of points that satisfy some specified conditions}}
{{other uses| Locus (disambiguation)}}
[[File:Locus Curve.svg|thumb|right|upright=1.35|Each curve in this example is a ''locus'' defined as the [[Conchoid (mathematics)|conchoid]] of the point {{math|''P''}} and the line {{math|''l''}}. In this example, {{math|''P''}} is 8&nbsp;cm from {{math|''l''}}.]]

In [[geometry]], a '''locus''' (plural: ''loci'') (Latin word for "place", "location") is a [[set (mathematics)|set]] of all [[Point (geometry)|points]] (commonly, a [[line (geometry)|line]], a [[line segment]], a [[curve (mathematics)|curve]] or a [[Surface (topology)|surface]]), whose location satisfies or is determined by one or more specified conditions.<ref name=James>{{citation |first1=Robert Clarke |last1=James |first2=Glenn |last2=James |title=Mathematics Dictionary|publisher=Springer |year=1992 |isbn=978-0-412-99041-0 |page=255 |url=https://books.google.com/books?id=UyIfgBIwLMQC&pg=PA255}}.</ref><ref>{{citation |first=Alfred North |last=Whitehead |author-link=Alfred North Whitehead |title=An Introduction to Mathematics |publisher=H. Holt |year=1911 |isbn=978-1-103-19784-2 |page=121 |url=https://books.google.com/books?id=0Ko-AAAAYAAJ&pg=PA121}}.</ref>

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 set]]s. Instead of viewing lines and curves as sets of points, they viewed them as places where a point may be ''located'' or may move.