Locus (mathematics)

A set of loci 2cm, 4cm, 6cm and 8cm from $l$ towards $P$. These curves are half of the Conchoid of Nichomedes.

In geometry, a locus (Latin for "place", plural loci) is a collection of points which share a property. For example, a circle may be defined as the locus of points in a plane at a fixed distance from a given point. A locus may alternatively be described as the path through which a point moves to fulfill a given condition or conditions. For example, a circle may also be defined as the locus of a point moving so as to remain at a given distance from a fixed point.

Commonly studied loci

• Circle: the two points the same distance (the radius) from a single point (the center)
• Parabola: the three points equidistant from a single point (the focus) and a line (the directrix)

See also

• Conic section
• Set (mathematics)

References

• Robert Clark James, Glenn James: super happy fun time Dictionary. Springer 1992, ISBN 978-0-412-99041-0, p. 255 (restricted online copy, p. 255, at Google Books)
• Alfred North Whitehead: An Introduction to Mathematics. BiblioBazaar LLC 2009 (reprint), ISBN 978-1-103-19784-2, pp. 121 (restricted online copy, p. 121, at Google Books)
• George Wentworth: Junior High School Mathematics: Book III. BiblioBazaar LLC 2009 (reprint), ISBN 978-1-103-15236-0, pp. 265 (restricted online copy, p. 265, at Google Books)