In
mathematics, a
locus (
Latin for "place", plural
loci) is a collection of
points which share a property. The term
locus is typically used of a condition which defines a continuous figure or figures, that is, a
curve. For example, in two-dimensional space a
line is the locus of points
equidistant from two fixed points or from two lines (
parallel or non parallel).
Examples
The
epitrochoid is an example of a locus generated by a point on a
disk rolling around a circle.
The
conic sections may be defined in terms of loci:
- A circle is the locus of points where the distance from a certain point, called the center of the circle, is equidistant to all points on the locus; the distance between the center and the locus is called as the radius.
- An ellipse is the locus of points, the sum of the distances from which to the foci is a given value.
- A hyperbola is the locus of points, the difference of the distances from which to the foci is a given value.
- A parabola is the locus of points, the distances from which to the focus and to the directrix are equal.
Very complex geometric shapes may be described as the locus of
zeros of a
function or
polynomial. Thus, for example, the
quadric surfaces are defined as the loci of zeros of the
quadratic polynomials. More generally, the locus of zeros of a
set of
polynomials is known as an
algebraic variety, the properties of which are studied in the branch of mathematics called
algebraic geometry.
In
complex dynamics:
Further examples of complex geometric shapes are generated by a point on a disk which is made to roll on a flat or curved surface.
See also
Category:Elementary geometryar:محل هندسيbg:Геометрично място на точкиca:Lloc geomètricde:Geometrischer Ortel:Γεωμετρικός τόποςes:Lugar geométricofa:مکان هندسیfr:Lieu géométriquehi:बिंदुपथid:Lokus (matematika)it:Luogo (geometria)ja:軌跡_(数学)he:מקום גאומטריhu:Mértani helynl:Meetkundige plaatspl:Miejsce geometrycznept:Lugar geométricoru:Геометрическое место точекsl:Geometrijsko mesto točksr:Геометријско место тачакаsv:Geometrisk ortth:โลกัสvi:Quĩ tíchzh:轨迹
