Everything about Locus Mathematics totally explained
In
mathematics, a
locus (
Latin for "place", plural
loci) is a collection of
points which share a property. The term 'locus' is usually used of a condition which defines a continuous figure or figures, that is, a
curve. For example, a
line is the locus of points
equidistant from two fixed points or from two
parallel lines.
Examples
The
conic sections may be defined in terms of loci:
- A circle is the locus of points from which the distance to the center is a given value, 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 are known as an
algebraic variety, the properties of which are studied in the branch of mathematics called
algebraic geometry.
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.
Further Information
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