Definition:Locus
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Definition
A locus is a set of points which satisfy a particular condition.
Such points usually form a curve or a surface, depending on the context.
Examples
Circle
Let $P$ be a point in the plane.
The locus of all points in the plane that are all a distance $r$ from $P$ is a circle.
Also known as
Some sources refer to a locus merely as a curve.
Also see
- Results about loci can be found here.
Linguistic Note
The plural of locus is loci, pronounced either loak-ee or loak-eye.
Ian Stewart opines that the word is obsolete.
Sources
- 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 1 (2nd ed.) ... (previous) ... (next): Introduction: Chapter $\text{II}$. Euclid's Other Works
- 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {II}$. The Straight Line: $1$. Equation of a locus
- 1958: P.J. Hilton: Differential Calculus ... (previous) ... (next): Chapter $1$: Introduction to Coordinate Geometry: $(1.1)$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): locus (plural loci)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): locus (plural loci)
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $6$: Curves and Coordinates: Fermat
- Weisstein, Eric W. "Locus." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Locus.html