A concept sometimes employed in geometry. It is usually understood to mean the set of points (forming a curve or a surface in "good cases") which, out of all the points in the space, satisfy some geometric requirement. Thus, an ellipse may be defined as the geometric locus of points in the plane for which the sum of the distances from two given points is a constant magnitude.


Comments

The phrase "geometric locus" is somewhat obsolete, and nowadays usually simply means a point set defined by some property.

References

[a1] H.S.M. Coxeter, "Introduction to geometry" , Wiley (1961)
[a2] D. Hilbert, S.E. Cohn-Vossen, "Anschauliche Geometrie" , Springer (1932)
How to Cite This Entry:
Geometric locus. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Geometric_locus&oldid=33423
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article