Pattern of Two Loci
According to G. Pólya, the method of finding geometric objects by intersection.
1. For example, the centers of all circles tangent to a straight line s at a given point P lie on a line t that passes through P and is perpendicular to s.
2. In addition, the circle c centered at P with radius R is the locus of the centers of all circles of radius R passing through P.
The intersection of c and t consists of two points A and B which are the centers of two circles of radius R tangent to s at P.
Many constructions with straightedge and compass are based on this method, as, for example, the construction of the center of a given circle by means of the perpendicular bisector theorem.
See also
Cartesian PatternThis entry contributed by Margherita Barile
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References
Pólya, G. Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving, 2 vols. in One. New York: Wiley, 1981.Referenced on Wolfram|Alpha
Pattern of Two LociCite this as:
Barile, Margherita. "Pattern of Two Loci." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PatternofTwoLoci.html