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In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions. [1] [2] The set of the points that satisfy some property is often called the locus of a point satisfying this ...
Cut locus C(P) of a point P on the surface of a cylinder. A point Q in the cut locus is shown with two distinct shortest paths , connecting it to P.. In the Euclidean plane, a point p has an empty cut locus, because every other point is connected to p by a unique geodesic (the line segment between the points).
(See Ellipse § Definition as locus of points and Hyperbola § As locus of points.) The foci F 1 , F 2 {\displaystyle F_{1},\,F_{2}} thus determine two pencils of confocal ellipses and hyperbolas. By the principal axis theorem , the plane admits a Cartesian coordinate system with its origin at the midpoint between foci and its axes aligned with ...
Locus (mathematics), the set of points satisfying a particular condition, often forming a curve; Root locus analysis, a diagram visualizing the position of roots as a parameter changes; Locus (archaeology), the smallest definable unit in stratigraphy; Locus (genetics), the position of a gene or other significant sequence on a chromosome
An ellipse can be defined as the locus of points for which the sum of the distances to two given foci is constant. A circle is the special case of an ellipse in which the two foci coincide with each other. Thus, a circle can be more simply defined as the locus of points each of which is a fixed distance from a single given focus.
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As you approach retirement, financial planning takes center stage. While many focus on savings and investments, there’s another often-overlooked strategy to bolster your nest egg: getting rid of ...
It is the locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. Equivalently, in polar coordinates ( r , θ ) it can be described by the equation r = b ⋅ θ {\displaystyle r=b\cdot \theta } with real number b .