
	Where results make sense

Topic: Locus of points

Related Topics

Slope

Abscissa

Open economy

Multiplier effect

Closed economy

Circular flow

Autarky

Aggregate demand

Investment

Keynesian economics

Deficit spending

Robert Mundell

John Maynard Keynes

Fiscal policy

1960s

In the News (Fri 4 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Conics
		An ellipse is the locus of points in a plane such that the sum of the distances from any point to the two fixed points is a constant.
		Locus of points in a plane such that the difference between the distances from any point to the two fixed points is a constant.
		Construct a circle, a point outside the circle P, and a segment from the point outside the circle to a point on the circle.
	www.niles-hs.k12.il.us /timmil/conics.htm (623 words)

	Loci
		Points on the dotted line are 6 km from the school and so are part of the catchment area, hence they are not part of the locus of points outside the catchment area.
		The locus of all points at a distance d from a fixed line segment is represented by two parallel lines either side of it at a distance d away, plus two semicircles of radius d centred on the end points of the line segment.
		The locus of all points equidistant from two intersecting lines is made up of the two lines that bisect the angles formed where the original lines intersect.
	www.crocodile-clips.com /absorb/AM4/sample/KCA014.html (2329 words)

	Analytic Geometry (Site not responding. Last check: 2007-11-02)
		A hyperbola is the locus of points so that the absolute value of the difference of the distances from two given points (the foci) is constant.
		A parabola is the locus of points equidistant from a point (the focus) and a line (the directrix).
		Billiards in a circle: the angle with the tangent is constant, an orbit is periodic iff this angle is a rational multiple of π, and otherwise the impact points are dense on the boundary of the billiard, Kroneckers' theorem on density of orbits of an irrational rotation.
	www.math.tau.ac.il /~rudnick/courses/analyticgeomsyll.html (520 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-02)
		Describe the locus of points that are 6 units from the point (3,-1) and give the equation of the locus.
		Describe the locus of points that are 3 units from the line x = -1 and give the equation of the locus.
		There is a theorem that tells you that the locus of points equidistant from two points is the perpendicular bisector of the segment they define.
	mathforum.org /library/drmath/view/52853.html (964 words)

	Step 7: Sketch the Locus: Examples
		Note that the part of the locus off the real axis is close to joining with the real axis, in which case break points would occur.
		In this locus, determining the points where the locus crosses the real axis is rather important, since there is only a small set of values for K for which the system is stable.
		Note the part of the locus that is to the right of the imaginary axis.
	www-me.mit.edu /lectures/rlocus/3.7-examples.html (280 words)

	Conics (Site not responding. Last check: 2007-11-02)
		A conic is the locus of points in a plane obtained from a circle after a finite number of projections in space [3].
		That is, transformations of points to points and lines to lines in the projective plane that preserve the relation of incidence [1].
		A conic is the locus of self-conjugate points of a hyperbolic polarity [3].
	www-math.cudenver.edu /~dlholder/proj_geom/conic/node1.html (2419 words)

	Locus of a variable point
		Vectors and the parametric equation of a locus
		It is the locus of the point P. Points as intersection points of associated curves.
		The locus is a circle with midpoint (1,0) and radius = 1.
	www.ping.be /~ping1339/locus.htm (980 words)

	Practice with Locus Theorem 4
		The locus of points equidistant from two parallel lines is...
		Describe the locus of the center of the wheel of a train that is moving along a straight, level track.
		The locus of points equidistant from the lines x = -1.5 and x = 1.5 is the x-axis.
	regentsprep.org /Regents/math/locusPar/PracLoc4.htm (87 words)

	Maths - Revise - Loci & Construction 2 (Site not responding. Last check: 2007-11-02)
		The locus of points equidistant from a fixed point is a circle.
		The locus of points equidistant from a fixed line is two lines parallel to the fixed line.
		The locus of points equidistant from a line segment is a 'running-track' or 'capsule' shape.
	www.subtangent.com /maths/loci2.php (341 words)

	2001-2002
		The locus of a given point or set of points is another point or set of points that satisfy a given condition.
		The locus, or the resulting set of points, is frequently a line, two lines, a circle, or the interection of two of the above.
		6) The locus of points equidistant from the sides of a given angle is the angle bisector.
	www.fontbonne.org /locus2.htm (478 words)

	Glencoe Mathematics - Online Study Tools
		What is the locus of all points in a plane that are 3 units from a given point in that plane?
		all points in a plane that are 4 units from a given segment in that plane
		all points in a plane that are 4 units from a given point in that plane
	www.glencoe.com /sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-825275-6&chapter=13&lesson=1 (146 words)

	Maths Unit 12 - Analytical Geometry - An introduction - 2.3 Introduction to locus
		the locus of points at a distance of 3 from the point (0, 0) is given by the equation
		Locus 1 could be the trajectory (path or orbit) of a planet around the sun.
		Locus 2 could be the path of the moon around the earth, or the path of a stone swung on a string.
	academic.sun.ac.za /mathed/Shoma/MATUNIT12_04.htm (691 words)

	CS 308-507 Project: Furthest Point Voronoi Diagrams (Site not responding. Last check: 2007-11-02)
		The most commonly studied is the closest point Voronoi diagram: the locus of all points in the plane closer to one site than all other sites.
		Each locus of points is a polygonal shape, and in the case of the FPVD, each of these "polygons" is unbounded.
		However, not all points may affect the diagram; those that do are called Voronoi sites, the subset of the inpute point set to which a locus of points in the plane (either furthest or closest) belongs.
	www.cs.mcgill.ca /~netty/html/507.html (577 words)

	Adam Coffman --- equidistant surfaces
		The locus of points in space which are equidistant from the line and the sphere is a "surface of Gerhard Miehlich." For a point P, let b denote the (non-negative) distance from P to L.
		Points on the negative x-axis (where the surface crosses itself) are equidistant from L and S, as are points on the line segment connecting the origin (0,0,0) to the center C = (1,0,0).
		The locus of points equidistant from L and S is the xy-plane, z = 0 (light green).
	www.ipfw.edu /math/Coffman/pov/miehlich.html (728 words)

	Mammography of computer tomography for imaging and therapy - Patent 6463122
		From each point of the locus of points 64, an angle is determined between a line from the source 32 to the isocenter 62 and a line from the source 32 to the tumor 60.
		Finally, a diameter of the tumor 60 from that point of the locus of points 64 is calculated.
		Further, the size of the aperture of the blades 54 is calculated based upon a distance of the tumor 60 from the source 32 and also a size of the tumor 60 from the perspective of the current point of the locus of points 64.
	www.freepatentsonline.com /6463122.html (4109 words)

	Maths Unit 12 - Analytical Geometry - An introduction - 7. More loci
		Locate one of the points of the locus, and label it with it’s coordinates as variables: e.g.
		Find the locus of a set of points that are equidistant from two points A and B. You know that geometrically, the answer is the perpendicular bisector of AB as illustrated in the applet.
		Locus 1 is a special line through the origin, and a special N on the X-axis.
	academic.sun.ac.za /mathed/Shoma/MATUNIT12_09.htm (430 words)

	Transitivity in Action
		The distance function dist(P,bb) here is the Hausdorff distance between the single point set {P} and the line (which is of course also a set of points) bb.
		Point O is equidistant from all three vertices.
		Q.E.D. To prove that the three medians intersect at a point, I refer to the notion of barycentric coordinates.
	www.cut-the-knot.org /triangle/remarkable.shtml (1236 words)

	Loci of Equi-angular Points
		In general, if AB is any chord of a circle, the angle APB for any point P on the circle is constant except at the singular points A and B themselves.
		We've labeled the angles taking advantage of the fact that the triangles with one vertex at the central point O and the other two vertices on the circle are isosceles.
		This shows that the angular velocity about the point T is always exactly 1/2 the angular velocity about the center of the circle.
	www.mathpages.com /home/kmath173.htm (511 words)

	Locus of Points in a Given Ratio to Two Points
		The locus is a circle, unless of course r = 1, in which case it's the perpendicular bisector of AB.
		For any P on the circle, the internal and external bisectors of angle APB pass through (the fixed points) M and N. The circle we just constructed is known as a Circle of Apollonius.
		The family of all such circles obtained for different values of r and fixed points A and B is known as the Apollonian Family of Circles defined by the points A and B. Note that one of these circles (corresponding to
	www.cut-the-knot.org /Curriculum/Geometry/LocusCircle.shtml (413 words)

	The Locus of an Equation
		However, the points whose coordinates satisfy most of the equations in x and y are normally not scattered in a random field.
		The locus of an equation is a curve containing those points, and only those points, whose coordinates satisfy the equation.
		For instance a circle may be said to be the locus of all points in a plane that is a fixed distance from a fixed point.
	www.tpub.com /math2/10.htm (635 words)

	Introduction
		It focuses on helping students to visualise and understand what is meant by a "locus of points".
		The resource could be used as an introduction to the topic of locus and could be followed up by lessons on the techniques of construction used to create accurate loci drawings.
		an activity to show the locus of points which describes the path of a football as it is kicked
	www.ngfl-cymru.org.uk /vtc/20050506/Mathematics/Keystage4/Shapespaceandme/locus/introduct (156 words)

	locus. The New Dictionary of Cultural Literacy, Third Edition. 2002
		In geometry, the set of all points (and only those points) that satisfy certain conditions; these points form a curve or figure.
		For example, the locus of all points in space one foot from a given point is a sphere having a radius of one foot and having its center at the given point.
		The locus of all points in a plane one foot from a given point is a circle having a radius of one foot and having its center at the given point.
	www.bartleby.com /59/19/locus.html (180 words)

	An Introduction To Root Locus Techniques
		The root locus is a widely used tool for design of closed loop systems, and it has the virtue of being a good design tool for continuous time systems (where you work in the s-plane) and for sampled (computer controlled) systems (where you work in the z-plane).
		A root locus is the locus of the closed loop poles (roots of the denominator polynomial) plotted as the open loop gain constant changes.
		Note that you are trying to calculate the gain for a point on the root locus that is at the center of the rectangle on the root locus plot.
	www.facstaff.bucknell.edu /mastascu/eControlHTML/RootLocus/RLocus1A.html (3784 words)

	Bienvenue dans Adobe GoLive 5 (Site not responding. Last check: 2007-11-02)
		I propose to rephrase the stated properties in terms of the pedal points of a point P. These are the orthogonal projections of P on the sides.
		This proves that, in any triangle, the distance between the pedal points of a given point P is proportional to the distance of P to the vertices of the triangle.
		So two other point of the locus are given by the intersections of the angular bisectors with the opposite side of the triangle.
	tecfa.unige.ch /problemes/en/dankaert.html (481 words)

	Minutes
		describe the locus of points at a given distance from a given point as "the circle with the given point as its center and the given distance as its radius" 2.
		draw the locus of points satisfying the first of two conditions, the locus of points satisfying the second condition, and locate the points of intersection of these loci 2.
		draw, in the coordinate plane, the locus of points satisfying the first of two conditions, the locus of points satisfying the second condition, and locate the points of intersection of these loci 2.
	www.amaps.org /term3all.html (4843 words)

	Locus - LoveToKnow 1911
		The theory of loci is thus identical with that of curves (see Curve and Geometry: § Analytical).
		The notion of a locus applies also to solid geometry.
		Here the locus of the points satisfying a single (or onefold) condition is a surface; the locus of the points satisfying two conditions (or a twofold condition) is a curve in space, which is in general a twisted curve or curve of double curvature.
	www.1911encyclopedia.org /Locus (121 words)

	Geometry/History Lesson Plan
		Have students discover certain features of the centroid; Locus of points of a median, properties of the segments that form the median, areas of the smaller sections(triangles) formed by the medians.
		The locus of points of the angle bisectors are equidistant from the sides of the triangle.
		The locus of points of the perpendicular bisectors are equidistant from the vertices of the triangle.
	courses.wcupa.edu /jkerriga/Lessons/T.Lauriahistgeom.html (1126 words)

Try your search on: Qwika (all wikis)