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In mathematics, an equidistant set (also called a midset, or a bisector) is a set whose elements have the same distance (measured using some appropriate distance function) from two or more sets. The equidistant set of two singleton sets in the Euclidean plane is the perpendicular bisector of the segment joining the two sets. The conic sections ...
When two cells in the Voronoi diagram share a boundary, it is a line segment, ray, or line, consisting of all the points in the plane that are equidistant to their two nearest sites. The vertices of the diagram, where three or more of these boundaries meet, are the points that have three or more equally distant nearest sites.
In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1 ...
Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. 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.
In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight line (its axis). Given a straight line L and a point P not on L , one can construct a hypercycle by taking all points Q on the same side of L as P , with perpendicular distance to L equal to that ...
Step 1 (red): construct a circle with center at P and some fixed radius r to create points A′ and B′ on the line AB, which will be equidistant from P. Step 2 (green): construct circles centered at A′ and B′ having radius r. P and Q will be the points of intersection of these two circles. Point Q is then the reflection of point P through ...
Indeed, it is shown in (Schwabhäuser 1983) that by specifying two distinguished points on a line, called 0 and 1, we can define an addition, multiplication and ordering, turning the set of points on that line into a real-closed ordered field. We can then introduce coordinates from this field, showing that every model of Tarski's axioms is ...
In the following, the rest length [3] or proper length [4] of an object is its length measured in the object's rest frame. (This length corresponds to the proper distance between two events in the special case, when these events are measured simultaneously at the endpoints in the object's rest frame.