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The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
Euclidean distance geometry studies properties of Euclidean distance such as Ptolemy's ... The distance formula itself was first published in 1731 by Alexis ...
Distance geometry is the branch of mathematics concerned with characterizing and studying sets of points based only on given values of the distances between pairs of points. [ 1 ] [ 2 ] [ 3 ] More abstractly, it is the study of semimetric spaces and the isometric transformations between them.
The same sense of distance is used in Euclidean geometry to define distance from a point to a line, distance from a point to a plane, or, more generally, perpendicular distance between affine subspaces. Even more generally, this idea can be used to define the distance between two subsets of a metric space.
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
1 Formula and proof. 2 See also. 3 References. ... the distance between the two lines is the distance between the two intersection points of these lines with the ...
The formula for the closest point to the origin may be expressed more succinctly using notation from linear algebra. The expression a x + b y + c z {\displaystyle ax+by+cz} in the definition of a plane is a dot product ( a , b , c ) ⋅ ( x , y , z ) {\displaystyle (a,b,c)\cdot (x,y,z)} , and the expression a 2 + b 2 + c 2 {\displaystyle a^{2 ...
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. [1] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry.