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In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are the radial distance r along the line connecting the point to a fixed point called the origin; the polar angle θ between this radial line and a given polar axis; [a] and
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.
The distance from a point to a plane in three-dimensional Euclidean space [8] The distance between two lines in three-dimensional Euclidean space [9] The distance from a point to a curve can be used to define its parallel curve, another curve all of whose points have the same distance to the given curve. [10]
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.
The distance of closest approach is sometimes referred to as the contact distance. For the simplest objects, spheres, the distance of closest approach is simply the sum of their radii. For non-spherical objects, the distance of closest approach is a function of the orientation of the objects, and its calculation can be difficult.
In classical physics, translational motion is movement that changes the position of an object, as opposed to rotation.For example, according to Whittaker: [1] If a body is moved from one position to another, and if the lines joining the initial and final points of each of the points of the body are a set of parallel straight lines of length ℓ, so that the orientation of the body in space is ...
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 ...
The vector of coordinates forms the coordinate vector or n-tuple (x 1, x 2, …, x n). Each coordinate x i may be parameterized a number of parameters t. One parameter x i (t) would describe a curved 1D path, two parameters x i (t 1, t 2) describes a curved 2D surface, three x i (t 1, t 2, t 3) describes a curved 3D volume of space, and so on.