Search results
Results From The WOW.Com Content Network
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 closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...
Because the lines are parallel, the perpendicular distance between them is a constant, so it does not matter which point is chosen to measure the distance. Given the equations of two non-vertical parallel lines = + = +, the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular ...
In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem , and therefore is occasionally called the Pythagorean distance .
Shortest path (A, C, E, D, F), blue, between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist.
3. The equality of the volumes of two tetrahedra of equal bases and equal altitudes. 4. Problem of the straight line as the shortest distance between two points. 5. Lie's concept of a continuous group of transformations without the assumption of the differentiability of the functions defining the group. 6. Mathematical treatment of the axioms ...
Example of a shortest path in a three-dimensional Euclidean space The Euclidean shortest path problem is a problem in computational geometry : given a set of polyhedral obstacles in a Euclidean space , and two points, find the shortest path between the points that does not intersect any of the obstacles.