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In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly-linear number of distinct distances. It was posed by Paul Erdős in 1946 [ 1 ] [ 2 ] and almost proven by Larry Guth and Nets Katz in 2015.
The Erdős Distance Problem consists of twelve chapters and three appendices. [ 5 ] After an introductory chapter describing the formulation of the problem by Paul Erdős and Erdős's proof that the number of distances is always at least proportional to n d {\textstyle {\sqrt[{d}]{n}}} , the next six chapters cover the two-dimensional version ...
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.
In computer science, the earth mover's distance (EMD) [1] is a measure of dissimilarity between two frequency distributions, densities, or measures, over a metric space D.
The spider is 1 foot below the ceiling and horizontally centred on one 12′×12′ wall. The fly is 1 foot above the floor and horizontally centred on the opposite wall. The problem is to find the minimum distance the spider must crawl along the walls, ceiling and/or floor to reach the fly, which remains stationary. [1]
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.
Weebly, a subsidiary of Block, Inc., is an American web hosting and web development company based in San Francisco, California. Founded in 2006 by David Rusenko, Chris Fanini , and Dan Veltri, the company offers WYSIWYG website creation services and hosting.
The term minimum distance may refer to Minimum distance estimation, a statistical method for fitting a model to data; Closest pair of points problem, the algorithmic problem of finding two points that have the minimum distance among a larger set of points; Euclidean distance, the minimum length of any curve between two points in the plane
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