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Dragonfall
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If you put n points on a plane, not all on a line, is there always a point with at least n/2 lines incident? The lines in question are determined by the points themselves.
Dragonfall said:If you put n points on a plane, not all on a line, is there always a point with at least n/2 lines incident? The lines in question are determined by the points themselves.
for any collection of n points, not all collinear, there exist at least n⁄2 lines containing exactly two points.
The term "points on a plane" refers to a set of points that lie on a two-dimensional surface, known as a plane. These points have two coordinates, typically denoted as (x,y), and are used to describe the location of a point on the plane.
The equation n/2 represents the number of lines that can be drawn between a set of n points on a plane. This is known as the line-connecting problem, and it asks whether it is possible to draw lines between all points without any lines crossing or overlapping.
The answer to this question depends on the arrangement of the points on the plane. If the points are randomly distributed, it is unlikely that n/2 lines can be drawn without any crossings. However, if the points are placed in a specific pattern, such as a regular grid, it is possible to draw n/2 lines without any crossings.
The number of lines that can be drawn between points on a plane depends on the number of points. If there are n points, there can be a maximum of n/2 lines without any crossings. This relationship is based on the fact that each point can be connected to n-1 other points, and each line connects two points.
The line-connecting problem has applications in various fields, such as transportation, computer science, and biology. For example, in transportation, it can be used to determine the most efficient routes for a network of cities. In computer science, it can be applied to data visualization and graph theory. In biology, it can be used to study the structures and connections in the human brain.