What Is a Collinear Antenna?

In geometry, the collinearity of a set of points is that they are on the same line at the same time. More generally, the term has been used to align objects, that is, everything in a row or in a row.

In any geometry, the set of points on a line is considered collinear. In Euclidean geometry, this relationship is visually displayed by points on "straight lines". However, in most geometries, including Euclidean, lines are usually primitive (undefined) object types, so this visualization is not necessarily appropriate. Geometric models provide concepts such as points, lines, and other object types being related to each other and collinear. For example, in spherical geometry, large circles with lines in the sphere are represented in the standard model, and the set of collinear points lies on the same large circle. These points are not on Euclidean's "straight line" and are not considered continuous.

Mapping a line to itself is called the collinearity of the line; it has a collinearity property. Linear diagrams (or linear functions) in vector space are considered geometrical maps that map lines to lines; that is, they map collinear point sets to collinear point sets and are therefore collinear. In projective geometry, these linear mappings are called isomorphisms and are just one type of collinearity.

triangle

In any triangle, the following point sets are collinear:

(1) The center of the center, the center of the periphery, the center of gravity, the characteristics of Exeter, the center of the Dronzi corner point and the nine-point circle are collinear, and all fall on a line called the Euler line.

(2) Any vertex, the tangent with the opposite side of the outer circle, and the Nagel point are collinear in a line called a triangle splitter.

(3) The midpoint on either side, the point equidistant from the triangle boundary in either direction (so these two points correspond to the perimeter), and the center of the Spieker circle is collinear on a line called a triangle cutter . (Spieker circle is the circle of the inner triangle, the center of which is the centroid of the triangle perimeter)

(4) At any vertex, the tangent of the opposite side to the circumference and the Gergonne point are collinear.

(5) Starting from any point on the circumscribed circle of the triangle, the nearest point on each of the three extended sides of the triangle is collinear in the Simson line on the circumscribed point.

(6) The line connecting the heights intersects the opposite side at a collinear point.

quadrilateral

(1) In the convex quadrilateral ABCD where E and F intersect on the opposite side, the midpoints of AC, BD and EF are collinear, and the line passing through them is called Newton's line (sometimes called Newton's Gauss line). If the quad is a tangent quad, its entrance is also on that line.

(2) In a convex quadrilateral, the quasi-center H, the "area center" G, and the quasi-basic center O are collinear in order, HG = 2GO. (See the obvious points and lines in the quad #convex quad)

(3) Tangent quadrilateral #collinear point gives other collinearity of tangent quadrilateral.

(4) In a circular quadrilateral, the center of the circle, the center of gravity of the apex (the intersection of two double borders), and the anticenter are collinear

(5) In the circular quadrilateral, the intersection of the center of the area, the center of gravity of the vertex, and the diagonal are collinear

(6) In a tangential trapezoid, the tangent to the circumference of the two bases is collinear with the entrance.

Hexagon [edit]

Pascal's theorem (also known as the hexagonal mystery theorem) states that if any six points are selected on a conical section (ie, ellipse, parabola, or hyperbola) and connected in any order to form a hexagon, then three pairs of six sides Opposite sides of the shape (if extended) meet at three points on a straight line, called a hexagonal Pascal line. The opposite is also true: Braikenridge-Maclaurin's theorem states that if three intersections of three pairs of lines passing through the opposite sides of a hexagon are on a straight line, then the six vertices of the hexagon are on a cone, which can be like Pappus's The hexagonal theorem is degraded like that.

Conical section

(1) Pass

In coordinate geometry, in an n-dimensional space, the set of 3 or more different points is collinear if and only if the rank of the coordinate matrix of these vectors is 1. For example, given three points

,

with

matrix

Equivalently, for each subset of three points

,

with

If matrix

With a rank of 2 or less, the points are collinear. In particular, for three points in the plane (n = 2), the points are collinear if and only if their determinant is zero (the above matrix is an n-th order matrix); due to the 3 × 3 determinant of the triangle The area is twice positive or negative, and these three points are vertices, which is equivalent to the three points being collinear if and only if a triangle with these points as vertices has a zero region.

Two numbers m and n are not coprime, that is, they share a common element other than 1, only if the rectangle is drawn with (0,0), (m, 0), (m, n) and (0, n), at least one interior point is collinear with (0,0) and (m, n).

Given a partial geometry P, where two points determine a maximum of one line, a collinear graph of P is a graph whose vertices are points of P, where two vertices are adjacent if and only if they determine a line in P.

In statistics, collinearity refers to the linear relationship between two variables. If there is a precise linear relationship between the two, then the two variables are completely collinear, so the correlation between them is equal to 1 or -1. That is, if parameters exist

And satisfy the following expression, then

Are collinear, for observed variables we have:

This means that if you put various observations

Draw on

In the plane, these points are collinear in the sense defined earlier in this article.

Multicollinearity refers to the case where k (k2) explanatory variables in a multiple regression model are completely linearly related. According to

In fact, we rarely face multicollinearity in the dataset for all observed variables i. More commonly, when there is a "strong linear relationship" between two or more independent variables, a multicollinearity problem occurs, which means

one of them

The variance is relatively small.

The concept of horizontal collinearity expands on this traditional view and refers to collinearity between explanatory and standard (ie, explanatory) variables. ^[1]

Collinear antenna array

In telecommunications, a collinear antenna array is a dipole antenna array mounted in such a way that the corresponding elements of each antenna are parallel and aligned, i.e. they are positioned along a common line or axis.

Collinear photography

A collinear equation is a set of two equations used for photogrammetry and remote sensing to associate coordinates in the image (sensor) plane (two-dimensional) with object coordinates (three-dimensional). In a photographic setting, the equation is derived by considering an image in which the center of a point of an object is projected into the image (sensor) plane through the optical center of the camera. Three points, object points, image points, and optical centers are always collinear. Another way of saying it is that the line segments connecting the object point and its image point are all concurrent at the optical center. ^[2]