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Look up collinearity or collinear in Wiktionary, the free dictionary. In geometry, collinearity of a set of points is the property of their lying on a...

In statistics, multicollinearity or collinearity is a situation where the predictors in a regression model are linearly dependent. Perfect multicollinearity...

Three or more points are said to be collinear if they lie on the same line. If three points are not collinear, there is exactly one plane that contains...

In telecommunications, a collinear antenna array (sometimes spelled colinear antenna array) is an array of dipole or quarter-wave antennas mounted in...

Altermagnetic structures are collinear and crystal-symmetry compensated, resulting in zero net magnetisation. Unlike in an ordinary collinear antiferromagnet, another...

{\displaystyle A,B,C} is one set of collinear points, and a , b , c {\displaystyle a,b,c} is another set of collinear points, then the intersection points...

lines to the graph of a cubic function at three collinear points intercept the cubic again at collinear points. This can be seen as follows. As this property...

hexagons, is the form used in Cairo and has the property that every edge is collinear with infinitely many other edges. In architecture, beyond Cairo, the Cairo...

intersection points of each of the three pairs of external tangent lines are collinear. For any two circles in a plane, an external tangent is a line that is...

equilateral triangle, and the three angles at B show that A, B and C are collinear.) This construction can be repeated as often as necessary to find a point...

of stating the theorem is that every finite set of points that is not collinear has an ordinary line. According to a strengthening of the theorem, every...

other words, the diagonal points of a complete quadrangle are always collinear. "The" Fano plane of 7 points and lines is "a" Fano plane. A standard...

will in turn radiate qq pairs and so on, with each new parton nearly collinear with its parent. This can be described by convolving the spinors with...

In mathematics, a comodule or corepresentation is a concept dual to a module. The definition of a comodule over a coalgebra is formed by dualizing the...

collinear port or to be transmitted to the other collinear port. Despite apparently being in direct communication with each other, the two collinear ports...

records of their first encounters with these indigenous people. Three non-collinear points determine a unique plane in a three dimensional affine space, and...

In phenomenology (physics), soft-collinear effective theory (or SCET) is an effective field theory of quantum chromodynamics (QCD) which describes the...

13-1/2-inch lens and five holders. 4 × 5 view camera, 6 lenses – 12-inch Collinear, 8-1/2 APO Lanthar, 9-1/4 APO Tessar, 4-inch Wide Field Ektar, Dallmeyer...

The collinearity equations are a set of two equations, used in photogrammetry and computer stereo vision, to relate coordinates in a sensor plane (in two...

a kinematic effect known as Thomas precession, whereby successive non-collinear Lorentz boosts become equivalent to the composition of a rotation of the...

another part of the body in the opposite direction. When the forces are collinear (aligned with each other), they are called tension forces or compression...

a projective space to itself, such that the images of collinear points are themselves collinear. A collineation is thus an isomorphism between projective...

circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. The line through these points is the Simson line of P, named for Robert...

Blackburne Shilling Gambit is a typical example of coffeehouse play. collinear move A move in which two opposing pieces face each other, and one slides...

In chemistry, molecules with a non-collinear arrangement of two adjacent bonds have bent molecular geometry, also known as angular or V-shaped. Certain...

three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct...

equation relating the magnitudes of three coplanar, concurrent and non-collinear force vectors, which keeps an object in static equilibrium, with the angles...

which provides some additional information about the relative order of collinear points. Here, the length AB is taken to be positive or negative according...

The Collinear Resonance Ionization Spectroscopy (CRIS) experiment is located in the ISOLDE facility at CERN. The experiment aims to study ground-state...

counterclockwise. The determinant is non-zero if points A, B, and C are non-collinear. In the above example, with points ordered A, B, C, etc., the determinant...

collinear. An angle consists of a point O (the vertex) and two non-collinear rays out from O (the sides). A triangle is given by three non-collinear points...

constructed by proving that three symmetrically constructed points are collinear; here Menelaus' theorem gives a useful general criterion. In this section...

using collinear dipole arrays. These consist of multiple half-wave dipoles mounted collinearly (in a line), fed in phase. The coaxial collinear (COCO)...

information relating to the combination of the row and column headings it is collinear with. A table consists of an ordered arrangement of rows and columns....

experiment uses the technique of collinear spectroscopy using lasers to access necessary atomic transitions. The Collinear Resonance Ionization Spectroscopy...

that finite sets of many points in the Euclidean plane either have many collinear points, or they have many points that are all mutually visible to each...

(1) ABCD is a cyclic quadrilateral if and only if points P and Q are collinear with the center O, of circle ω {\displaystyle \omega } . (2) ABCD is a...

projective plane. Given three non-collinear points, there are three lines connecting them, but with four points, no three collinear, there are six connecting...

deviation) of an estimated regression coefficient is increased because of collinearity. Cuthbert Daniel claims to have invented the concept behind the variance...

to 0.5 dBd). The Super-J variation of the J-pole antenna adds another collinear half-wave radiator above the conventional J and connects the two with...

(no three collinear) in a plane and the system of conics which pass through a fixed set of four points (again in a plane and no three collinear) is called...

(no three collinear) in a plane and the system of conics which pass through a fixed set of four points (again in a plane and no three collinear) is called...

for his work on effective field theories and for developing the Soft Collinear Effective Theory (SCET). Stewart attended college at the University of...

the wave is said to be a longitudinal wave if the vectors are always collinear with the vector n → {\displaystyle {\vec {n}}} , and a transverse wave...

problem for the number of points that can be placed on an n × n lattice without any three being collinear – in this case, 16 pawns on a regular chessboard...

non-collinear members meet in an unloaded joint, both are zero-force members. If three members meet in an unloaded joint, of which two are collinear, then...

meaning that exactly n - 1 of the points are collinear. The theorem is clearly true for three non-collinear points. We proceed by induction. Assume n > 3...

The figure presents a triangle with dimensions 'b', 'h' and 'a', along with axes 'x' and 'y', 'x' being collinear with the base....

Three Sisters. The belt consists of three bright and easily identifiable collinear star systems – Alnitak, Alnilam, and Mintaka – nearly equally spaced in...

Similarly, three generic points in the plane are not collinear; if three points are collinear (even stronger, if two coincide), this is a degenerate...

quadrangle are collinear, some authors have augmented the axioms of projective geometry with Fano's axiom that the diagonal points are not collinear, while others...

that in any triangle, the orthocenter, circumcenter and centroid are collinear. This property is also true for another triangle center, the nine-point...

M represents a cation. The uranium atom in uranates(VI) has two short collinear U–O bonds and either four or six more next nearest oxygen atoms. The structures...

plane, which lacks a notion of distance but preserves the notion of collinearity. Conversely, in adding more structure, one may view the plane as a 1-dimensional...

The COLlinear LAser sPectroScopy (COLLAPS) experiment is located in the ISOLDE facility at CERN. The purpose of the experiment is to investigate ground...

ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line. Given four points A...

The Multi Ion Reflection Apparatus for Collinear Laser Spectroscopy (MIRACLS) is a permanent experiment setup being constructed at the ISOLDE facility...

proportions of this linkage are possible. Since points O, B, D must be collinear at all points in the linkage's motion, and countless arm length combinations...

revolving body is the geometric plane in which its orbit lies. Three non-collinear points in space suffice to determine an orbital plane. A common example...

There are two major types of the acousto-optic filters, the collinear and non-collinear filters. The type of filter depends on the geometry of acousto-optic...

the major fault relationship is approaching, overlapping, collateral or collinear. Since transfer zones are normally found in extensional settings many...

three-dimensional space (3D), as one vertex and two endpoints (assumed non-collinear) define an Euclidean plane in 3D. For example, an arc of a great circle...

lengths (except for the ratio of the lengths of two line segments that are collinear). It is therefore true for triangles in any affine plane over any field...

projection plane. The projected point on the plane is chosen such that it is collinear with the corresponding three-dimensional point and the centre of projection...

{\displaystyle \geq } AC with equality if and only if A, B, and C are collinear (on the same line). This in turn is equivalent to the proposition that...

points is an oval if and only if |Ω| = n + 1 and no three points are collinear (on a common line). An ovoid in a projective space is a set Ω of points...

the coefficient estimates do not need to be unique if covariates are collinear. Though originally defined for linear regression, lasso regularization...

rejecting what they perceive as a misappopriation of the term, preferring collinearity instead. The analysis of synteny in the gene order sense has several...

connecting the orthocenter with the Spieker center, thus establishing three collinearities involving the mittenpunkt. The three lines connecting the excenters...

as one. One or more unique polar axes could be made through two such collinear unmoved points. Polar crystallographic point groups include 1, 2, 3, 4...

significance (for example, when x {\displaystyle \mathbf {x} } is almost collinear with e 1 {\displaystyle \mathbf {e} _{1}} , ‖ u ‖ {\displaystyle \|\mathbf...

the intersection of tangents at opposite vertices (A, C) and (B, D) are collinear in four points; the tangents being degenerate 'sides', taken at two possible...

collinear and no seven points out of P1, ..., P8 are co-conic. Then no five points of P1, ..., P8 and no three points of P5, P6, P7, P8 are collinear...

each of an external angle bisector with the opposite extended side, are collinear (fall on the same line as each other). Three intersection points, two...

Angles CAB and BAG are both right angles; therefore C, A, and G are collinear. Angles CBD and FBA are both right angles; therefore angle ABD equals...

(quanta of spin wave excitations) was theoretically proposed in 2016 in collinear antiferromagnetic materials, but its experimental confirmation remains...

Velocity-addition formula for details. The composition of two non-collinear Lorentz boosts (i.e., two non-collinear Lorentz transformations, neither of which involve...

an invertible (or more generally one-to-one) map which sends collinear points to collinear points. One can define a projective space axiomatically in terms...

centers; for example, the points Q, Q' in Figure 4. Points which are collinear with respect to the homothetic center but are not homologous are said...

adjustable) shapers and programmable shapers. Collinear static: propagation in dispersive medium, chirped mirror Collinear programmable: AOPDF Transverse static:...

metal. However, it is not as efficient as a draw hoe for moving soil. The collinear hoe or collineal hoe has a narrow, razor-sharp blade which is used to...

duality of plane projective geometry (where points correspond to lines and collinearity of points corresponds to concurrency of lines), the statement of Desargues's...

aimed to reduce costs and materials used. It employs a technique known as collinear holography, whereby a blue-green and red laser beam are collimated in...

In theoretical physics, the composition of two non-collinear Lorentz boosts results in a Lorentz transformation that is not a pure boost but is the composition...

{\displaystyle n)} , for 0 ≤ i < n {\displaystyle 0\leq i<n} , contains no three collinear points. When n {\displaystyle n} is not prime, one can perform this construction...

a circle. The other case of equality occurs when the four points are collinear in order. The inequality does not generalize from Euclidean spaces to...

magnetic field, the z-axis of the coordinate system is required to be collinear with the magnetic field to obtain a Hamiltonian in the form above (the...

{A}{\pi }}}} The radius of the circle that passes through the three non-collinear points P1, P2, and P3 is given by r = | O P 1 → − O P 3 → | 2 sin ⁡ θ...

The previous year, he conjectured that n points in the plane, not all collinear, must span at least ⌊ n / 2 ⌋ {\displaystyle \lfloor n/2\rfloor } two-point...

a related structure, this time the collinearity graph of the incidence structure. The vertices of the collinearity graph are the points of the incidence...

light, and using Cartesian coordinates so that the x and x′ axes are collinear. In the fundamental branches of modern physics, namely general relativity...

circles associated with an arbelos. An arbelos is determined by three collinear points A, B, and C, and is the curvilinear triangular region between the...

{\displaystyle B_{1}B_{2}} , and C 1 C 2 {\displaystyle C_{1}C_{2}} are collinear. The theorem was stated by Arnold Droz-Farny in 1899, but it is not clear...

the other lines through P, making sure that these points are not all collinear (this last condition can not be satisfied if n = 2.) This produces a minimal...

preserves: collinearity between points: three or more points which lie on the same line (called collinear points) continue to be collinear after the transformation...

unique. If no four points are collinear, then five points define a unique conic (degenerate if three points are collinear, but the other two points determine...

magnetic field when the electron density and temperature gradients have non-collinear (perpendicular) components, and was first identified by Ludwig Biermann...

of a hexagon), the lines defined by opposite sides intersect in three collinear points. This can be reversed to construct the possible locations for a...

self-crossing quadrilateral, the Varignon parallelogram can degenerate to four collinear points, forming a line segment traversed twice. This happens whenever...

method. Another important source of cospectral graphs are the point-collinearity graphs and the line-intersection graphs of point-line geometries. These...

visual field (stimuli) organised coherently by Gestalt factors such as collinearity, closure, and symmetry. Early researchers initially postulated that space-based...

electron–positron pair production. In reality the produced pair are nearly collinear. The black dot labelled 'Z' represents an adjacent atom, with atomic number...

'conjunction', 'yoked together') may refer to: Syzygy (astronomy), a collinear configuration of three celestial bodies Syzygy (mathematics), linear relation...

illusion by Italian researcher Gianni A. Sarcone shows that though the collinear blue and red segments seem to oscillate up and down, they are always the...

five points in the plane in general linear position, meaning no three collinear, there is a unique conic passing through them, which will be non-degenerate;...

area of geometric figures and the alignment and relative distances of collinear points. For fonts that do not implement true-italics, a shear mapping...

parallel line construction to all possible lines, not just the ones with a collinear bisected line segment. To construct a parallel line of any given line...

antennas, while base stations usually use larger fiberglass whips or collinear arrays of vertical dipoles. For directional antennas, the Yagi antenna...

that do not form an orthocentric system such that no three of them are collinear. The nine-point circles of triangles △ABC, △BCD, △CDA, △DAB meet at one...

shifters. For example, most commercial FM Radio and TV antenna towers use a collinear antenna array, which is a fixed phased array of dipole elements. In radar...

circle being inverted and the center of its image under inversion are collinear with the center of the reference circle. This fact can be used to prove...

displaced Abbe–Koenig prism projects image forward, rotated by 180° and collinear (4 internal reflections [2 reflections are on roof plains]) Bauernfeind...

acousto-optic programmable dispersive filter (AOPDF) is a special type of collinear-beam acousto-optic modulator capable of shaping spectral phase and amplitude...

to consider these points again. (If at any stage the three points are collinear, one may opt either to discard or to report it, since in some applications...

point theorem). The midpoints of a set of parallel chords of a conic are collinear (midpoint theorem for conics). Chords were used extensively in the early...

exterior angle bisectors and the extended triangle sides D, E, F are collinear, that is they lie on a common line. The angle bisector theorem appears...

forces acting on the object. The normal force N is equal, opposite, and collinear to the gravitational force mg so the net force and moment is zero. Consequently...

Lagrange point Robert Farquhar (1966). "Station-Keeping in the Vicinity of Collinear Libration Points with an Application to a Lunar Communications Problem"...

Winner, Larry (March 25, 2002). "Influence Statistics, Outliers, and Collinearity Diagnostics". Belsley, David A.; Kuh, Edwin; Welsh, Roy E. (1980). Regression...

isoperimetric point, the incenter and the Gergonne point of a triangle are collinear, that is all four points lie on a common line. Furthermore, they form...

astronomer Joseph-Louis Lagrange obtained two constant-pattern solutions (collinear and equilateral) of the general three-body problem. In the restricted...

each point P ∈ {\displaystyle \in } k the points P, T(P)= P' and D are collinear. Remark: This property is the basis for the construction of the center...

in Euclidean geometry, Longuerre's theorem is a result concerning the collinearity of points constructed from a cyclic quadrilateral. It is a generalization...

that for each point p ∈ P and each line l ∈ L, the set of points of l collinear to p is either a singleton or the whole l. Finite polar spaces (where...

theorem Botje, Michiel. "Quantum Chromo Dynamics, Section 7. Soft and Collinear Singularities" (PDF). Retrieved May 30, 2014. Soper, Davison. "Jet Definitions"...

{fg}}.} If the incircle is tangent to the bases at P, Q, then P, I, Q are collinear, where I is the incenter. The angles ∠ AID and ∠ BIC in a tangential trapezoid...

elements. However, if each dipole is vertically oriented, in a so-called collinear antenna array (see graphic), that null direction becomes vertical and...

varieties of six-pointed stars are used in cultures around the world: If the collinear edges of a regular six-pointed star are connected, so that two interlaced...

leads to a high tooling flexibility, as the motion of the electrodes is collinear. Unlike the C-type, the so-called X-type arrangement provides less rigidity...

(1 January 1999). "Hyperfine structure in the 576 nm line of Pr II by collinear fast-ion-beam laser spectroscopy". Journal of Physics B: Atomic, Molecular...

the Gergonne point. The Nagel point, the centroid, and the incenter are collinear on a line called the Nagel line. The incenter is the Nagel point of the...

are collinear and distinct. If (A,B|C,D), then (C,D|A,B) and (B,A|D,C). If (A,B|C,D), then not (A,C|B,D). If points A, B, C and D are collinear and distinct...

Angles CAB and BAG are both right angles; therefore C, A, and G are collinear. Angles CBD and FBA are both right angles; therefore angle ABD equals...

cluster within 7° of longitude on September 12. Syzygy (astronomy), a real collinear configuration of three or more celestial bodies Conjunction (astronomy)...

with M3 being the midpoint of JK, then the points M3, M1, I, and M2 are collinear. The line containing them is the Newton line of the quadrilateral. If...

their actual natural geometry (may also be referred to as ’’mates’’): collinearity, perpendicularity, tangency, symmetry, coincidency, and parallelism are...

generic point. Points that are incident with the same line are said to be collinear. The set of all points incident with the same line is called a range....

order to estimate total flow velocity. This measurement is made in a collinear direction with the flow. In planar Doppler velocimetry (optical flow meter...

R . {\displaystyle c(x,y,z)={\frac {1}{R}}.} If the three points are collinear, R can be informally considered to be +∞, and it makes rigorous sense...

metal antenna elements. For example, a dipole antenna consists of two collinear metal rods. If the rods are horizontal, it radiates horizontally polarized...

dimensions, a plane is uniquely determined by any of the following: Three non-collinear points (points not on a single line). A line and a point not on that line...

divisible by a prime number that does not divide any other denominator. If collinear points A, B, C, and D are such that D is the harmonic conjugate of C with...

550 AU that began with random orientations were sculpted into roughly collinear and coplanar groups of spatially confined orbits by a massive distant...

Cambridge University Press. ISBN 0-521-08139-4. Abdilkadir Altintas, "Some Collinearities in the Heptagonal Triangle", Forum Geometricorum 16, 2016, 249–256.http://forumgeom...

BC, CA, AB and perpendiculars of AP, BP, CP through P respectively are collinear. The line which includes these three points is called the orthotransversal...

Latin linea align, alignment, ambilineal, ambilineality, bilinear, collinear, collinearity, collineation, curvilinear, curvilinearity, delineate, delineation...

one-dimensional set of points; through any three points that are not collinear, a two-dimensional plane can be drawn; and, in general, through k + 1...

superexchange center and the magnetic moments it connects to are non-collinear, namely the atomic bonds are canted, the superexchange will be accompanied...

necessary and sufficient to determine a unique curve. For example, three (non-collinear) points determine a circle: the generic circle is given by the equation...

example is looking at a cube in the direction where the face normal is collinear with the view vector. The first type of silhouette edge is sometimes troublesome...

circumcircle of three collinear points is the line on which the three points lie, often referred to as a circle of infinite radius. Nearly collinear points often...

Although there can be no infinite non-collinear set of points with integer distances, there are infinite non-collinear sets of points whose distances are...

particularly natural example of a nonassociative medial magma is given by collinear points on elliptic curves. The operation x • y = −(x + y) for points on...

central atom, they adopt a trigonal bipyramidal molecular geometry with two collinear axial positions and three equatorial positions. An electron pair in an...

triangle. However, other horn triangles, such as the arbelos (with three collinear vertices and three semicircles as its sides) are interior to one of the...

the position where the illuminator, the observer, and the object are collinear (all lying along the same line), with the illuminator and the observer...

Perles configuration, a set of nine points in the Euclidean plane whose collinearities can be realized only by using irrational numbers as coordinates. Perles...

lines intersect at the isotomic conjugate of P. We assume that P is not collinear with any two vertices of △ABC. Let A', B', C' be the points in which the...

Simple Collinear edges Complex polygon Convex Concave Regular pentagon (108° internal angles) Adjacent right angles (60° 150° 90° 90° 150°) Reflexed regular...

on cell phone tower. Collinear arrays of dipoles stacked inside the tall white cases radiate a flat, fan-shaped beam. VHF collinear array of folded dipoles...

relationship does not hold, or is ambiguous, include cases like: Three or more collinear points, where the circumcircles are of infinite radii. Four or more points...

measure of variability The geometric median is unique unless the sample is collinear. Subsequent scholars appear to concur with Eisenhart that Boroughs' 1580...

shape, typically a rectangle, appears misaligned when, in fact, they are collinear. The Müller-Lyer illusion, where two lines of the same length appear to...

in O'Gorman, Frank; Clowes, MB (1976). "Finding Picture Edges Through Collinearity of Feature Points". IEEE Trans. Comput. 25 (4): 449–456. Bibcode:1976ITCmp...

1st Brocard cubic is the locus of X for which the points XA, XB, XC are collinear. The 1st Brocard cubic passes through the centroid, symmedian point, Steiner...

effects. Calculates P values, model fit and quality indices, and full collinearity coefficients. Calculates effect sizes and Q-squared predictive validity...

be turned with respect to the outer coil. When the two coils' axes are collinear, with the magnetic fields pointing in the same direction, the fields add...

p_{(n/2)+1}} .) The geometric median is unique whenever the points are not collinear. The geometric median is equivariant for Euclidean similarity transformations...

elements arranged end-to-end, and lying along essentially the same axis (or collinear), each feeding one side of a two-conductor transmission wire. The physical...

M)   Polar circle of △ABC (d; centered at orthocenter H) The centers of these circles relating to △ABC are all collinear–they fall on the Euler line....

two perpendicular bisectors M. (They meet because the points are not collinear). Construct the circle with centre M passing through one of the points...

thousands of miles in size. VHF collinear array of folded dipoles Sector antennas (white bars) on cell phone tower. Collinear dipole arrays, radiating a flat...

Pollak, J. Romelt 'A classical analysis of quantum resonances in isotopic collinear H + H2 Reactions' Chemical Physics letters, 1982. Donald G. Fleming, Jorn...

centers. Usually there is a single dipole driven element consisting of two collinear rods each connected to one side of the transmission line, and a variable...

triangle, which implies the points are collinear. The determinant, therefore, provides a useful tool to test for collinearity. Since two points uniquely identify...

each of an external angle bisector with the opposite extended side, are collinear. In a triangle, three intersection points, two between an interior angle...

full collinearity assessment approach. International Journal of e-Collaboration, 11(4), 1-10. Kock, N.; Lynn, G. S. (2012). "Lateral collinearity and misleading...

line. (Playfair's axiom) There exist four points such that no three are collinear (points not on a single line). In an affine plane, two lines are called...

w ) , − ℘ ′ ( z + w ) ) {\displaystyle R=(\wp (z+w),-\wp '(z+w))} are collinear, the geometric form of the group law of an elliptic curve. This can be...

{\displaystyle {\begin{aligned}P&=p:q:r\\U&=u:v:w\\X&=x:y:z\\\end{aligned}}} are collinear if and only if the determinant D = | p q r u v w x y z | {\displaystyle...

Alexandria. Pappus's hexagon theorem states that every two triples of collinear points ABC and abc (none of which lie on the intersection of the two lines)...

logarithm Cr {\displaystyle \operatorname {Cr} } is the cross-ratio of four collinear points P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} are the...

of freedom with limiting cases of a cubic convex hull at one limit of collinear edges, and a rhombic dodecahedron as the other limit as 6 edges are degenerated...

lines are taken to be a type of generalised circle with infinite radius, collinear points (points along a single line) are considered to be concyclic. This...

Retrieved 20 August 2014. Belsley, David (1991). Conditioning diagnostics : collinearity and weak data in regression. New York (NY): Wiley. ISBN 978-0471528890...

directions. In the laboratory frame, there is a small angular deviation from collinearity, which is caused by the momentum of the electron. Hence, measuring the...

discovered. John N. Mather and Richard McGehee prove that for the Newtonian collinear four-body problem there exist solutions which become unbounded in a finite...

Mifflin, p. 245; reprint, Dover Books, 1960. Tabov, Jordan (1995), "Four Collinear Griffiths Points", Mathematics Magazine, 68 (1): 61–64, JSTOR 2691382...

general position, i.e., no three points are collinear. The algorithm may be easily modified to deal with collinearity, including the choice whether it should...

expired uncollected in 1882). He used a dipole antenna consisting of two collinear one-meter wires with a spark gap between their inner ends, and zinc spheres...

spirals the golden spiral has the distinguishing property that for four collinear spiral points A, B, C, D belonging to arguments θ, θ + π, θ + 2π, θ +...

Cauchy–Schwarz inequality is met with equality when the two vectors involved are collinear. In the way it is used in the above proof, this occurs when all the non-zero...

'inferior' those planets (Mercury and Venus) whose epicycle remained collinear with Earth and the Sun, compared to the 'superior' planets (Mars, Jupiter...

constant acceleration. Since the position, velocity, and acceleration are collinear (parallel, and lie on the same line) – only the magnitudes of these vectors...

(average) of the centers of the three circles of Apollonius, which are collinear on the Lemoine axis. The center also lies on the trilinear polar of the...

of the probability that any given subset of k points is approximately collinear in the way defined above, consider the line between the "leftmost" and...

molecular structural formulas Variance inflation factor, a measure of collinearity in statistical regression models Visual information fidelity, measure...

diffeomorphisms. Jointly with Richard McGehee, he gave an example of collinear four-body problem which has initial conditions leading to solutions that...

this case, a triple (A,B,C) is in the relation if the three points are collinear—that is, they lie on the same straight line. Another geometric example...

Cauchy–Schwarz inequality, equality occurs if and only if J(v1) and v2 are collinear, which is equivalent to the span of v1, v2 being closed under J. Let v1...

the line. In this formulation, the theorem states that if A, B, C are collinear points, and P is any point, then ( P A ¯ 2 ⋅ B C ¯ ) + ( P B ¯ 2 ⋅ C A...

The first is the inverse Dzyaloshinskii–Moriya mechanism, where non-collinear spins generate a local electric dipole proportional to the spiral's chirality...

theory (which expands around heavy quark mass near infinity), and soft-collinear effective theory (which expands around large ratios of energy scales)...

arises when two or more of the explanatory variables are close to being collinear. PCR can aptly deal with such situations by excluding some of the low-variance...

Collinearity of the midpoints of parallel chords in a conic...

cross behaves like a four-legged stool. Geometrically, any three non-collinear points can self-consistently define a plane; three legs are inherently...

zero, so placements that maximize the smallest triangle will not have collinear triples of points. The assumption that the shape is compact implies that...

these points, which is the Euler line of the given triangle. Thus, it is collinear with all the other triangle centers on the Euler line, which along with...

example, in the case of a first degree polynomial exactly fitting three collinear points). In general, however, some method is then needed to evaluate each...

woodtreks.com (Video) How to mark dovetail joints without the transfer step - from tailspintools.com "Collinear Marking Tools For Dovetails". TailSpin Tools....

to highly ionize gas without contact with any capillary or target. A collinear setup[clarification needed] is usually used, enabling the synchronization...

{\displaystyle X,I,C} and Y , I , B {\displaystyle Y,I,B} are triples of collinear points. Pascal's theorem on hexagon X C A B Y T A {\displaystyle XCABYT_{A}}...

apex. For any isosceles triangle, there is a unique square with one side collinear with the base of the triangle and the opposite two corners on its sides...

_{N})(2\rho _{F-}+\chi \rho _{N})}}.} Here the subscript of R denote collinear and oppositely oriented magnetization in layers, χ = b/a is the thickness...

statistical techniques reduces the specification bias, the effects of collinearity between the variables, to the same order as the uncertainty due to the...

A permutation of the seven points that carries collinear points (points on the same line) to collinear points is called a collineation or symmetry of...

{(t+1)(st+\alpha )}{\alpha }}} ⁠. The point graph (also known as the collinearity graph) of a p g ( s , t , α ) {\displaystyle \mathrm {pg} (s,t,\alpha...

whether six points lie on a conic to checking whether three points are collinear. The dual version may be proved using Brianchon's theorem. In 2021, Traves...

from having direct line-of-sight to Earth for data transfer. The three collinear Lagrange points (L1, L2, L3) were discovered by the Swiss mathematician...

the three excircles. S is the cleavance center of triangle △ABC S is collinear with the incenter (I), the centroid (G), and the Nagel point (N) of triangle...

phase-matched. For example, all the optical frequencies involved can be collinear, can have the same polarization, and travel through the medium in arbitrary...

(equivalently) photons.  The simplest form of radiative transfer involves a collinear beam of radiation traveling through a sample to a detector.  That flux...

linearly dependent. This occurs in linear regression when predictors are collinear, causing the normal equations matrix X T X {\displaystyle X^{T}X} to be...

in Spain, she completed her doctorate in 1993. Her dissertation was Collinearity in Mixed Models, and was advised by Ronald W. Helms. She joined Duke...

incidence geometry states that if n points of Euclidean geometry are not collinear then there must exist a 2-secant of them. And the original orchard-planting...

shows that two quaternions commute if and only if their vector parts are collinear. Hamilton showed that this product computes the third vertex of a spherical...

mausoleum Xiuliang stood, demarcated by Kappa Aquarii and three other collinear stars. Ku ("crying") and Qi ("weeping"), each composed of two stars, were...

the axis of the waveguide. This has a radiation pattern similar to a collinear dipole antenna, and is usually mounted vertically. The radiation pattern...

instead, it satisfies: a + b = c {\displaystyle a+b=c} . It has thus collinear vertices and zero area. If the three vertices are all distinct, it has...

coincide. No three points of a hypercycle are collinear. If the points A, B, C of a hypercycle are collinear then the chords AB, BC are on the same line...

coefficient of restitution of zero. The line of impact is the line that is collinear to the common normal of the surfaces that are closest or in contact during...

meant in the sense defined below. The classic example is the relation of collinearity among three points in Euclidean space. In an abstract set, a ternary...

composition is a bijective map of the points of S2 onto itself which preserves collinear points and is called a perspective collineation (central collineation...

economic dimension'. As it states in the academic article: 'Confounding and collinearity in regression analysis: a cautionary tale and an alternative procedure...

a point of the segment AC. ( B 4 ) ∀ A , B , C , l ( ( A , B , C  non-collinear ) ∧ ( l  intersects  A B ) ∧ ¬ ( l  passes through  A , B , C ) ) → (...

Q + R = O {\displaystyle P+Q+R=O} we have that these three points are collinear, thus there is some linear f ∈ K [ x , y ] {\displaystyle f\in K[x,y]}...

paradox: Which formula should be used to transform velocities between non-collinear reference frames in special relativity? Paradox of radiation of charged...

in cellphones. Higher gain omnidirectional UHF antennas can be made of collinear arrays of dipoles and are used for mobile base stations and cellular base...

mechanical device for transmitting torque between two shafts that are not collinear. It consists of a flexible joint fixed to each shaft. The two joints are...

S P 2 ¯ {\displaystyle {\overline {SP_{2}}}} ⁠. The image of a point collinear with P 1 , Q 1 {\displaystyle P_{1},Q_{1}} can be determined using ⁠ P...

found three families of periodic solutions in which the three masses are collinear at each instant. In 1772, Lagrange found a family of solutions in which...

per line axiom above by: There exist four points, no three of which are collinear. To avoid the non-Desarguesian planes, include Pappus's theorem as an...

arbelos is a shape bounded by three mutually-tangent semicircular arcs with collinear endpoints, with the two smaller arcs nested inside the larger one; let...

of a projective line is a collineation, since every set of points are collinear. However, if the projective line is embedded in a higher-dimensional projective...

is not really a polarity at all, for poles of concurrent lines are not collinear points." It was Jean-Victor Poncelet (1788–1867), a French engineer and...

(142, 143 and 145) at relatively small magnetic fields up to 334 G by collinear laser ion beam spectroscopy". The European Physical Journal D. 71 16....

movements are highly curved. The current density vector, J, is no longer collinear with the electric field vector, E. The two vectors J and E make the Hall...

. The big-line-big-clique conjecture on the existence of either many collinear points or many mutually visible points in large planar point sets The...

products on the unit hyperbola illustrates the additivity of rapidities for collinear velocities. Simultaneity of events depends on rapidity a; { z = σ j e...

three-center four-electron bond can be alternatively viewed as consisting of two collinear two-center one-electron bonds, with the remaining two nonbonding electrons...

quantum-mechanical argument; see the article Landé g-factor. μJ and J vectors are not collinear, so only their magnitudes can be compared. The muon, like the electron...

to distances or angles; it can be studied as an affine space, where collinearity and ratios can be studied but not distances; it can be studied as the...

in situations anytime there are three or more inertial frames in non-collinear motion, as can be seen using Lorentz transformations. Thomas precession...

infinite Diophantine figures must be collinear in the Diophantine plane. Hence, any process of extending a non-collinear Diophantine figure by adding vertices...

{N}} _{1}} and N ^ 2 {\displaystyle \mathbf {\hat {N}} _{2}} are not collinear N ^ 1 {\displaystyle \mathbf {\hat {N}} _{1}} , N ^ 2 {\displaystyle \mathbf...

two faces are coplanar (lying in the same plane) and no two edges are collinear (segments of the same line), it can be considered as being strictly convex...

either | S | ≤ 2 {\displaystyle |S|\leq 2} or S consists of three non-collinear points. As a matroid, it has been called the MacLane matroid, after the...

model. This model, first proposed in 1951, considers bonding of three collinear atoms. For example, bonding in XeF 2 is described by a set of three molecular...

{\displaystyle T>T_{v}} or T < T v {\displaystyle T<T_{v}} . 2. Collisions are collinear and rotational energy effects are negligible. 3. The duration of collision...

each other (unlike, for example, in a naive Bayes classifier); however, collinearity is assumed to be relatively low, as it becomes difficult to differentiate...

respective convex hulls are disjoint (colloquially, do not overlap). Three non-collinear points in two classes ('+' and '-') are always linearly separable in two...

Pappus of Alexandria had solved a special case: when the three points are collinear. But the general case had the reputation of being very difficult. After...

includes the rotation given by Rodrigues' formula, in terms of two non-collinear boost velocities, and the axis of rotation is perpendicular to their plane...

valence partons. A parton distribution function (PDF) within so called collinear factorization is defined as the probability density for finding a particle...

distinct points are either collinear or determine a unique plane. On the other hand, four distinct points can either be collinear, coplanar, or determine...

SPACE". IAA. Robert Farquhar (1966). "Station-Keeping in the Vicinity of Collinear Libration Points with an Application to a Lunar Communications Problem"...

nonlinear crystals are birefringent, beams that are collinear inside a crystal may not be collinear outside of it. The phase fronts (wave vector) do not...

Roboraptor Shiva laser Signal transfer function Slide projector Soft-collinear effective theory Solar gain Space-Based Infrared System Space-Based Infrared...

invertible. This happens if and only if the triangle vertices aren't collinear and the ray isn't parallel to the plane. The algorithm can use Cramer's...

Miquel's theorem the points A´, B´ and C´ form a triangle (that is, are not collinear) then the theorem was named the Pivot theorem in Forder (1960, p. 17)...

their gene expression, typically into an early and late phase, using collinear systems regulated by anti-terminators (lambda phage) or splicing modulators...

variant of parallelism is used in the affine plane. Clifford parallel Collinearity Concurrent lines Limiting parallel Parallel curve Ultraparallel theorem...

This alignment of eight Yersinia bacteria genomes reveals 78 locally collinear blocks conserved among all eight taxa. Each chromosome has been laid out...

century that these six points lie on four lines, each line having three collinear points. Many special cases of Apollonius's problem involve finding a circle...

Junru Wu, "An Experimental Investigation of the Interaction of Two Non-Collinear Beams of Sound", Proceedings of the 13th International Symposium on Nonlinear...

collection of n {\displaystyle n} points in the plane that are not all collinear, if n {\displaystyle n} is large enough then there must exist at least...

curved) that is perpendicular to the light's wavefronts; its tangent is collinear with the wave vector. Light rays in homogeneous media are straight. They...

demonstration of spin precession and dephasing in a magnetic field non-collinear to the injected spin orientation, called the Hanle effect. Antiferromagnetic...

Suppose the zeroes z1, z2, and z3 of a third-degree polynomial p(z) are non-collinear. There is a unique ellipse inscribed in the triangle with vertices z1...

two other points is defined by the following construction: Given three collinear points A, B, C, let L be a point not lying on their join and let any line...

xi2) for the four roots xi of the quartic. These four points are not collinear because they lie on the irreducible quadratic y = x2 and thus there is...

given as y = m x + k {\displaystyle y=mx+k} . In the case of three non-collinear points in the plane, the triangle with these points as its vertices has...

wave in two or three dimensions, the gradient of the field is always collinear with the direction n → {\displaystyle {\vec {n}}} ; specifically, ∇ F...

2-15, 2-20 and 2-30, respectively. The 6-15 resembles the 5-15, but with collinear horizontal pins, spaced 23⁄32 in (18.3 mm) center-to-center. The 20 A...

consequence, one obtains an equation for the circle determined by three non-collinear points P i = ( x i , y i ) {\displaystyle P_{i}=\left(x_{i},\,y_{i}\right)}...

of magnetization and spin–orbit interaction (exceptions related to non-collinear magnetic order notwithstanding) and its detailed mechanism depends on...

phase of the sound wave. The phase can be changed by an arbitrary amount. Collinear transverse acoustic waves or perpendicular longitudinal waves can change...

light energetic (collinear) particles, the interactions with low-energetic (soft) degrees of freedom are described by the soft-collinear effective theory...

antenna Beverage antenna Cantenna Cassegrain antenna Choke ring antenna Collinear antenna array Conformal antenna Corner reflector antenna Curtain array...

triangle has a 180° angle and two 0° angles, making the three vertices collinear, as shown in the bottom example. Thus, in Euclidean geometry, the shortest...

; Mehen, Thomas (May 2006). "J/Ψ PHOTO-PRODUCTION AT LARGE Z IN SOFT COLLINEAR EFFECTIVE THEORY". New Trends in HERA Physics 2005: 239–250. arXiv:hep-ph/0512194...

measurement of spin and magnetic moment Laser-induced optical pumping Collinear laser spectroscopy Resonance ionization mass spectroscopy Rubbia, Carlo...

and left base angle 60 degrees, so that two edges of the triangle are collinear with sides of the parallelogram. Scaling the parallelogram in ratio ⁠...

projections of only two points of the knot, and these points are not collinear. In this case, by choosing a projection side, one can completely encode...

generalized quadrangle. The collinearity graph having as vertices the points of a generalized quadrangle, with the collinear points connected. This graph...

(vesica piscis) bounded by two congruent arcs of circles together with two collinear rays having their apexes at the corners of the lens, and a "fish-shaped"...

in-phase. Consider two dipole antennas placed in a line end-to-end, or collinear. If the resulting array is pointed directly at the source signal, both...

{\vec {b}}={\vec {f}}_{1}t_{2}+{\vec {f}}_{2}{\tfrac {1}{t_{1}}}} are collinear with the center of the hyperbola (see diagram). The simple proof is a...

S2CID 22442636. Robert Farquhar (1966). "Station-Keeping in the Vicinity of Collinear Libration Points with an Application to a Lunar Communications Problem"...

Jaroń-Becker, Agnieszka; Kapteyn, Henry C; Murnane, Margaret M (2015). "Non-collinear generation of angularly isolated circularly polarized high harmonics"...

points are collinear. Every set of three of these four circles has among them three crossing points, and (by the assumption of non-collinearity) there exists...

vectors are said to be scalar multiples of each other, or parallel or collinear, if there is a scalar λ such that x = λ y . {\displaystyle \mathbf {x}...

G^{1}} (tangent continuity) requires the neighboring control points to be collinear with the join. This is less strict than C 1 {\displaystyle C^{1}} continuity...

the Lanzhou–Haikou Expressway to Hainan. As of December 2022, only the collinear section with G15, within Haikou city, is opened for service. The northern...

plane, etc. This property is analogous to the property that three non-collinear points determine a unique circle in a plane. Consequently, a sphere is...

which use total internal reflection in a prism set designed for efficient collinear transmission. Media that reduce the amplitude of certain polarisation...

circumcenter of triangle △ABC. This fact provides a tool for proving collinearity of the circumcenter, centroid and orthocenter. The medial triangle is...

antennas use a spring of non-conducting material for support and comprise a collinear array antenna. Such antennas are still called rubber ducky antennas even...

shell, as some thinkers of the day had suggested. c. 1750 – The three collinear Lagrange points (L1, L2, L3) were discovered by Leonhard Euler, a decade...

of the Fano plane's seven points that carries collinear points (points on the same line) to collinear points is called a collineation of the plane. The...

parallelogram is a degenerate quadrilateral of area zero, consisting of four collinear points. The convex hull of an antiparallelogram is an isosceles trapezoid...

between 3D and 2D coordinates.[citation needed] Camera resectioning Collinearity equation Entrance pupil, the equivalent location of the pinhole in relation...

forms of PDS: Collinear and Transverse. Collinear PDS was introduced in a 1980 paper by A.C. Boccara, D. Fournier, et al. In collinear, two beams pass...

antenna Beverage antenna Cantenna Cassegrain antenna Choke ring antenna Collinear antenna array Conformal antenna Corner reflector antenna Curtain array...

(ANSI/RIA R15.06-1999) defines a singularity as "a condition caused by the collinear alignment of two or more robot axes resulting in unpredictable robot motion...

diabatic representations for atom-molecule collisions: Treatment of the collinear arrangement". Chemical Physics Letters. 35 (1): 112–118. Bibcode:1975CPL...

by everyone involved. The roads of Cincinnati and Covington were laid collinear with each other, in the hope that a bridge would be built sometime in...

into a similar triangle and an obtuse silver gnomon. The trisector is collinear with a medium diagonal of the octagon. Sharing the apex of the parent...

sets do not exist. According to the Erdős–Anning theorem, infinite non-collinear point sets with all distances being integers cannot exist. This does not...

Coherent differential phase-shift keying – Coherer – Coilgun – Collinear antenna array – Collinear antenna array – Collins Radio – Colpitts oscillator – Combat-net...

with a powerful external electric field E {\displaystyle \mathbf {E} } collinear with an external magnetic field B {\displaystyle \mathbf {B} } that exploits...

sides include the arbelos, which is formed from three semicircles with collinear endpoints, and the Bézier triangle. The Reuleaux triangle may also be...

quasiorthocenter H, the "area centroid" G, and the quasicircumcenter O are collinear in this order, and HG = 2GO. There can also be defined a quasinine-point...

{e}}\cdot \mathbf {E} .} The electron's electric dipole moment (EDM) must be collinear with the direction of the electron's magnetic moment (spin). Within the...

at NikkeiBP". Nikkei Business Productions. コリニア方式ホログラフィーの原理と応用展開 aka Collinear Holography/Principle and Applications The Original Japanese Essay that...

{Z}},} ⁠ and ⁠ ( 1 , tan ⁡ θ ) {\displaystyle (1,\tan \theta )} ⁠ are collinear points. In fact, Z {\displaystyle {\mathcal {Z}}} is the inversion of...

incenter and the three excenters of a triangle ABC. Then I and J are collinear with one of the three triangle vertices. The circle with IJ as diameter...

time. The "Sofia" is a two-section, three-bogie unit with the Bo'2'Bo' collinear formula, while the "Sofia 70" is a three-section, Bo'2'2'Bo' unit. All...

opposite sides of the trapezoid and the intersection of the diagonals are collinear. The angles in the quadrilateral ABCD satisfy sin ⁡ A sin ⁡ C = sin ⁡...

3D reconstruction from multiple images 3D scanner Binocular disparity Collinearity equation Photogrammetry Essential matrix, Fundamental matrix Trifocal...

high-quality phased genome of T. wallichiana has been sequenced, and collinearity analysis between it and other closely related species to gymnosperms...

{\displaystyle s} is the maximum number of times each triple of points can become collinear, β s + 2 ( q ) = λ s + 2 ( q ) q {\displaystyle \beta _{s+2}(q)={\frac...

cloverleaf and quadrifilar antennas, which do not have vulnerable zones unlike collinear "pins". Also, the dome EW has the possibility of expanding the spectrum...

dimension of the Sierpinski gasket can be calculated. Consider three non-collinear points a1, a2, a3 in the plane R2 and let ψ i {\displaystyle \psi _{i}}...

For large data matrices, or matrices that have a high degree of column collinearity, NIPALS suffers from loss of orthogonality of PCs due to machine precision...

3640546 Erdogan, F. (1962), "On the stress distribution in plates with collinear cuts under arbitrary loads", Proceedings of the Fourth US National Congress...

configurations. The third, fourth and fifth of these have a face with collinear adjacent edges, and the sixth has a face that is not simply connected...

first CARS microscope was demonstrated. In 1999, CARS microscopy using a collinear geometry and high numerical aperture objective were developed in Xiaoliang...

1 {\displaystyle \omega _{1}} and ω 2 {\displaystyle \omega _{2}} are collinear, the generated radiation propagates in the same direction and the phase...

infrared pulse with a time duration of few to tens femtoseconds are collinearly focused on the studied sample. At this point, by varying the delay of...

{\displaystyle \mathbf {R^{n}} } ; since the vectors are not required to be collinear, the value of this relaxed program can only be higher than the value of...

directions to steer the acoustic beam. Using three independent (i.e. non-collinear) axes is enough to retrieve the three components of the wind speed, although...

Scribner's Sons, New York, p. 15: "Any vector r coplanar with two non-collinear vectors a and b may be resolved into two components parallel to a and...

parallel to the line and through the point. Axiom 3 requires three non-collinear points. Axiom 4a requires a translation to move any point to any other...

successor. Thus the commonly used notation places each down-chain x axis collinear with the common normal, yielding the transformation calculations shown...

transformation happens to be another boost, B(w), where w is collinear with u and v. If u and v are not collinear but in different directions, the situation is considerably...

(a+b)c=ac+bc.} Geometrically, affine transformations (affinities) preserve collinearity: so they transform parallel lines into parallel lines and preserve ratios...

the circumcircle. Then their centers and the center of the incircle are collinear. Until 2003, academia thought this third problem of Thébault the most...

impedance when the maximum power transfer theorem is looked for. Three non-collinear points u , v , w {\displaystyle u,v,w} in the plane determine the shape...

UV laser. Plain-wave geometry or loose focusing geometry allows highly collinear phase matching and maximum flux extraction at the driving wavelengths...

include ANI, digital DNA–DNA hybridization (dDDH) and Kr distance. Genomic collinearity was suggested as a possible source of markers to resolve species complexes...

+ 1 {\displaystyle |{\mathcal {O}}|=n^{2}+1} and no three points are collinear (on a common line). Replacing the word projective in the definition of...

possible implementations are the "boxcar geometry" and the "partially collinear geometry". The boxcar geometry is a configuration where all the pulses...

plane or a near-pencil (meaning that exactly n − 1 of the points are collinear). In another direction, Ray-Chaudhuri and Wilson proved in 1975 that in...

relevance, then smaller groups are favored over large groups. If there are collinear features, the procedure may fail to identify important features. A solution...

face-in-the-crowd effect: Threat detection versus iso-feature suppression and collinear facilitation". Journal of Vision. 19 (7): 6. doi:10.1167/19.7.6. ISSN 1534-7362...

circular motion. This system postulated the existence of a Counter-Earth collinear with Earth and central fire, with the same period of revolution around...

et al. suggested that the (outer) jet of the quasar 3C 273 is nearly collinear to the Earth's line-of-sight. Superluminal motion of up to ~9.6c has been...

Systems – Safety Requirements to define it as "a condition caused by the collinear alignment of two or more robot axes resulting in unpredictable robot motion...

Kaufman's laboratory at Indiana University confirmed Lewis's theory. Collinearity is found between the order of the genes on the chromosome and the order...

linear polarization by 90° using seven internal reflections to induce collinear rotation, as shown in the diagram. The polarization is rotated in the...

circles with a common tangent circle, and in Monge's theorem on the collinearity of intersection points of certain bitangents. Overmars, M. H.; van Leeuwen...

Within the central genomic region, LSDV genes share a high degree of collinearity and amino acid identity with the genes of other mammalian poxviruses...

Hertz's transmitters consisted of a dipole antenna made of a pair of collinear metal rods of various lengths with a spark gap (S) between their inner...

independent and span the entire plane. If the rank is 1, then B and AB are collinear and do not span the plane. Assume that the initial state is zero. At time...

problem. In 1975, he, with John N. Mather, proved that for the Newtonian collinear four-body problem there exist solutions which become unbounded in a finite...

given tangent circles and of the circle in the chain whose center is collinear with the two given circles. All the centers of the circles in the Pappus...

PMID 7913880. S2CID 39168197. Gaunt SJ (2018). "Hox cluster genes and collinearities throughout the tree of animal life". The International Journal of Developmental...

containing them lies in the plane. Unique plane assumption. Through three non-collinear points, there is exactly one plane. Intersecting planes assumption. If...

Eigenschaften kollinearer Gebilde (translated On the Metrical Properties of Collinear Structures) with Fiedler as advisor. In 1907, he was appointed full professor...

crystal-controlled relay receivers Hoisington 16-element horizontally polarized collinear receive antenna 15 kW gasoline-fueled emergency generator The downtown...

in this regard; Pauling has suggested the use of three closely spaced collinear dots to represent the three-electron bond (see illustration). A common...

maximum likelihood estimation, subject to the condition that the points are collinear, will give the parameters for the line of best fit. She then deduced formulae...

{\displaystyle C} , A {\displaystyle A} , and I {\displaystyle I} are collinear. Therefore, the areas of triangles △ A B C {\displaystyle \triangle ABC}...

require the points to be in general position, meaning no 3 points are collinear and no 4 points are cocircular, then it is an open problem. Currently...

intersecting a curve at a point and parallel to the curve at that point. Collinear – in the same line Parallel – in the same direction. Transverse – intersecting...

two planes. (This condition means that every three points may be non-collinear and dually three planes may not have a line in common.) However, there...

the second harmonic at the output of a Michelson interferometer, in a collinear geometry. In this case, the signal recorded by a slow detector is I M...

the majority electrons are chosen to point up). In the most simple (collinear) cases of antiferromagnetism, there is still a common quantization axis...

the three midpoints of the diagonals of a complete quadrilateral are collinear. There are several proofs of the result based on areas or wedge products...

property. The curve is a line if and only if all the control points are collinear. The start and end of the curve is tangent to the first and last section...

triangles that do not connect edge-to-edge, or as quadrilateral with two collinear edges. Symmetry given assumes all faces are the same color. There are...

{o}}|=n+1} and if no three points of o {\displaystyle {\mathfrak {o}}} are collinear. According to this theorem of Beniamino Segre, for Pappian projective...

vertically with a spacing of approximately one wavelength, to create a collinear array. This generates an omnidirectional radiation pattern with increased...

in which points P lying on the cubic and their isogonal conjugates are collinear with a fixed point Q known as the pivot point of the cubic. The Neuberg...

subgroup of M24.(Griess 1998, p. 55) A hyperoval has no 3 points that are collinear. A Fano subplane likewise satisfies suitable uniqueness conditions. To...

T-shaped portals of its 10 m (33 ft) radius great kiva were north–south collinear, and axes joining opposing windows passed within 10 cm (4 in) of its center...

silver atoms adopt two different coordination environments, one having two collinear oxide neighbours and the other four coplanar oxide neighbours. tetrasilver...

VP1 and overlaps the start of VP1 by 13 nucleotides. Similarly, VP3 is collinear to VP1 and VP2 and results from initiation of translation at a downstream...

of P2. Even in this degenerate case when an angle of π arises, the two collinear edges are still considered as distinct for the purposes of the construction...

Latin linea align, alignment, ambilineal, ambilineality, bilinear, collinear, collinearity, collineation, curvilinear, curvilinearity, delineate, delineation...

dimension of hyperbolic spaces. A hyperbolic triangle consists of three non-collinear points and the three segments between them. Hyperbolic triangles have...

in pictures), called a sector antenna, usually consists of a vertical collinear array of dipoles. It has a flat, fan-shaped radiation pattern, that is...

three other points that are not collinear with it. But in the Desargues configuration, these three points are always collinear with each other (if the chosen...

Euler centre and the circumcenter) of triangle ABC. So there are 6 points collinear on a single line. Kimberling, Clark. "Encyclopedia of Triangle Centers:...

rigid, it is sufficient to describe the position of at least three non-collinear particles. This makes it possible to reconstruct the position of all the...

the explosives environments of nova, supernova, and x-ray bursters. The Collinear Fast-Beam Laser Spectroscopy (CFBS) experiment at TRIUMF is designed to...

discovery of the first molecule exhibiting a toroidal moment. The non-collinear arrangement of Ising spins in a Dy3 triangular coordination complex is...

t ) {\displaystyle (l,R,t)} , at least N = 3 {\displaystyle N=3} non-collinear points in each point set are required. More recently, Briales and Gonzalez-Jimenez...

link be displaced off to the side, the third joint can also be displaced collinear to the original links, allowing for the links to remain as bars. Example...

Desarguesian) a set A of k (k ≥ 3) points such that no three points of A are collinear (on a line) is called a k - arc. If the plane π has order q then k ≤ q...

1687 and 1999 (transl.), see also Tisserand, 1894). In 1767, Euler found collinear motions, in which three bodies of any masses move proportionately along...

covering. If the polygon is in general position (i.e. no two edges are collinear), then every triangle can cover at most 3 polygon edges. Hence every polygon...

curve that is perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). A slightly more rigorous definition of a light...

of Engineering and Technology, Hyderabad, Andhra Pradesh, India Soft-collinear effective theory Spacecraft Event Time This disambiguation page lists...

points is an oval if and only if |Ω| = n + 1 and no three points are collinear (on a common line). A set of points in an affine plane satisfying the...

which are not antipodal, on the great circle they determine, three non-collinear points do not determine a unique triangle. However, if we only consider...

making it ideal for emergency communications. Repeaters typically use a collinear antenna array with vertical polarization, which allows the repeater to...

Despegar – Latin America’s largest online travel agency, HK Express airline, Collinear, Gulf Air, Repsol and Bittensor. Sense Worldwide York, Peter; Damazer...

triangle meet the opposite extended sides of its reference triangle at three collinear points. In any acute triangle, the inscribed triangle with the smallest...

instance, algorithms that may misbehave when some three input points are collinear) into algorithms that work robustly, correctly, and efficiently in the...

{\displaystyle A} can be oriented along two non-collinear directions. When A {\displaystyle A} is a vector collinear with n ^ {\displaystyle {\hat {n}}} , the...

curve will have a sharp corner if the neighbour control points are not collinear. Using the definitions of the basis functions N i , n {\displaystyle N_{i...

orthogonality. When two non-zero Euclidean vectors are orthogonal, they are not collinear. The intersections of any Euclidean linear subspace with its orthogonal...

translation. A screw motion S {\displaystyle S} is the product of four non-collinear reflections, and thus S = a b c d {\displaystyle S=abcd} . But according...

arcs, which he named "trilaterals") and proves Menelaus' theorem on collinearity of points on the edges of a triangle (which may have been previously...

an orthogonal polarity form an oval (that is, n + 1 points, no three collinear), while if n is even, the absolute points lie on a non-absolute line....

Rai PK, Pareek S, Joshi H (1 January 2013). "Regression Analysis of Collinear Data using r-k Class Estimator: Socio-Economic and Demographic Factors...

springs usually bear on a pad alongside the stub-axle. Often, the shock is collinear with the spring forming a coil-over. In many cases, the damper is also...

"right-handed" coordinate system, if the result is 0, the points are collinear; if it is positive, the three points constitute a positive angle of rotation...

Becquart, Charlotte S.; Domain, Christophe; Kermode, James R. (2024-03-22). "Collinear-spin machine learned interatomic potential for ${\mathrm{Fe}}_{7}{\ma...

I′ and II′. The origins of these four plane coordinate systems may be collinear with the axis of the optical system; and the corresponding axes may be...

number defined from any four collinear points. In the realization derived from the regular pentagon, the four collinear points have cross-ratio 1 + φ...

= n + 1 {\displaystyle |{\mathfrak {o}}|=n+1} and no three points are collinear (on a common line). Theorem Let be o {\displaystyle {\mathfrak {o}}} an...

5. Three cards form a set if and only if the corresponding points are collinear in that space. More generally, in the variant, n {\displaystyle n} cards...

field will be circular in a plane that is perpendicular to the field and collinear to the direction of particle motion, and free in the direction orthogonal...

Regression diagnostics: Identifying influential data and sources of collinearity. Vol. 571. John Wiley & Sons, 2005. Ruotsalo, Tuukka; Aroyo, Lora; Schreiber...

Fresnel rhomb, has the additional feature that the emerging beam can be collinear with the original incident beam. In order to specify the phase shift on...

transmission experiments. The interaction of rigid line inclusions in parallel, collinear and radial configurations have been studied using the boundary element...

76 km2), all land. La Belle is located on Missouri Route 6, which is collinear with State Street throughout much of the city. As of the census of 2010...

most appropriate set of independent variables has been chosen; there is collinearity present in the data on the explanatory variables; the model might be...

dimensional data in the real world will just by chance exhibit some degree of collinearity across at least some variables, the problem that LARS has with correlated...

and Néel temperatures, spin-wave spectra, magnetic phase diagrams, non-collinear and chiral magnetic structures. Because spin–orbit coupling can be treated...

Piyush Kant; Pareek, Sarla; Joshi, Hemlata (2013). "Regression Analysis of Collinear Data using r-k Class Estimator: Socio-Economic and Demographic Factors...

observations Stereoscopy Levenberg–Marquardt algorithm Sparse matrix Collinearity equation Structure from motion Simultaneous localization and mapping...

transformations). Some invariants of projective transformations include collinearity of three or more points, concurrency of three or more lines, conic sections...

the Euclidean circle that joins all three of them, or +∞ if they are collinear. The Menger curvature c(x, y, z) is defined to be c ( x , y , z ) = 1...

coverage in the horizontal plane. Variants include shortened, loaded, and collinear designs. Printed antennas are widely used due to their low profile and...

isometry is completely determined by its effect on three independent (not collinear) points. So suppose p1, p2, p3 map to q1, q2, q3; we can generate a sequence...

residues also led to varying or relaxed specificity. Additionally, the NRPS collinearity principle/rule dictates that given the order of adenylation domains (and...

 581–591. Wold, Svante; Ruhe, Axel; Wold, Herman; Dunn, W.J. (1984). "The collinearity problem in linear regression. the partial least squares (PLS) approach...

chromosome is of 3.06 megabases (of which the GC-content is 73.0), mostly collinear, and contains 2 rRNA operons, and 45 tRNAs. As of 2011[update] when a...

(2016-10-19). "Spontaneous decays of magneto-elastic excitations in non-collinear antiferromagnet (Y,Lu)MnO3". Nature Communications. 7 (1) 13146. doi:10...

the east–west direction, and, perpendicular to that, by two lengthy, collinear roads located on either side of a parking lot. The campus is thus divided...

with the consequent discovery of the two constant-pattern solutions, collinear and equilateral, 1772. Those solutions were later seen to explain what...

as molecules of Ni3(acac)6. The three nickel atoms are approximately collinear and each pair of them is bridged by two μ2 oxygen atoms. Each nickel atom...

angle tuning is that the optical frequencies involved do not propagate collinearly with each other. This is due to the fact that the extraordinary wave...

antenna Beverage antenna Cantenna Cassegrain antenna Choke ring antenna Collinear antenna array Conformal antenna Corner reflector antenna Curtain array...

left and right of a slice do not have the same magnitude and are not collinear. This allows for a simple static equilibrium calculation, considering...

the point set. This criterion is satisfied by a single convex hull edge collinear with an edge of the box, or by two distinct hull edges lying in adjacent...

multiple regression regressors in the presence of interactions and collinearities] (PDF). La Revue de Modulad (in French) (22): 41–77 – via rocq.inria...

altitude aircraft American Society for Photogrammetry and Remote Sensing Collinearity equation – Two equations relating 2D sensor plane coordinates to 3D object...

sides, possibly extended, of a triangle. Suppose A, B, C are distinct non-collinear points, and let △ABC denote the triangle whose vertices are A, B, C. Following...

or φ (the Greek letter phi), is measured as the offset from the line collinear with the x-axis in the positive direction; the angle is typically reduced...

straight angle (180°), while others disallow this, instead requiring collinear segments of a closed polygonal chain to be merged into a single longer...

it spans the whole d {\displaystyle d} -dimensional space, no two are collinear with the same sign, and the sum of the set is the zero vector. The polytope...

outer coil. The two coils are connected in series. When the two coils are collinear, with their magnetic fields pointed in the same direction, the two magnetic...

G_{B}={\tfrac {3}{2}}G_{A}.} Thus the two centroids and the incenter are collinear. Concyclic points Tom M. Apostol and Mamikon A. Mnatsakanian (December...

Diacu, E. Pérez-Chavela and M. Santoprete, Saari's conjecture for the collinear n-body problem, Transactions of the American Mathematical Society 357...

antenna Beverage antenna Cantenna Cassegrain antenna Choke ring antenna Collinear antenna array Conformal antenna Corner reflector antenna Curtain array...

source and receiver moving directly along their line of sight, i.e. in collinear motion. Fig. 11 illustrates a scenario in two dimensions. The source moves...

that can indeed be shattered using this model (any 3 points that are not collinear can be shattered). However, no set of 4 points can be shattered: by Radon's...

plane, three points in general position are not collinear. This is because the property of not being collinear is a generic property of the configuration space...

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: John Wiley & Sons. pp. 100–104. ISBN 0-471-05856-4. Pesaran...

transverse deflection of the member. Axial loading – The applied forces are collinear with the longitudinal axis of the member. The forces cause the member...

However, as one is a subsect of the other, the two figures generally move collinearly. Despite a lower female labor force participation rate and a smaller...

particles above about 0.5 MeV/nucleon. The main telescope consisted of five collinear elements (three solid state, one Caesium iodide (CsI), and one sapphire...

development of the first Russian tunable acousto-optic filter with a non-collinear geometry of light and hypersound interaction taking place in lithium niobate...

\mathbf {r} _{2}} , and r 3 {\displaystyle \mathbf {r} _{3}} would be collinear and would not form a triangle). Thus, we can rearrange the above equation...

projective plane of order n2 (the subsets of the design become sets of collinear points in the projective plane). In this case of embedded unitals, every...

elements (with omnidirectional reception characteristics) must form a non-collinear basis. The comparison is made for different azimuth and elevation values...

In particular, he showed how he and Pieri define a line in terms of collinear points. Smith 2000, p. 49 Kennedy (1980), page 86 Smith 2000, pp. 46–47...

independent of the hydrostatic component of the Cauchy stress tensor is collinear with the deviatoric stresses (isotropic material) (d) The increment in...

limes limit- delimit, limes, limit, limitation linea line- line align, collinear, collineation, linea, lineage, linear, linearity, multicollinearity lingua...

each of an external angle bisector with the opposite extended side, are collinear. In a triangle, three intersection points, two of them between an interior...

than ε | V | {\displaystyle \varepsilon |V|} elements must contain 3 collinear points” where V {\displaystyle V} is an n {\displaystyle n} -dimensional...

Geometrical frustration is also possible if the spins are arranged in a non-collinear way. If we consider a tetrahedron with a spin on each vertex pointing...

{\displaystyle \Sigma _{YY}^{-1/2}\Sigma _{YX}\Sigma _{XX}^{-1/2}c} are collinear. In addition, the maximum of correlation is attained if c {\displaystyle...

general position means that no two points coincide and no three points are collinear. This was the original problem, proved by Esther Klein. According to Erdős...

och Fysik. 4: 1–4. Mather, J.; McGehee, R. (1975). "Solutions of the collinear four-body problem which become unbounded in finite time". In Moser, J...

transfer. Semiclassical three-dimensional generalizations of the classical collinear model". Physical Chemistry Chemical Physics (Incorporating Faraday Transactions)...

nanowires, polymer chains). It can also handle collinear (i.e., spin-polarized wave functions) and non-collinear (spinors) magnetic systems. Typical systems...

alternating corners. Remarkably, this single-molecule magnet exhibits non-collinear magnetism, in which the atomic spin moments of the four Fe atoms point...

"Market Excess Demand in Exchange Economies with Identical Preferences and Collinear Endowments". The Review of Economic Studies. 53 (3): 457–463. doi:10.2307/2297640...

Presentation of collinear stimuli flanking a target can enhance responses to the target in cortex, an effect known as flanker or collinear facilitation,...

sides, provided that Q is chosen in "general position" so that it is not collinear with any of the finitely many edges in the triangulation. Translating...

cul-de-sac just east of Landra Gardens. The western frontage road begins collinear to the eastern frontage road at Landra Gardens, travels through roundabouts...

{\displaystyle \Delta E_{p}={\frac {1}{2}}k(r_{2}-r_{1})^{2}} where r2 and r1 are collinear coordinates of the free end of the spring, in the direction of the extension/compression...

theorem, that if a finite point set does not have a linear number of collinear points, then it determines a quadratic number of distinct lines. Similarly...

antenna Beverage antenna Cantenna Cassegrain antenna Choke ring antenna Collinear antenna array Conformal antenna Corner reflector antenna Curtain array...

Moser involving configurations of n points of which at most n − k are collinear, for some 0 < k < O(√n). They showed that if n is sufficiently large,...

circles, making them Archimedean circles. An arbelos is formed from three collinear points A, B, and C, by the three semicircles with diameters AB, AC, and...

in-phase and out-of-phase combinations of the central atom's p orbital (collinear with the bond axis) with the p orbitals of the peripheral atoms. This...

Neutron diffraction studies reveal that the spiral moments in β-CrPO4 are collinear and anti-ferromagnetically coupled along the chains in the 001 planes...

can cause issues, especially when longer lines and shorter lines are collinear, obscuring each other and their destinations. They can also have a haphazard...

tangents are the absolute lines; or if n is even, the absolute points are collinear on a non-absolute line. An upper bound on the number of absolute points...

every point P is mapped into a new point P' such that O, P, and P' are collinear, and the product of the distances of P and P' to the center O equal the...

in standard form, ie, counter clockwise order, distinct vertices, no collinear vertices. ANGLE(m, n) is a procedure that returns the clockwise angle...

^{3}\setminus \{p_{1},\ldots ,p_{k}\}} for k {\displaystyle k} distinct collinear points p 1 , … , p k {\displaystyle p_{1},\ldots ,p_{k}} and the harmonic...

unusual genetic journey of lycophytes Extraordinary preservation of gene collinearity over three hundred million years revealed in homosporous lycophytes Wikström...