Collinear

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 the plane.

Fano subplanes A Fano subplane is a subplane isomorphic to PG(2,2), the unique projective plane of order 2. If you consider a quadrangle (a set of 4 points no three collinear) in this plane, the points determine six of the lines of the plane.

For two or more consecutive boosts that are not collinear but in different directions, the result is still a Lorentz transformation, but not a single boost.

Gino Fano (1871–1952), in developing a new set of axioms for Euclidean geometry, took as an axiom that the diagonal points of any quadrangle are never collinear.

In Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space ).

It also shows that two quaternions commute if and only if their vector parts are collinear.

Nearby, the emperors' mausoleum Xiuliang stood, demarcated by Kappa Aquarii and three other collinear stars.

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

Similarly, lines associated with a triangle are often constructed by proving that three symmetrically constructed points are collinear: here Menelaus' theorem gives a useful general criterion.

That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices.

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

The purpose of stacking multiple dipoles in a vertical collinear array is to increase the power radiated in horizontal directions and reduce the power radiated into the sky or down toward the earth, where it is wasted.

The relative velocities can be in the same or opposite directions, but must be collinear.

Thus rapidities add if the boosts are collinear as they are here, while the relative velocities do not.

When the inner coil is turned 180° so the coils are collinear with their magnetic fields opposing, the two fields cancel each other and the inductance is very small.