Collinear

Collinearity - Points On A Line
... in the standard model by great circles of a sphere, sets of collinear points lie on the same great circle ... Of course, if the geometry is Euclidean, then collinear points lie on a straight line ... as geometric maps, preserve the collinearity property (that is, they map collinear point sets to collinear point sets), which is another way to say that they map lines to lines ...

Collinear Antenna Array
... In telecommunications, a collinear (or co-linear) antenna array is an array of dipole antennas mounted in such a manner that the corresponding elements of each antenna are parallel and collinear, that is ... A collinear array is usually mounted vertically, in order to increase overall gain and directivity in the horizontal direction ...

Magic Tee - Magic
... matched, then by symmetry, reciprocity and conservation of energy it may be shown that the two collinear ports are also matched, and are magically isolated from each other ... then the power in this signal must be divided equally between the two collinear ports ... port, then the power entering it must be divided equally between the two collinear ports ...

Menelaus' Theorem - Proof - A Non-computational Proof Using Homothecies
... Whether or not D, E, F are collinear, there are three homothecies with centers D, E, F that respectively send B to C, C to A, and A to B ... This composition fixes the line DE if and only if F is collinear with D and E (since the first two homothecies certainly fix DE, and the third does so only ... Therefore D, E, F are collinear if and only if this composition is the identity, which means that the product of the three ratios is 1 which is equivalent to the given equation ...

Pappus's Hexagon Theorem
... of Alexandria) states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are ... Collinear means the points are incident on a line.) It holds in the projective plane over any field, but fails for the projective plane over any ...