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One approach to cross ratio interprets it as a homography that takes three designated points to 0, 1, and ∞. Under restrictions having to do with inverses, it is possible to generate such a mapping with ring operations in the projective line over a ring. The cross ratio of four points is the evaluation of this homography at the fourth point.
The cross-ratio (,;,) = () is a ratio of division ratios, or a double ratio. Setting the double ratio to minus one means that when t(c) + t(d) = 0, then c and d are harmonic conjugates with respect to a and b. So the division ratio criterion is that they be additive inverses. Harmonic division of a line segment is a special case of Apollonius ...
A typical one-line diagram with annotated power flows. Red boxes represent circuit breakers, grey lines represent three-phase bus and interconnecting conductors, the orange circle represents an electric generator, the green spiral is an inductor, and the three overlapping blue circles represent a double-wound transformer with a tertiary winding.
The cross-ratio of four collinear points is an invariant under the homography that is fundamental for the study of the homographies of the lines. Three distinct points a , b and c on a projective line over a field F form a projective frame of this line.
For example, if the feed is a saturated liquid, q = 1 and the slope of the q-line is infinite (drawn as a vertical line). As another example, if the feed is saturated vapor, q = 0 and the slope of the q-line is 0 (a horizontal line). [2] The typical McCabe–Thiele diagram in Figure 1 uses a q-line representing a partially vaporized feed.
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The Keynesian cross diagram includes an identity line to show states in which aggregate demand equals output. In a 2-dimensional Cartesian coordinate system, with x representing the abscissa and y the ordinate, the identity line [1] [2] or line of equality [3] is the y = x line. The line, sometimes called the 1:1 line, has a slope of 1. [4]
Use of cross-ratios in projective geometry to measure real-world dimensions of features depicted in a ... the width of only one shop is needed. Template documentation ...