In geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly...

triangle. Cross ratio Dilution ratio Displacement–length ratio Dimensionless quantity Financial ratio Fold change Interval (music) Odds ratio Parts-per...

Cohen's h Cross-ratio Diagnostic odds ratio Forest plot Hazard ratio Likelihood ratio Rate ratio Szumilas M (August 2010). "Explaining Odds Ratios". Journal...

"The Cross", a song by Prince from Sign o' the Times Cross product, a binary operation on vectors in a three-dimensional Euclidean space Cross-ratio, an...

the point at infinity, then the cross-ratio has to be defined by taking the appropriate limit; e.g. the cross-ratio of z 1 , z 2 , z 3 , ∞ {\displaystyle...

indicated circle satisfies the given ratio. A closely related property of circles involves the geometry of the cross-ratio of points in the complex plane....

line points U[0, 1], U[1, 1], U[1, 0] is called the cross-ratio homography. Sometimes the cross-ratio is taken as the value of h on a fourth point x : (x...

complement of a fixed quadric in a projective space which is defined using a cross-ratio. The construction originated with Arthur Cayley's essay "On the theory...

call the collineation group the automorphism group of the design. The cross-ratio of four collinear points is an invariant under the homography that is...

projective geometry, harmonic conjugacy can also be defined in terms of the cross-ratio as (A, B; C, D) = −1. The four points are sometimes called a harmonic...

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed...

In materials science and solid mechanics, Poisson's ratio (symbol: ν (nu)) is a measure of the Poisson effect, the deformation (expansion or contraction)...

calculation can be achieved by considering the ratios as those of similar triangles. In practice, the method of cross-multiplying means that we multiply the numerator...

". Two types of ratio comparisons can be made, cross-sectional and time-series. Cross-sectional analysis compares the financial ratios of different companies...

PMID 19127890. S2CID 1908108. Lee, James (1994). "Odds Ratio or Relative Risk for Cross-Sectional Data?". International Journal of Epidemiology. 23...

federal cross. Its arms are equilateral, and their ratio of length to width is 7:6. The size of the cross in relation to the field was set in 2017 as 5:8...

monohybrid cross to create the dihybrid cross. From these experiments, he determined the phenotypic ratio (9:3:3:1) seen in dihybrid cross for a heterozygous...

the monohybrid ratio. Generally, the monohybrid cross is used to determine the dominance relationship between two alleles. The cross begins with the...

The price-to-book ratio, or P/B ratio, (also PBR) is a financial ratio used to compare a company's current market value to its book value (where book value...

coordinates of a point a ≠ a0 are (r, 1), where r is the cross-ratio (a, a2; a1, a0). If a = a0, the cross ratio is the infinity, and the projective coordinates...

and is the unique such map that does so. This is the cross-ratio (x, b; a, c) – see Cross-ratio § Transformational approach for details. For n ≥ 3, PGL(n...

another national flag), and the overall shape of a flag, such as the aspect ratio of a rectangular flag (whether the flag is square or rectangle, and how...

The digit ratio is the ratio taken of the lengths of different digits or fingers on a hand. The most commonly studied digit ratio is that of the 2nd (index...

them conforming to a pattern: a blue rectangle, with ten instances of the Cross of Vytis appearing in gold, acts as a fringe to the central feature of the...

(KJ/AG)(AG/JL) = (JD/GD)(BG/JB). The last compound ratio (namely JD : GD & BG : JB) is what is known today as the cross ratio of the collinear points J, G, D, and B...

the cross ratio invariant: (g(a),g(b);g(c),g(d)) = (a,b:c,d). Since the Möbius group acts simply transitively on triples of points, the cross ratio can...

ISBN 9781461249085. Milne, John J. (1911). An Elementary Treatise on Cross-Ratio Geometry with Historical Notes. Cambridge University Press. p. 11. Attribution:...

In statistics, the likelihood-ratio test is a hypothesis test that involves comparing the goodness of fit of two competing statistical models, typically...

In aerodynamics, the lift-to-drag ratio (or L/D ratio) is the lift generated by an aerodynamic body such as an aerofoil or aircraft, divided by the aerodynamic...

points are used in the cross ratio which defines the Cayley–Klein metric. Linear fractional transformations leave cross ratio invariant, so any linear...