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...

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...

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....

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...

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

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...

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...

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...

3190170508. MR 1242180. Futamura, F.; Frantz, M.; Crannell, A. (2014). "The cross ratio as a shape parameter for Dürer's solid". Journal of Mathematics and the...

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...

aspect ratio is 189:335 ≈ 1:1.772  Switzerland The aspect ratio is 1:1 — square-shaped  Togo: The aspect ratio is of Fibonacci's golden ratio that is...

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...

called the cross ratio. Their estimate of the cross ratio is close to MacGillavry's, and has a numerical value close to the golden ratio. Based on this...

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...

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...

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 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...

definition is that the cross ratio of the four points is ± 1 {\displaystyle \pm 1} . It is allowed for the quadrilateral sides to cross. The Apollonius quadrilaterals...

the projective harmonic conjugate of B with respect to A, D, i.e. the cross ratio (A,D;B,C) has the singular value −1. The golden spiral is the only logarithmic...

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...

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

making cross-sector comparisons less reliable. Financial ratio Price-to-earnings ratio Price-to-cash-flow ratio "Price-to-Sales Ratio (P/S Ratio)". Investopedia...

(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...

square and the cross ratio of its vertices. Four points in the complex plane define a harmonic quadrilateral when their complex cross ratio is − 1 {\displaystyle...

circular points, natural logarithm and cross-ratio: The angle between two lines is the logarithm of the cross-ratio of the pencil formed by the two lines...

projective geometry became understood. The incidence structure and the cross-ratio are fundamental invariants under projective transformations. Projective...

authors consider 1/X to be the cross-ratio, and that is why X is called the inverse cross ratio. The inverse cross ratio is invariant under projective...

action is sharply 3-transitive. The computational aspect of this is the cross-ratio. Indeed, a generalized converse is true: a sharply 3-transitive group...