Search results
Results from the WOW.Com Content Network
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.
The ratio of width to height of standard-definition television. In mathematics, a ratio (/ ˈ r eɪ ʃ (i) oʊ /) shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
The metric distance between two points inside the absolute is the logarithm of the cross ratio formed by these two points and the two intersections of their line with the absolute. In mathematics, a Cayley–Klein metric is a metric on the complement of a fixed quadric in a projective space which is defined using a cross-ratio.
A proportion is a mathematical statement expressing equality of two ratios. [1] [2]: =: a and d are called extremes, b and c are called means. Proportion can be written as =, where ratios are expressed as fractions.
The cross-ratio between 4 points ,,, is invariant under an inversion. In particular if O is the centre of the inversion and r 1 {\displaystyle r_{1}} and r 2 {\displaystyle r_{2}} are distances to the ends of a line L, then length of the line d {\displaystyle d} will become d / ( r 1 r 2 ) {\displaystyle d/(r_{1}r_{2})} under an inversion with ...
The cross product with respect to a right-handed coordinate system. In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol .
5 Cross-Ratio Definition. 6 comments. 6 A symmetric function on the cross ratio. 2 comments. 7 Cross-ratio and fundamental theorem of Galois, example 3. 1 comment.