Ratios {cross ratio} can be distance from line-segment point to line-segment end divided by distance from line-segment point to other line-segment end. Cross ratio can apply in non-metric geometries. Cross ratio is relation of projective harmonic conjugates. Cross ratios are invariant in projective geometry. Cross ratio is ratio of distance ratios. For four distinct collinear points A, B, C, and D in sequence, the cross ratio is (AC/BC)*(BD/AD) = (medium1/short)*(medium2/long) = (AC/BC) / (AD/BD) = (medium1/short)/(long/medium2) = (AC*BD)/(BC*AD) = (13*24)/(23*14) = (medium1*medium2)/(short*long). For a line, if three points and the cross ratio are known, the fourth point is known.
Mathematical Sciences>Geometry>Kinds>Projective Geometry
3-Geometry-Kinds-Projective Geometry
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Date Modified: 2022.0224