Lines and points are duals in plane projective geometry. For plane figures, true theorems {reciprocal theorem} about non-metric properties can interchange the words "line" and "point" {duality}| {principle of duality}. For example, "a unique line intersects two points" and "a unique point intersects two lines".
three dimensions
Planes and points are duals in three-dimensional projective geometry. For plane figures, true theorems about non-metric properties can interchange the words "plane" and "point", if the word "line" does not change.
metric
These duality principles are not true for metric properties.
Mathematical Sciences>Geometry>Transformation
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Date Modified: 2022.0224