In mathematics, projective geometry is the study of geometric properties which are invariant under projective transformations. The field of projective geometry is itself divided into many subfields, two examples of which are projective algebraic geometry (the study of projective varieties) and projective differential geometry (the study of differential invariants of the projective transformations).
Projective geometry, like affine and Euclidean g...
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In mathematics, projective geometry is the study of geometric properties which are invariant under projective transformations. The field of projective geometry is itself divided into many subfields, two examples of which are projective algebraic geometry (the study of projective varieties) and projective differential geometry (the study of differential invariants of the projective transformations).
Projective geometry, like affine and Euclidean geometry, can be developed from the Erlangen program of Felix Klein. As such its geometric properties are invariant under the group action of the group of projective transformations. In Klein's Erlangen program, projective geometry is characterized by invariants under transformations of the projective group. The incidence structure and the cross-ratio are fundamental invariants under projective transformations.
Projective geometry is an elementary non-metrical form of geometry featuring configurations of points and lines (or hyperplanes in...
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