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Book: ProjectiveGeometry

See: Geometry, Geometries

Understand what projective geometry is all about.



Wildberger's key theorems


Incidence geometry

Perspective maps lines to lines, conics to conics.

Do parallel lines going one way and going the other way meet at the same point at infinity? Or two different points at infinity? This is answered by considering a line as a vector space. So going around we get to the same line. But we have a different orientation. So the notion of orientation of a point becomes relevant. The line of infinity consists of oriented points.

Line geometry



Projective geometry

The (n+p-1)-dimensional projective space associated with a quadratic space with signature (n,p), is divided by its (n+p-2)-dimensional surface (images of null vectors), which is a conformal space with signature (n-1,p-1), into 2 curved spaces: one with signature (n-1,p) and positive curvature, the other with dimension (n,p-1) and negative curvature. Just by changing convention, the one with signature (n-1,p) and positive curvature can also seen as a space with signature (p,n-1) and negative curvature; and similarly for the other.

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Puslapis paskutinį kartą pakeistas 2020 balandžio 13 d., 17:28