Theorems

- The Fundamental Theorem of Projective Geometry Any four planar non-collinear points (a quadrangle) can be sent to any quadrangle via a projectivity, that is a sequence of perspectivities.

Wildberger's key theorems

- Pappus's hexagon theorem Two sets of collinear points yield a third set of collinear points.
- Pascal's theorem The same but where all six points are on a conic section, with a pair of lines being a degenerate case.
- Desargues' theorem Two triangles are in perspective axially if and only if they are in perspective centrally.

Concepts

Incidence geometry

Perspective maps lines to lines, conics to conics.

Questions

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.

Parsiųstas iš http://www.ms.lt/sodas/Book/ProjectiveGeometry

Puslapis paskutinį kartą pakeistas 2018 gruodžio 30 d., 16:30