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数学

Discovery

Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

Lietuvių kalba

Introduction E9F5FC

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software


See: Geometry, Geometries

Understand what projective geometry is all about.


Theorems

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.

ProjectiveGeometry


Naujausi pakeitimai


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