Source: coq-highschoolgeometry
Section: math
Priority: optional
Maintainer: Riley Baird <BM-2cVqnDuYbAU5do2DfJTrN7ZbAJ246S4XiX@bitmessage.ch>
Build-Depends: debhelper (>= 9), coq, camlp4
Standards-Version: 3.9.6
Homepage: http://www-sop.inria.fr/lemme/Frederique.Guilhot/geometrie.html

Package: coq-highschoolgeometry
Architecture: all
Depends: ${misc:Depends}, coq
Description: coq library for high school geometry proofs/formalisation
 Created by Frédérique Guilhot, this library consists of a collection of
 "chapters" spanning most of the geometry taught in French high schools.
 .
 The first part "2-3 dimensional affine geometry" deals with formalising:
  points, vectors, barycenters, oriented lengths
  collinearity, coplanarity
  parallelism and incidence of straight lines
  proofs of Thales and Desargues theorems.
 .
 In the second part "3 dimensional affine geometry", theorems about these
 things are proven:
  relative positions of two straight lines in the space
  relative positions of a straight line and a plane
  relative positions of two planes
  parallelism and incidence properties for several planes and straight lines
 .
 The third part "2-3 dimensional euclidean geometry" deals with formalising:
  scalar product, orthogonal vectors, and unitary vectors
  Euclidean distance and orthogonal projection on a line
  proofs of Pythagorean theorem, median theorem
 .
 The fourth part "space orthogonality" deals with formalising:
  orthogonal line and plan
 .
 The fifth part "plane euclidean geometry" deals with formalising:
  affine coordinate system, orthogonal coordinate system, affine coordinates  
  oriented angles
  trigonometry
  proofs of Pythagorean theorem, median theorem, Al-Kashi and sine theorems
  perpendicular bisector, isocel triangle, orthocenter
  circle, cocyclicity, tangency (line or circle tangent) 
  signed area, determinant
  equations for straight lines and circles in plane geometry 
 .
 The sixth part "plane transformations", deals with formalising:
  translations, homothety 
  rotations, reflexions
  composition of these transformations.
  conservation of tangency for these transformations.
 .
 In the seventh part "applications", these are proven:
  Miquel's theorem, orthocenter theorem, Simson line
  circle power and plane inversion
  Euler line theorem and nine point circle theorem
 .
 The eighth part "complex numbers", deals with formalising:
  the field properties of complex numbers
  application to geometry of complex numbers
