Descartes and Mathematics - Traditional figures

DescartesPatrice Debart present (french language) :
  – Work Practise plane geometry with GeoPlan, GeoGebra or Cabri,
  – Solid geometry with GeoSpace,
  – Computer TI-92: formal calculation and programming,
  – History of mathematics : the geometry of Rene Descartes.

The address of the website is :

Geometry - Secondary school

Cabri in first year
Cabri in fourth year

Remarkable lines in the triangle
The geometry of triangle

Theorem of Thales

Pythagore : geometrical demonstrations
The equilateral triangle

Constructions with the rule and the compass
Problems of construction

Constructions - foldings
Exercises of geometry

Configurations in fifth form
The problems of BOA - rotations

Geometry - Lower sixth

To build a regular pentagon

The barycentre


       Arbelos of Achimedes

The projective plan

Scalar product

Academic Olympiads

Interactive figures

History of mathematics

The geometry of Descartes
The problem of Pappus

Elements of Euclide
Great problems of greek geometry

Solid geometry

First year : Parallelepiped Owners
Second year : Pyramid
Fourth year : Plane sections : cubes, pyramids
Fifth form : Orthocentric tetrahedron

Lower sixth : Tetrahedrons, cubes
Activities : straight line parallel with a plan
Functions - active importation

Upper sixth : Paraboloids and surfaces
Scalar product
Volume of a trunk of cylinder

Analysis with GeoPlan

Graphic solution of quadratic equations

Tangent with a curve : introduction

Method of Euler

Curve of the dogs - study of geometrical continuations

Parabolas - place of the orthocentre

Option - Lower sixth

Analysis with GeoPlan

Geometrical plays

APMEP   Archives

APMEP : play and maths

Play of the close tiles

The rise





The Geometry
of Descartes

Upper sixth


Presentation of website « Descartes and Mathematics »

Patrice Debart

Adress :
Col de Rousset
26420 Saint Agnan en Vercors

Profil Google + :

… with GeoPlan-GeoSpace


Curriculum Vitæ

Patrice Debart, 2010

As a professor of mathematics, I taught data processing during more than 10 years to the high school Jean Rostand of Caen and fact of research with the IREM then with the CRDP of Low-Normandy within the one half-time old framework data processing-telematics. After the removal of this station I seized the expatriation appropriateness in Africa (Egypt, Ivory Coast, Morocco) where I professed eight years within the french school abroad.

LVDEnded my career at the secondary school Val de Durance in Pertuis, then until 2011, I was member of the team Matice responsable for MIAM, mathematical part in the website of the academy of Aix-Marseille.

Because of my past of trainer I frequently use data processing during my courses (geometry with GeoPlan and GeoSpace or computer TI-92).
In the same way I had an important extra-curricular activity in data-processing clubs or computer TI-92.

This website presents the synthesis as of my work directed towards active mathematics and the teaching use of data processing.

Dynamic geometry with GeoPlan and GeoSpace

In 200 pages covering the whole of the chapters of the traditional geometry « …with GeoPlan » presents 1500 exercises of geometry. The application presents a synthesis of the geometrical activities of the class of college.
These documents are intended for the use on line of the pupils and the documentation of the professors of mathematics.

Installation of GeoPlan-GeoSpace

GeoPlan-GeoSpace is diffused, by the Champagne-Ardenne CRDP. The licence establishment allows all the pupils and professors to use the software on their micro-computers.

Free download

The team of the AID-CREEM, which developed GeoPlan-GeoSpace, offers it to you the last version for any teaching use not commerciale…
The whole is in remote loading on the site

For that :
1 - create a file on hard disk (named for example « gg » ou « geoplan-geospace »)
2 - download the 3 compressed files,
3 - decompress these files to obtain program, bookshops and assistances,
4 - create a short cut towards the program « GeoplanGeospace.exe » and to associate the extensions « .g2w » et « .g3w » to this program.

Geometrical figure

Many problems of geometry can be translated in the form of problems of existence or construction of a geometrical figure, in general described implicitly by a text ;
to solve a problem with this software is to transform this implicit description into an explicit description with the objects of GeoPlan-GeoSpace.

Thus, a figure described by a text starting with : « an isosceles triangle Is ABC basic BC », must it « be clarified » for GeoPlan :

In small the option-language, it is possible to choose English or German, thus obtaining descriptions facilitating the internationnaux exchanges.



Natural language

isosceles triangle

B free point  ;

C free point  ;

D mediator of segment [BC]

A free point on the line D

Segment [AB],
Segment [BC],
Segment [AC].

English flag English activX version

B free point
  Free object B, parameters: -4, -3
C free point
  Free object C, parameters: 4, -3

D perpendicular bisector of segment [BC]

A free point one line D
  Free object A, parameter: 7

Segment [AB]
Segment [BC]
Segment [AC]

logo g2w To download the figure GeoPlan tri_iso_en.g2w

German version

B freier Punkt freies
  Objekt B, Parameter: -4, -3
C freier Punkt freies
  Objekt C, Parameter: 4, -3

D Mittelsenkrechte der Strecke [BC]

With freier Punkt auf der Geraden D
  freies Objekt A, put Parameter: 7

Strecke [AB]
Strecke [BC]
Strecke [AC]

logo g2w To download the figure GeoPlan tri_iso_de.g2w

The dynamic representation makes it possible to take into account the invariants of the figure : the isosceles triangle is not that a simple drawing and the remainder when the tops are moved.


Activate a figure while clicking above… it becomes interactive !
In above clicking double, you will have the menus of the software GeoPlan or GeoSpace.
All the usual keys of displacement, zoom or order are available.
The click slipped right relocates the figure under GeoPlan, the right click makes it possible to make it turn under GeoSpace.

In my examples almost all the figures are controllable with the keyboard : click on the figure and press on the arrows of displacement.
In GeoSpace in general the key W makes it possible to return to the initial sight and the key F makes it possible to obtain a front view.

Cabri-Geometre : work practise in first year and fourth year

Cabri is the software of plane geometry ideal for the use of data processing in class.
The cards make it possible to the pupils to carry out a certain number of traditional figures.
The computer makes it possible to release from them the useful elements for the resolution of a problem and makes it possible to check conjectures.
    Cabri in first year
    Cabri in fourth year

Computer TI-92 : formal calculation and programming

These documents present a series of explanations for the use of formal calculation.

TI-92Sequence in S or ES
Probabilities in upper sixth - ES
Statistics in upper sixth - ES
Small programs TI-92
      Submerge a ball
      Egyptian fractions
Angles and trigonometry

The Geometry of Rene Descartes

Professor of the old secondary school Rene Descartes de Bouake (Ivory Coast) I wanted to present the texts of this author on the theorem of Thales, the problems of the second or the third degree.
I thus propose extracts and comments for the use of the pupils allowing to find a historical step in the teaching of mathematics.

The conical ones like places of points (level upper sixth + 2) : the problem of Pappus


creem Documentation on the interactive figures using of ActivX controls
Character special

GeoPlan : tricks and easy ways


Traditional figures



The Geometry
of Descartes

Upper sixth


Website « Descartes and Mathematics »

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Page no 67, created 1/4/2004 - update 1/3/2006