Descartes and Mathematics - Traditional figures

Patrice 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.

Presentation of website « Descartes and Mathematics »

Patrice Debart Adress : Col de Rousset 26420 Saint Agnan en Vercors France Profile Google +

… with GeoPlan-GeoSpace Curriculum Vitæ Genealogical tree

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.

Ended 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 150 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 aid-creem.org.

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.

ActivX for Internet Explorer (not compatible Windows Vista)

If you are equipped with Windows, for a free version, simplest controls ActiveX CREEM is to download and to use a virgin page HTML for GeoPlan or GeoSpace with Internet Explorer.

There is no bar of menus, nor of buttons : double to click on the figure to have access to the orders.
The menus file and option miss.
Currently ActivX controls do not make it possible to charge or record a figure.
To work of « copy-to stick » while swapant between the editor of the text of the figure and a text processing or an editor of Of the same pages HTML the images copies themselves and prints themselves in an application software such as for example Paint.

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.

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.

Interactivity

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.

Sequence 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

Derive : initiation with formal calculation

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

Summary

Technique

 Documentation on the interactive figures using of ActivX controls
Character special
GeoPlan : tricks and easy ways
Bibliography

 ^e visit.