Descartes and Mathematics - Traditional figures
Patrice Debart present (french language) :
– Work Practise plane geometry with GeoGebra,
– Solid geometry with GeoGebra,
– History of mathematics : the geometry of Rene Descartes.
The address of the website is :
https://debart.fr
Geometry - Secondary school
Remarkable lines in the triangle
Pythagore : geometrical demonstrations
Constructions with the rule and the compass
Configurations in fifth form
The problems of BOA - rotations
Geometry - Lower sixth
Angles
Rotations
To build a regular pentagon
The barycentre
Minimum-maximum
Arbelos of Achimedes
Functions
The projective plan
History of mathematics
The geometry of Descartes
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
Analysis with GeoPlan
Graphic solution of quadratic equations
Tangent with a curve : introduction
Curve of the dogs - study of geometrical continuations
Parabolas - place of the orthocentre
Option - Lower sixth
Presentation of website « Descartes and Mathematics »
Patrice Debart
Adress :
Col de Rousset
26420 Saint Agnan en Vercors
France
… with GeoPlan-GeoSpace
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 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.
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
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 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]
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]
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.
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.
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
Small programs TI-92
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
Technique
GeoPlan : tricks and easy ways
Website « Descartes and Mathematics »
https://debart.fr
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Page no 67, created 1/4/2004 |