|| Symmetry : a workshop
A Workshop of Scientific Practice is being set up in the Lycée Antoine Roussin (Saint-Louis, La Réunion) at the start of the 1999/2000 school year. It concerns one of the "Première S" classes (Première S. : Sixth formers taking maths, physics, and science, as their main subjects).
What does it consist in ?
It is a project which involves the whole form and may include the subjects studied in the class.
The original Project
The mathematical theme of the two-dimensional periodic patterns has guided our steps us, via the superb book entitled "Géométrie douce" to The Alhambra Palace in Granada. The classification of the crystallographic groups - that are associated to the periodic patterns - was completed in the 19th century through extremely sophisticated calculations.There are seventeen classes of periodic patterns all together and it is remarkable that the Moorish artists should have used all of them. Thirteen of these classes can be found in the Alhambra palace.
The starting point of the project is to take the pupils of one Première S class to the Alhambra palace in Granada, at the end of several months' training :
-mathematical training : study of the transformations linked to each class of periodic patterns, drawing of these patterns in order to learn to recognize them.
-language training : the Spanish language is essential to the project. As a matter of fact it is its very cornerstone. The pupils are going to follow this year's Spanish course thanks to an essential guideline : the study of the Muslim period of the Spanish history, the history of the Alhambra, and the impact of Muslim art on that of Andalusia.
At the start, this project is therefore fundamentally cultural and linguistic.It will permit to relate Islamic culture - that some pupils have already appropriated - to Hispanic culture that they will discover throughout their Spanish course. As a matter of fact, the Koranic ban on representing figures with a human face has forced the Moors to use geometrical motifs in their adornments. This is how most of the 17 regular patterns in the plane can be found in the Alhambra in Granada in the form of splendid mosaics.
The project at present
The idea of symmetry underlying the original project has become the key idea in so far as symmetry pervades the whole of nature. Hence, the idea of extending the project, as long as it remains feasible, to all the subjects taught in the Première S involved. Thus the pupils would be guided along the year's curriculum through a single federating theme : the notion of symmetry understood in the wider extent of its meaning.
Aims of the project
- the pupils will be given a scientific culture and they will be shown that the questions seen in class have practical applications.
- also, the year's curriculum will take on additional coherence thanks to the guideline offered by the theme of symmetry.
- the pupils will learn to use an Internet search engine with a view to enriching the various exposés they will have to give throughout the year.
- the pupils will give free rein to their imagination and creativity while composing palindroms and ambigrams ( during the French classes )
- they will be given the opportunity to improve their knowledge in such fields as :
- their artistic and cultural heritage: in maths the pupils will learn to recognize pelmets as one of the 7 types of friezes. It will be an opportunity to give them a new approach to their architectural heritage ( the pelmets in the village of L'Entre Deux ). They will also learn to differentiate the patterns of the Alhambra.
- their industrial heritage : the partnership with the "Sucrière de la Réunion" (sugar cane refining company) is an opportunity for these future technicians and engineers to see at closer quarters an already familiar industrial environment ( The Gol factory in St Louis ).
Description of the implementation
symmetry in mathematics
study of transformations
- practice on friezes : classification of the 7 types of friezes, outing at "L'Entre Deux" to recognize the pelmets as friezes.
- practice on patterns : classification of the 17 types of patterns , practice on photos of patterns from the Alhambra to learn to recognize them , practice on the Escher patterns , visit of web sites on Escher.
symmetry in physics
crystalline networks reveal patterns in space, salt is a cubical network with a centred face and sugar has a more complex structure that the pupils will discover. Study of the properties of chiral molecules. Study of the various stages of sugar processing.
In physics, the words symmetry and invariant are swapped almost indifferently. The law of energy conservation is an illustration of symmetry in physics. Why the Gol factory ? Because it is the place where the energy is transformed. The biomass (as well as coal) are transformed there in thermal energy.
In chemistry, symmetry is to be found in the arrangement of atoms to form crystals or that of that of complex carbon based molecules such as sugars.
symmetry in biology
bilateral symmetry of the human body and of many other human beings.
symmetry in French
- As the curriculum allows for the study of a book freely chosen , study of symmetry in NogegoN, a cartoon by Luc and François Schuiten published by Humanoïdes Associés in 1990,
- as to the books included in the curriculum, the study will bear on the characters whose situation or fate is symmetrical either through similitude or opposition : "Pierre et Jean" by Guy de Maupassant, " Le jeu de l'amour et du hasard" by Marivaux,
- as to the theme of the Alhambra, the book " Tales of the Alhambra " by the American writer Washington Irving will be exploited and studied in french.
- construction of ambigrams and palindroms.
symmetry in Spanish
Andalusia is the jewel of Muslim civilisation in Spain, and shelters the gist of Moorish art.The three great cultural centres in of Andalusia (Granada, Seville and Cordoba) will be studied in texts (poetry and prose).
history and geography
will bring the essential complement about the history of Spain and its Muslim period, the
geographical situation of Granada. Its evolution since the Arab invasion and the impact of Muslim culture on the present inhabitants at the human, ethnological, cultural and religious levels. Are the town dwellers aware of this jewel of Arab art that has been left to them ?
symmetry in English
would it be possible to make the pupils write out poems and work on their form, on the position of words, lines and paragraphs. Why not let the pupils use their imagination and illustrate their compositions ?
symmetry in physical education
the pupils will be initiated to synchronised swimming. The ballet presented at the end of the school year will include symmetrical tableaux.
symmetry in music
will be approached through a ten hour module presented by a pianist who teaches music at the Conservatoire Régional de Musique. As the pupils in the class have probably never played an instrument, it is out of the question that they should learn to do so, they will simply be introduced to the idea of symmetry in a musical composition, and to the composers who have used this mathematical theme. We shall ponder the questions of whether it is easy to structure a musical piece around a symmetry axis. Can an untrained ear recognise symmetry in a musical piece ?
symmetry in philosophy
During a ten hour module of initiation the pupils will study : Determinism and chaos in physics. It will include an approach of epistemology. It will deal with the aim of scientific activity and the limits of the mechanical approach. Philosophy cannot do without a reflection on sciences. The problem of the existence of regular forms will be set. An attempt will be made at provoking the metaphysical question : "Why is there existence rather than nothingness ?", in a word, "wonderment" will act as the engine of scientific discovery.
symmetry in cartoons
A conference : "Symmetry in cartoons" will be given by a specialist : Mr. Pierre-Louis Mangeard, who is in charge of the audio visual department at the St Pierre library.
history of symmetry
Mr. Christian Houzel, who is a lecturer of the history of mathematics at the I.U.F.M. of Paris will give a conference.
Scheduled visits of sites in La Réunion :
- visit of the village of L'Entre Deux for its great variety of pelmets.
- visit of the saltern at La Pointe au sel (salt is a cubic crystalline network with a centred face )
- several visits of the Gol factory will take place to observe the processing of sugar, and particularly the transformation of the remnants of sugar cane into thermal energy.
- visits of Stella Matutina (Museum dedicated to the history of the sugar industry), group work in the library.
Means of assessing the project
- an Internet site will be set up and kept up to date by the pupils.
- exposés will be presented and marked in several classes (Maths, French, Physics...)
Methods criteria and tools for final assessment
- An exhibition inside the Lycée is scheduled at the end of the school term. If the pupils turn out to be creative the exhibition will be shown at Stella Matutina.
- In mathematics one of the main criteria to assess the success of the project will be the pupils ability to classify pelmets as friezes
- the patterns in the Alhambra at Granada that they will have to recognise among the seventeen periodic patterns studied throughout the school year
- the synchronised swimming ballet will be filmed and shown during the exhibition.
- How will the result of the project be made public ?
- The pupils will keep a kind of diary of the project on the Internet site.
- A final exhibition of all the works related to the theme will be held at the end of the year.
, it may also be found the web site of the Lycée Antoine Roussin.
A partnership with the "Sucrière de la Réunion" was set up and made into a contract last July.
-manager of the industrial and agricultural department of the "Sucrière de la Réunion" : Dominique Girardo.
- This project is to some extent the sequel of the Projet d'Action Educative (Project generally involving several subjects and implemented outside the traditional classes) " Cités Obscures "
This PAE took place in the Lycée Antoine Roussin during the 1995/96 school year. The text of the play written by the pupils on the theme of networks : "Le réseau d'Urbicande" can be found at the following Internet address :
- for information please contact : Responsable de communication (du groupe Quartier Français) Madame Grandjean Joëlle (tel: 588282 / Fax: 465301/ e-mail: email@example.com) with whom the contract was signed.
As the pupils involved may be future engineers and technicians, this partnership will entail a series of scientific actions :
- visit of the Gol factory
- study of the processing of sugar
- a series of exposés on the discovery of the industrial world.
A partnership with Stella Matutina will enable the pupils to have access to the library of the museum and to the new exhibition as they come up throughout the year, and finally to benefit from an exhibition room.
As the project is related to all the subjects taught in Première S it will take place during school time, nevertheless for three main subjects three extra hours, fitted in the class's timetable will be required.
Although it is at the start of the project, the trip to the Alhambra is not a goal in itself. The trip would be the ideal conclusion of this Workshop of Scientific Practice but the present project stands on its own. The study of symmetry for a whole school year by the Première S involved is a fully fledged objective.
The teachers in charge of the project should be the following :
- Mathematics : Nathalie Aymé
- Physics : Thérèse Derolez
- French : Geneviève Palmas
- Spanish : Hassim Amode
- History Geography : Sabera Moolant
- English : Vilasnee Hautain
- Physical Education : Monique Klein
- Biology : Isabelle Auger et Jean-Paul Fontaine
- Philosophy : Bernard Pitou
- Music : Philippe Hoarau
Cathy Phalip, the librarian in the Lycée is also deeply involved in the project and is already playing an essential part in its conception.
The forecast budget for the project, not including the trip, amounts to 70 000 F. It will enable all the subjects taught in the Première S involved to take part.
- to start with, this will permit to acquire a large enough set of books on symmetry (about twenty titles are already waiting to be ordered ). Once the books have been bought they will complete the library since they will be included in its catalogue.
- the class will need several copies of the key books of the project (NogegoN, La Symétrie aujourd'hui, l'architecture maure etc...)
- several CD ROM's will have to be bought for the pupils to consult on the multimedia computer in the library, particularly a CD about Escher which includes several games dedicated to patterns.
- the pupils will, no doubt want to print the result of their searches on the Internet. Many sites dedicated to Symmetry, Escher and ambigrams are graphically very rich, they include a lot of colour pictures. Quality printing of these will require special paper worth 10 F a sheet !
- the final exhibition will also have to be sponsored.
- the outings planned throughout the year will entail big expenses for buses.
The means allotted to the project will not be wasted, they will enable the teaching staff involved in the project to implement the actions in optimum conditions.
Then trip to he Alhambra in Granada will amount to approximately 9 000 f per pupil. This trip is scheduled for May 2000, during the ten days' holiday. The team of teachers concerned by the project has started contacting the AREA (an association specialised in school trips).
At the moment we are thinking of means to raise funds by ourselves : Sales of Tee shirts, organisation of a ball at the beginning of the school year, the pupils will wrap up packets in supermarkets ; but to raise the 350 000 F required for the complete organisation of the trip, we will need substantial subsidies - although numerous actions have been planned to finance the project unaided (see forecast budget).
Finally, let us note that the year 2000 has been declared the year of mathematics in the world by the UNESCO and that, thanks to this project, we wish to give our students the opportunity to enjoy a unique school year structured by the unifying notion of symmetry.