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Art, mathématique et créativité

Semaine de la science 2017
by

Christian Mercat

on 21 April 2018

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Transcript of Art, mathématique et créativité

&
Art, mathématiques
1. Plantear la pregunta correcta
2. Mundo real →formulación matemática
3. Cálculo
4. De vuelta a la realidad, verificación
nstitut
de
echerche
sur l'
nseignement
athématiques
Université Claude Bernard
1
Institut Camille Jordan
mc
Squared
¿Qué es la matemática?
http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers
matemática >> computación
*
Mathematics are better left to experts and initiated people

Mathematics can not be the subject of a conversation (contrarily to literature or philosophy)

Mathematics are only an abstraction, they don’t deal with reality

There is no room for uncertainty in mathematics

There is no room for creativity and imagination in mathematics

In mathematics, there is nothing left to discover

The mathematic courses are not pratical enough

Courses haven’t changed in the last decades when the world is evolving greatly and fast

With new means available to students, learning is no longer required, one just has to quickly find solutions to problems that are encountered

The structure of math courses doesn’t allow learning autonomy

A teacher only purpose is to bring knowledge to students

Mathematics weight too much in engineer training

There is almost no connection between math teaching and the engineer job reality

In engineer school, theory are taught without taking into account their applications

In engineer school, mathematics are mostly pure and abstract

Aprender matemáticas en las clases de primeros sirve sobre todo con el propósito de ayudar a los niños moverse en la vida
Natural phenomena are too complex to be apprehended by mathematics

Only applied mathematics are interesting

Mathematics are used mostly in technical domains

Mathematics have an interest, especially for solving concrete problems

Mathematics are a human construction

A mathematical theory can not be refuted

A mathematical model is necessarily limited

Only math can approach truth

Mathematics raised from concrete needs

Mathematics are only a tool for science

The mathematic courses are extremely pratical

The mathematics courses are not theoretical enough

The mathematic courses are extremely theoric

Mathematics can not be avoided in engineer training

Math teaching doesn’t try to establish links with other sciences

We need more applied mathematics in engineer training

Las matemáticas pueden aplicarse a los objetos artificiales elaborados y mucho menos a los objetos encontrados en la naturaleza
Mathematics serve no purpose in human sciences

Mathematics are useles in everyday life

Модуль 1 - Для чего нужна математика?

Objectif 1 – A quoi servent les mathématiques?

Genre

Модуль 2 - Математика в инженерных курсах
(содержание и методы)

Objectif 2 - Perceptions de l’enseignement des
mathématiques dans des écoles d’ingénieur

Perceptions of mathematics in engineering
courses

Общая информация

Informations Démographiques

Модуль 3 - Общее восприятие математики

Objectif 3 - Perceptions des mathématiques

Perception of Mathematics

Comité científico
Comisiónes Inter IREM (CII)
Investigación-Acción
Épistémologie et histoire
CII APMEP Publimath
Collège
COPIRELEM
CORFEM
Didactique
Lycée
Lycée professionnel
Pop’Math
Repères
Statistique et probabilités
TICE
Université
http://research.meumesmo.com.br/pesquisa/limesurvey/index.php?r=survey/index/sid/137861/lang/es
https://drive.google.com/file/d/0B7DYMJTPXwBbZmd0MzBRSUVsYms/view?usp=sharing
https://drive.google.com/file/d/0B7DYMJTPXwBbYXV2eXNma2dsZFU/view?usp=sharing
http://www.m2real.org/
© Régis Goiffon
no sufren
las matemáticas,
¡disfrutan las!

https://imaginary.org/program/surfer
http://www.fondationvasarely.fr/
Il y a de la créativité dans une expression algébrique
De belles choses derrière une fonction
http://www.nctm.org/Publications/Mathematics-Teacher/2016/Vol110/Issue5/Mathematical-Modeling-in-the-High-School-Curriculum/
http://archive.boston.com/bostonglobe/ideas/brainiac/2010/11/april_11_1954_t.html
http://jeffdegraff.com/blog/2014/01/doing-the-creative-work-the-company-cant-part-1-the-way-of-the-cafe/
Enseignement
motivation
Csíkszentmihályi, Liljedahl
ZPD
Persévérance
Tolérance
Frustration
Henri Poincaré
La science & l'hypothèse
Jacques Hadamard
Essai sur la psychologie de l'invention dans le domaine mathématique
Théorème vivant
Cédric Villani
https://fr.wikipedia.org/wiki/Cité_idéale
https://fr.wikipedia.org/wiki/L%27École_d%27Athènes
https://fr.wikipedia.org/wiki/Homme_de_Vitruve
Leonard de Vinci, 1490
Raphaël, 1508
Piero della Francesca, 1490
______________________
Albrecht Dürer, 1525
https://fr.wikipedia.org/wiki/Albrecht_Dürer
https://www.geogebra.org/m/wdkmGMuJ
https://fr.wikipedia.org/wiki/Chambre_noire
https://fr.wikipedia.org/wiki/Guernica_(Picasso)
https://fr.wikipedia.org/wiki/Toutânkhamon
-1350aC
Une perspective sur les fonctions
Suite Géométrique
http://www.dimensions-math.org
http://www.chaos-math.org
Webcam conforme
http://bit.ly/webcamconf
http://www-history.mcs.st-and.ac.uk/Posters/203.html
Gaston Julia
Pierre Fatou
Benoît Mandelbrot
https://fr.wikipedia.org/wiki/Nu_descendant_un_escalier
Marcel Duchamp 1912
https://www.geogebra.org/m/UwD66Rss
Benoit Ray, Lycée de Tunis
Benoit Ray, Lycée de Tunis
http://math.univ-lyon1.fr/irem/spip.php?article640
http://math.univ-lyon1.fr/irem/spip.php?article496
https://www.geogebra.org/m/cZxdEBJe
https://www.geogebra.org/m/fY7Wstbr
http://2.mc2dme.appspot.com/dwo/dwo.jsp?profile=78&language=en&courseViewNr=5732225890910208
Zbigniew Rybczyński - The 4th dimension (1988)
http://www.dailymotion.com/video/xjbiop_zbigniew-rybczynski-the-fourth-dimention_shortfilms
http://bit.ly/WebcamSliced
Modélisation

Créativité
Lady Shalott
Cédric Villani
© Cédric Villani
Alfred Lord Tennyson
par William Maw Egley
Bridget Riley
one
roximale
de
éveloppement
rebond
Clochettes de Galilée
M.C. Escher (1958)
Belvédère
Poder de la función lineal (John Jair Angulo Valencia)
Francisco Pizarro

IMAGINARY.org
préparation
incubation
Ilumination
traduction
verification
Préparation
Incubation
Ilumination
Traduction
Vérification
Préparation
Incubation
Ilumination
traduction
vérificatión
Divergente
Convergente
Henri de Toulouse-Lautrec, Au lit (huile sur carton, 1892, Musée d'Orsay, Paris)
publication
réflexion
Action, formulation, validation
Changement du milieu
https://www.geogebra.org/m/sDcFxqfB
https://www.geogebra.org/m/WeKh8aTg
https://www.geogebra.org/m/eZe3Vwm9
https://www.geogebra.org/m/wdkmGMuJ#chapter/109513
https://www.geogebra.org/m/w9K75qsF

https://pt.wikipedia.org/wiki/Os_Embaixadores
https://pt.wikipedia.org/wiki/Anamorfose
Brunelleschi (1415)
= +
Thierry Boutonnier (2005)
Christian Mercat
IREM de Lyon
Pedro Lealdino Filho

Eduardo Kac (1998)
http://www.editions-hermann.fr/ficheproduit.php?lang=fr&menu=7&ref=Histoire+de+l%27Art+LA+SCIENCE+n%27EsT+pas+L%27ART&prodid=794
https://pt.wikipedia.org/wiki/Eduardo_Kac
Ennui
Annonciation c.1489 - Sandro Botticelli
Contrapposto << serpentinado
Man Ray, Francis Picabia en grande vitesse 1924
https://www.geogebra.org/m/wCjHPYDU
Bifurcation de Feigenbaum

MichaelHoggUK
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