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Art, Mathematics and Creativity

Oman Math Days 2017
by

Christian Mercat

on 23 August 2018

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Transcript of Art, Mathematics and Creativity

Teaching
Art, mathematics
nstitute
for
esearch
on
T aching
athematics
Université Claude Bernard
1
Institut Camille Jordan
*
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
© Régis Goiffon
https://imaginary.org/program/surfer
http://www.fondationvasarely.fr/
There is creativity in an algebraic expression!
Beauty behind a function
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/
motivation
Csíkszentmihályi, Liljedahl
ZPD
Perseverance
Tolerance
Henri Poincaré
Science & hypothesis
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
A perspective on functions
Geometric sequence
http://www.dimensions-math.org
http://www.chaos-math.org
Conformal webcam
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
Modeling

Creativity
Lady Shalott
Cédric Villani
© Cédric Villani
Alfred Lord Tennyson
by William Maw Egley
Bridget Riley
one
roximal
of
evelopment
bouncing ball
Galileo bells
M.C. Escher (1958)
Belvédère
Francisco Pizarro

IMAGINARY.org
preparation
incubation
translation
verification
Illumination
Preparation
Incubation
Illumination
Translation
Verification
Preparation
Incubation
Illumination
translation
verificatión
Divergent
Convergent
Henri de Toulouse-Lautrec, Au lit (huile sur carton, 1892, Musée d'Orsay, Paris)
publication
reflexion
Action, formulation, validation
Changes in the
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)
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
Annonciation c.1489 - Sandro Botticelli
Contrapposto
Man Ray, Francis Picabia en grande vitesse 1924
https://news.missouri.edu/2013/learning-by-growing/
&
Clifford A. Pickover
Julio Le Parc
https://www.researchgate.net/publication/317784785_Creativity_and_Technology_in_Mathematics_From_Story_Telling_to_Algorithmic_with_Op%27Art
Christian Mercat
IREM Lyon
Pedro Lealdino Filho

model
What are you dealing with?

What is the universe?

What are the relationships?
Identify
Define
Connect
Validate
> ≠ =
>
Iterate
make genuine choices that matter
Nobody likes to be wrong. There is not a unique model for a situation.
Abstraction is not the problem, reality is messy, simplifying it means making choices.
Create a world for your situation, give names to your creation.
What are the rules in your game? How do we get around your world?
the little scientist (Jean Piaget)
https://www.geogebra.org/m/wdkmGMuJ
http://bit.ly/webcamconf
http://www.fetedeslumieres.lyon.fr/en
https://www.mathenjeans.fr/
http://bit.ly/WebcamSliced
https://www.geogebra.org/m/wCjHPYDU
Bifurcation de Feigenbaum

MichaelHoggUK
https://montaga.github.io/droste/
Full transcript