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Cell[CellGroupData[{
Cell["Pavages du plan", "Title",
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Cell[TextData[{
 "Il existe partout des dessins obtenus par r\[EAcute]p\[EAcute]titions d'un \
motif unique: carreaux d'une fen\[EHat]tre, tuiles d'une toiture, lattes de \
bois d'une cl\[OHat]ture, briques d'un mur, papier peint, tissu,... On ne les \
trouve pas seulement dans des objets produits par l'homme: le rayon de cire \
d'abeille, la corolle des fleurs, le cristal de sel,...\nLa couverture d'un \
plan par r\[EAcute]p\[EAcute]titions d'un m\[EHat]me motif, sans \
chevauchements ni trous, s'appelle un ",
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 ". Comme c'est le cas pour toutes les t\[AHat]ches \
r\[EAcute]p\[EAcute]titives, l'informatique s'av\[EGrave]re tr\[EGrave]s \
utile pour produire des pavages."
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Cell["D\[EAcute]finition du motif", "Subsubtitle"],

Cell[TextData[{
 "Pour d\[EAcute]finir une forme, on proc\[EGrave]de comme ci-dessous. On \
donne un nom sans espaces ou symboles ayant une signification \
sp\[EAcute]ciale dans ",
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 " (comme - par exemple). Vient ensuite le signe =. Enfin, entre accolades, \
on indique la couleur, puis, apr\[EGrave]s une virgule, viennent la ou les \
primitives graphiques."
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Cell["\<\
Une fois toutes les parties du dessin d\[EAcute]finies, on indique l'ordre \
dans lequel elles doivent \[EHat]tre dessin\[EAcute]es:\
\>", "Text",
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Cell[TextData[{
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 " dessinera d'abord le carr\[EAcute] puis la croix. Changez l'ordre pour \
voir la diff\[EAcute]rence ! \nRien ne sera dessin\[EAcute] \[AGrave] l'\
\[EAcute]cran tant que vous ne direz pas \[AGrave] ",
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 " de le faire ! Voici l'instruction \[AGrave] utiliser:"
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Cell["\<\
(on peut r\[EAcute]duire ou agrandir de dessin en cliquant dessus et en \
manipulant les poign\[EAcute]es).\
\>", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["R\[EAcute]p\[EAcute]tition du motif", "Subsubtitle"],

Cell[TextData[{
 "Le motif g\[EAcute]n\[EAcute]rique de pavage sera d\[EAcute]fini comme \
suit. On doit d'abord donner les deux directions de translation (pour couvrir \
un plan il faut deux directions). On peut faire une analogie avec les \
machines \[AGrave] \[EAcute]crire. En tapant sur une touche, la touche \
\"avance\" automatiquement d'un cran vers la droite; cela correspond pour \
nous \[AGrave] notre direction ",
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recommencer une nouvelle ligne; c'est notre direction ",
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 " et ",
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\[EHat]tre non colin\[EAcute]aires."
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Cell[TextData[{
 "Comme notre dessin a une largeur de 2, on se d\[EAcute]calera de deux unit\
\[EAcute]s vers la droite (",
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en quinconce, la direction ",
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vers la droite et de deux vers le haut par rapport \[AGrave] la ligne pr\
\[EAcute]c\[EAcute]dente."
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Cell["\<\
On d\[EAcute]finit maintenant le motif g\[EAcute]n\[EAcute]rique qui \
permettra de paver notre plan:\
\>", "Text",
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 ". On peut maintenant cr\[EAcute]er une liste en faisant varier ",
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 " et ",
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  FontFamily->"Courier",
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veut en horizontal et en vertical. Dans notre exemple, on a d\[EAcute]cid\
\[EAcute] de r\[EAcute]p\[EAcute]ter 5 fois selon la direction ",
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Cell["Dessinons enfin ce pavage :", "Text",
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Cell["\<\
Vous trouverez ci-dessous trois pavages de difficult\[EAcute]s croissantes.\
\>", "Text"],

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Cell["Exemple 1 : le carrelage", "Subsection",
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Cell["\<\
D'apr\[EGrave]s le travail de Pauline Bart, classe 1BD', mars 1997.\
\>", "Text",
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Cell["\<\
Exemple 2 : le troupeau d'\[EAcute]l\[EAcute]phants\
\>", "Subsection",
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Cell["\<\
D'apr\[EGrave]s le travail de Fr\[EAcute]d\[EAcute]ric Girardin, classe 1C, \
mars 1997.\
\>", "Text",
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