source: Backup NB/@Work/pavages.nb@ 687

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1(* Content-type: application/mathematica *)
2
3(*** Wolfram Notebook File ***)
4(* http://www.wolfram.com/nb *)
5
6(* CreatedBy='Mathematica 6.0' *)
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20(* Beginning of Notebook Content *)
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23Cell[CellGroupData[{
24Cell["Pavages du plan", "Title",
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28Cell[TextData[{
29 "Il existe partout des dessins obtenus par r\[EAcute]p\[EAcute]titions d'un \
30motif unique: carreaux d'une fen\[EHat]tre, tuiles d'une toiture, lattes de \
31bois d'une cl\[OHat]ture, briques d'un mur, papier peint, tissu,... On ne les \
32trouve pas seulement dans des objets produits par l'homme: le rayon de cire \
33d'abeille, la corolle des fleurs, le cristal de sel,...\nLa couverture d'un \
34plan par r\[EAcute]p\[EAcute]titions d'un m\[EHat]me motif, sans \
35chevauchements ni trous, s'appelle un ",
36 StyleBox["pavage",
37 FontWeight->"Bold"],
38 ". Comme c'est le cas pour toutes les t\[AHat]ches \
39r\[EAcute]p\[EAcute]titives, l'informatique s'av\[EGrave]re tr\[EGrave]s \
40utile pour produire des pavages."
41}], "Text",
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48Cell[CellGroupData[{
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50Cell["D\[EAcute]finition du motif", "Subsubtitle"],
51
52Cell[TextData[{
53 "Pour d\[EAcute]finir une forme, on proc\[EGrave]de comme ci-dessous. On \
54donne un nom sans espaces ou symboles ayant une signification \
55sp\[EAcute]ciale dans ",
56 StyleBox["Mathematica",
57 FontSlant->"Italic"],
58 " (comme - par exemple). Vient ensuite le signe =. Enfin, entre accolades, \
59on indique la couleur, puis, apr\[EGrave]s une virgule, viennent la ou les \
60primitives graphiques."
61}], "Text",
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116Cell["\<\
117Une fois toutes les parties du dessin d\[EAcute]finies, on indique l'ordre \
118dans lequel elles doivent \[EHat]tre dessin\[EAcute]es:\
119\>", "Text",
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130Cell[TextData[{
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133 " dessinera d'abord le carr\[EAcute] puis la croix. Changez l'ordre pour \
134voir la diff\[EAcute]rence ! \nRien ne sera dessin\[EAcute] \[AGrave] l'\
135\[EAcute]cran tant que vous ne direz pas \[AGrave] ",
136 StyleBox["Mathematica",
137 FontSlant->"Italic"],
138 " de le faire ! Voici l'instruction \[AGrave] utiliser:"
139}], "Text",
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149
150Cell["\<\
151(on peut r\[EAcute]duire ou agrandir de dessin en cliquant dessus et en \
152manipulant les poign\[EAcute]es).\
153\>", "Text"]
154}, Open ]],
155
156Cell[CellGroupData[{
157
158Cell["R\[EAcute]p\[EAcute]tition du motif", "Subsubtitle"],
159
160Cell[TextData[{
161 "Le motif g\[EAcute]n\[EAcute]rique de pavage sera d\[EAcute]fini comme \
162suit. On doit d'abord donner les deux directions de translation (pour couvrir \
163un plan il faut deux directions). On peut faire une analogie avec les \
164machines \[AGrave] \[EAcute]crire. En tapant sur une touche, la touche \
165\"avance\" automatiquement d'un cran vers la droite; cela correspond pour \
166nous \[AGrave] notre direction ",
167 StyleBox["u",
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170 ". \[CapitalAGrave] la fin d'une ligne, on descend d'un cran avant de \
171recommencer une nouvelle ligne; c'est notre direction ",
172 StyleBox["v",
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175 ". Remarquez que les vecteurs ",
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179 " et ",
180 StyleBox["v",
181 FontFamily->"Courier",
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183 " n'ont pas besoin d'\[EHat]tre perpendiculaires; ils doivent seulement \
184\[EHat]tre non colin\[EAcute]aires."
185}], "Text",
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188
189Cell[TextData[{
190 "Comme notre dessin a une largeur de 2, on se d\[EAcute]calera de deux unit\
191\[EAcute]s vers la droite (",
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195 "). Comme on a envie que nos dessins soient r\[EAcute]p\[EAcute]t\[EAcute]s \
196en quinconce, la direction ",
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202\[EAcute]c\[EAcute]dente."
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217Cell["\<\
218On d\[EAcute]finit maintenant le motif g\[EAcute]n\[EAcute]rique qui \
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253 "La fonction ",
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269 " par ",
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277 " et ",
278 StyleBox["dy",
279 FontFamily->"Courier",
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281 " entre 0 et le nombre de r\[EAcute]p\[EAcute]titions moins une que l'on \
282veut en horizontal et en vertical. Dans notre exemple, on a d\[EAcute]cid\
283\[EAcute] de r\[EAcute]p\[EAcute]ter 5 fois selon la direction ",
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319Cell["\<\
320Vous trouverez ci-dessous trois pavages de difficult\[EAcute]s croissantes.\
321\>", "Text"],
322
323Cell[CellGroupData[{
324
325Cell["Exemple 1 : le carrelage", "Subsection",
326 Evaluatable->False,
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328 AspectRatioFixed->True],
329
330Cell["\<\
331D'apr\[EGrave]s le travail de Pauline Bart, classe 1BD', mars 1997.\
332\>", "Text",
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492Cell["\<\
493Exemple 2 : le troupeau d'\[EAcute]l\[EAcute]phants\
494\>", "Subsection",
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497 AspectRatioFixed->True],
498
499Cell["\<\
500D'apr\[EGrave]s le travail de Fr\[EAcute]d\[EAcute]ric Girardin, classe 1C, \
501mars 1997.\
502\>", "Text",
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1221
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