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  • Committer: Hilaire Fernandes
  • Date: 2016-02-15 08:53:02 UTC
  • Revision ID: hilaire.fernandes@gmail.com-20160215085302-sky2a9tz123dgs68
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<TeXmacs|1.99.4>
 
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<style|<tuple|article|french>>
 
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<\body>
 
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  <doc-data|<doc-title|La spirale de Fibonacci>|<doc-author|<\author-data|<author-name|Hilaire
 
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  Fernandes>>
 
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    \;
 
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  </author-data|<author-email|hilaire@drgeo.eu>>>>
 
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  <abstract-data|<\abstract>
 
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    La spirale de Fibonacci s'appuie sur la suite �ponyme pour la
 
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    consturction d'une courbe en forme de spirale, cette spirale et ses
 
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    variantes apparaissent dans des constructions du vivant. Dans cet article
 
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    nous proposons une construction calcul�e d'une forme interactive de cette
 
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    courbe, � l'aide de <hlink|Dr. Geo|http://drgeo.eu>, logiciel de
 
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    g�om�trie interactive et de programmation. Nous relaterons ensuite les
 
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    liens � faire avec les programmes d'enseignement secondaire de
 
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    math�matiques.
 
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  </abstract>>
 
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  <section|Introduction>
 
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  Leonardo Fibonacci, marchand, comptable, math�maticien italien du
 
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  XIII<rsup|e> si�cle, est connu pour sa <with|font-shape|italic|suite de
 
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  Fibonacci> dont les termes sont appel�s <with|font-shape|italic|nombres de
 
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  Fibonacci>. Ses contributions math�matiques vont bien au del� de cette
 
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  suite, somme toute assez anecdotique en regard de l'ensemble de son �uvre.
 
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  Il a introduit en Europe les chiffres arabes et son syst�me positionnel de
 
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  construction des nombres, il a �crit plusieurs trait�s de math�matiques et
 
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  comptabilit�.
 
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  \;
 
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  La suite est d�finie par deux termes initiaux et une relation de r�currence
 
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  :
 
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  <\equation*>
 
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    f<rsub|0>=1<space|1em>f<rsub|1>=1<space|1em>f<rsub|n+1>=f<rsub|n>+f<rsub|n-1>
 
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  </equation*>
 
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  Les premiers termes de la suite sont donc 1, 1, 2, 3, 5, 8. La spirale de
 
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  Fibonacci se construit en consid�rant les carr�s de longueur les termes de
 
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  la suite, � l'int�rieur de ces carr�s sont inscrits des arcs de cercle \U
 
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  portions de la spirale \U dont le centre est un des sommets du carr� et le
 
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  rayon la longueur du carr� :
 
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  La logique de la construction est ais�e � comprendre : � l'image des termes
 
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  logiciel de g�om�trie interactive. La suite de l'article s'attache � en
 
55
  pr�senter les grandes lignes.
 
56
 
 
57
  <section|L'amorce>
 
58
 
 
59
  Puisque la suite de Fibonacci voit ses deux premiers termes d�finis,
 
60
  interessons nous aux deux premiers carr�s et leur arc de cercle de .
 
61
 
 
62
  <\enumerate-alpha>
 
63
    <item>Nous pla�ons deux points <with|font-shape|italic|<with|font-shape|right|<with|font-shape|italic|A>(1
 
64
    ; 0)>> et <with|font-shape|right|<with|font-shape|italic|B>(-1 ; 0)>,
 
65
    puis nous construisons leur milieu <with|font-shape|right|<with|font-shape|italic|M>(0
 
66
    ; 0)>.
 
67
 
 
68
    <item>Pour le premier carr�, avec <math|f<rsub|1>=1>,
 
69
    <with|font-shape|italic|M> est un sommet, c'est �galement le centre de
 
70
    l'arc correspondant. Le point <with|font-shape|italic|A> est consid�r�
 
71
    comme son origine. Pour d�terminer l'arc il nous suffit de construire son
 
72
    extr�mit� <with|font-shape|italic|E>=<with|font-shape|italic|r>(<with|font-shape|italic|A>)
 
73
    avec la rotation <with|font-shape|italic|r><with|font-shape|right|(><with|font-shape|right|<with|font-shape|italic|M>>,-90<math|<rsup|\<fullnote\>>>).
 
74
    Le quatri�me sommet du carr� est construit par la translation de vecteur
 
75
    <math|<wide|<math-it|MA>|\<vect\>><math-it|>>.
 
76
 
 
77
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|png>|300px|180px||>|Construction
 
78
    des deux arcs initiaux de la spirale>
 
79
 
 
80
    <item>Pour le deuxi�me carr�, avec <math|f<rsub|2>=2>,
 
81
    <with|font-shape|italic|M> est toujours le centre de son arc inscrit. Le
 
82
    point <with|font-shape|italic|E> devient son origine. L'extr�mit�
 
83
    <with|font-shape|italic|B> de l'arc se construit par la m�me rotation
 
84
    <with|font-shape|italic|r>. Le quatri�me sommet du carr� est construit
 
85
    par la translation de vecteur <math|<wide|<math-it|ME>|\<vect\>>.>
 
86
  </enumerate-alpha>
 
87
 
 
88
  D�gageons les �tapes de cette it�ration :
 
89
 
 
90
  <\description>
 
91
    <item*|Rotation>Elle construit l'extr�mit� de l'arc connaissant son
 
92
    origine. Son centre est le centre de l'arc, l'angle -90 degr�s.
 
93
 
 
94
    <item*|Translation>Elle construit le quatri�me sommet du carr�. Son
 
95
    origine est le centre de l'arc, son extr�mit� l'origine de l'arc.
 
96
 
 
97
    <item*|It�ration>L'extr�mit� du premier arc devient l'origine du suivant,
 
98
    le centre est rest� inchang�.
 
99
  </description>
 
100
 
 
101
  Nous traduisons cette description en un code Dr. Geo :
 
102
 
 
103
  <\verbatim-code>
 
104
    \|canvas shape alpha a b m s\|
 
105
 
 
106
    canvas := DrGeoCanvas new fullscreen.
 
107
 
 
108
    alpha := canvas freeValue: -90 degreesToRadians.
 
109
 
 
110
    shape := [:c :o :f\| \| e p \|
 
111
 
 
112
    \ \ \ "c,o,e: center, origin and extremity of the arc"
 
113
 
 
114
    \ \ \ e := canvas rotate: o center: c angle: alpha.
 
115
 
 
116
    \ \ \ canvas arcCenter: c from: o to: e.
 
117
 
 
118
    \ \ \ p := canvas translate: e vector: (canvas vector: c to: o).
 
119
 
 
120
    \ \ \ (canvas polygon: { c. o. p. e }) name: f.
 
121
 
 
122
    \ \ \ e].
 
123
 
 
124
    a := canvas point: 1@0.
 
125
 
 
126
    b := canvas point: -1 @0.
 
127
 
 
128
    m := canvas middleOf: a and: b.
 
129
 
 
130
    s := shape value: m value: a value: 1.
 
131
 
 
132
    shape value: m value: s value: 1.
 
133
  </verbatim-code>
 
134
 
 
135
  Quelques commentaires :
 
136
 
 
137
  <\itemize-minus>
 
138
    <item><code*|alpha> est l'angle de la rotation
 
139
    <with|font-shape|italic|r>, il est converti en radian pour �tre utilis�
 
140
    par Dr. Geo.
 
141
 
 
142
    <item>Le bloc de code <code*|shape> ex�cute la construction d'un arc et
 
143
    du carr� associ� connaissant dans cet ordre les centre, origine de l'arc
 
144
    et le nombre de Fibonacci. Le bloc de code retourne l'extr�mit� de l'arc
 
145
    construit qui est aussi l'orgine de l'arc suivant.
 
146
 
 
147
    <item>Les deux derni�res lignes montrent que l'extr�mit� <verbatim|s> du
 
148
    premier arc devient l'origine du second. Le centre <verbatim|m> reste
 
149
    inchang�.
 
150
  </itemize-minus>
 
151
 
 
152
  A l'image des deux premiers termes de la suite, ces deux premi�res portions
 
153
  de la spirale sont particuli�res : de m�mes centre et rayon. Dans la
 
154
  section suivante, nous g�n�ralisons le proc�d� au reste de la spirale.
 
155
 
 
156
  <section|Encore une transformation>
 
157
 
 
158
  A la troisi�me �tape de la construction :
 
159
 
 
160
  <\enumerate-alpha>
 
161
    <item>Pour ce brin de la spirale, <math|f<rsub|3>=2>, nous avons besoin
 
162
    de son centre et de son origine : ce sont les points
 
163
    <with|font-shape|italic|A> et <with|font-shape|italic|B>. Notre bloc de
 
164
    code <verbatim|shape> construit l'arc et le carr� associ�.
 
165
 
 
166
    <item>Le point <with|font-shape|italic|E> retourn� par le bloc
 
167
    <verbatim|shape> est l'origine de l'arc suivant, <math|f<rsub|4>=3>.
 
168
 
 
169
    <item>Le rayon de cet arc passera de 2 � 3 par rapport au pr�c�dent, soit
 
170
    une dilatation de <math|<frac|3|2>>. Le centre de cet arc est donc
 
171
    <with|font-shape|italic|h>(<with|font-shape|italic|A>) avec l'homoth�tie
 
172
    <with|font-shape|italic|h>(<with|font-shape|italic|E>,<math|<frac|3|2>>).
 
173
  </enumerate-alpha>
 
174
 
 
175
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  des brins pour <math|f<rsub|3> et f<rsub|4>.>>
 
177
 
 
178
  D�gageons les �tapes de cette it�ration :
 
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180
  <\description>
 
181
    <item*|Construction>Le brin de spirale est construit � partir de son
 
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    centre <with|font-shape|italic|A> et origine <with|font-shape|italic|B>
 
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    connus.
 
184
 
 
185
    <item*|Arc suivant>La construction pr�c�dente donne l'origine de l'arc
 
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    suivant <with|font-shape|italic|E>. Son centre est d�termin� par l'image
 
187
    du centre pr�c�dent <with|font-shape|italic|A> par l'homoth�tie de centre
 
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    <with|font-shape|italic|E>, l'origine de l'arc, et rapport
 
189
    <math|<frac|f<rsub|4>|f<rsub|3>>>.
 
190
  </description>
 
191
 
 
192
  A noter que <math|<frac|f<rsub|n+1>|f<rsub|n>>> tend vers le nombre d'or.
 
193
 
 
194
  Nous traduisons cette description en un bloc de code <verbatim|fibo>
 
195
  r�cursif :
 
196
 
 
197
  <\verbatim-code>
 
198
    fibo := [ :f :o :c :k \| \| e f1 f2 f3\|
 
199
 
 
200
    "f1: term Fn, f2: term Fn+1,\ 
 
201
 
 
202
    o & c: origin and center of the arc
 
203
 
 
204
    e: extremity of the arc/orgin of the next arc"
 
205
 
 
206
    \ \ \ f1 := f first.
 
207
 
 
208
    \ \ \ f2 := f second.
 
209
 
 
210
    \ \ \ f3 := f1 + f2.
 
211
 
 
212
    \ \ \ e := shape value: c value: o value: f2.\ 
 
213
 
 
214
    \ \ \ c := (canvas scale: c center: e factor: f3 / f2).
 
215
 
 
216
    \ \ \ k \<gtr\> 0 ifTrue: [\ 
 
217
 
 
218
    \ \ \ \ \ \ fibo value: {f2. f3} value: e value: c value: k - 1 ]].
 
219
  </verbatim-code>
 
220
 
 
221
  Quelques commentaires n�cessaires :
 
222
 
 
223
  <\itemize-minus>
 
224
    <item>L'argument <verbatim|f> est une liste de deux termes de la suite.
 
225
 
 
226
    <item><verbatim|k> est un compteur d'it�ration.
 
227
 
 
228
    <item>L'it�ration suivante a lieu tant que <verbatim|k \<gtr\> 0>, le
 
229
    bloc de code est alors appel� avec comment arguments : une liste de deux
 
230
    termes, les orgine et centre du nouvel arc et <verbatim|k - 1>.
 
231
  </itemize-minus>
 
232
 
 
233
  \;
 
234
 
 
235
  Le code complet, propos� en annexe, est assez court. Il est constitu� des
 
236
  deux extraits pr�sent�s pr�c�dement. Cet exemple illustre bien toute la
 
237
  puissance de la programmation, avec une <acronym|API><\footnote>
 
238
    Interface de programmation
 
239
  </footnote> appropri�e de fonctions g�om�triques nous nous concentrons
 
240
  directement sur le probl�me, et un code concis permet alors de d�crire le
 
241
  probl�me pos� de la construction.
 
242
 
 
243
  \ L'autre int�r�t est de construire un grand nombre d'objets, parfois des
 
244
  miliers. Enfin la figure obtenue se doit d'�tre d�formable interactivement
 
245
  : d�placer le point initial <with|font-shape|italic|A> d�forme l'ensemble
 
246
  de la spirale.
 
247
 
 
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|png>|700px|||>|Une
 
249
  spirale d�formable interactivement>
 
250
 
 
251
  <section|Conclusion>
 
252
 
 
253
  Alors pourquoi programmer des figures interactives avec des �l�ves du
 
254
  secondaire ? Plusieurs th�mes sont abord�s :
 
255
 
 
256
  <\itemize-minus>
 
257
    <item>Les transformations g�om�triques et leurs utilit�s. C'est souvent
 
258
    une question pos�e par les �l�ves. Il r�torqueront mais � quoi sert la
 
259
    spirale ! Dans sa r�sultante interactive, elle est un bel exemple de
 
260
    proc�ssus interd�pendants rencontr�s dans le monde de la m�canique.
 
261
 
 
262
    <item>La programmation et, par un code obtenu court, sa puissance
 
263
    d�multiplicatrice. Les jeunes n'ont pas conscience d'�tre entour� de
 
264
    proc�ssus programmatique : \S C'est fatiguant d'appuyer 50 fois sur le
 
265
    bouton, il n'y a pas un autre moyen ? \T, \S Si ! \T\ 
 
266
 
 
267
    <item>R�solution de probl�me.
 
268
  </itemize-minus>
 
269
 
 
270
  Des �l�ves du secondaire II sont math�matiquement outill�s pour d�cortiquer
 
271
  cette spirale. La partie programmation demandera une connaissance pr�lable,
 
272
  � acqu�rir avec des probl�mes plus simples. Le language et l'environnement
 
273
  Smalltalk de Dr. Geo furent con�us pour des enfants, certes des enfants des
 
274
  ann�es '70 pour qui l'ordinateur avait une dimension magique et atractive,
 
275
  mais la puissance d�multiplicatrice de la programmation reste un facteur
 
276
  fort d'int�r�t.
 
277
 
 
278
  <appendix|>
 
279
 
 
280
  <\verbatim-code>
 
281
    \|canvas shape alfa fibo a b m s\|
 
282
 
 
283
    canvas := DrGeoCanvas new fullscreen.
 
284
 
 
285
    alfa := (canvas freeValue: -90 degreesToRadians) hide.
 
286
 
 
287
    shape := [:c :o :f\| \| e p \|
 
288
 
 
289
    \ \ \ e := (canvas rotate: o center: c angle: alfa) hide.
 
290
 
 
291
    \ \ \ (canvas arcCenter: c from: o to: e) large.
 
292
 
 
293
    \ \ \ p := canvas translate: e vector: (canvas vector: c to: o) hide.
 
294
 
 
295
    \ \ \ (canvas polygon: { c. o. p hide. e }) name: f.
 
296
 
 
297
    \ \ \ e].
 
298
 
 
299
    fibo := [ ].
 
300
 
 
301
    fibo := [ :f :o :c :k \| \| e f1 f2 f3\|
 
302
 
 
303
    "f1: term Fn-1, f2: term Fn, o & c: origin and center of spiral arm
 
304
 
 
305
    e: extremity of the spiral arm"
 
306
 
 
307
    \ \ \ f1 := f first.
 
308
 
 
309
    \ \ \ f2 := f second.
 
310
 
 
311
    \ \ \ f3 := f1 + f2.
 
312
 
 
313
    \ \ \ e := shape value: c value: o value: f2.\ 
 
314
 
 
315
    \ \ \ c := (canvas scale: c center: e factor: f3 / f2) hide.
 
316
 
 
317
    \ \ \ k \<gtr\> 0 ifTrue: [\ 
 
318
 
 
319
    \ \ \ \ \ \ fibo value: {f2. f3} value: e value: c value: k - 1 ]].
 
320
 
 
321
    \;
 
322
 
 
323
    a := canvas point: 1@0.
 
324
 
 
325
    b := canvas point: -1 @0.
 
326
 
 
327
    m := (canvas middleOf: a and: b) hide.
 
328
 
 
329
    s := shape value: m value: a value: 1.
 
330
 
 
331
    shape value: m value: s value: 1.
 
332
 
 
333
    fibo value: {1. 2} value: b value: a value: 10
 
334
 
 
335
    \;
 
336
  </verbatim-code>
 
337
</body>
 
338
 
 
339
<\initial>
 
340
  <\collection>
 
341
    <associate|font-base-size|11>
 
342
  </collection>
 
343
</initial>
 
344
 
 
345
<\references>
 
346
  <\collection>
 
347
    <associate|auto-1|<tuple|1|1>>
 
348
    <associate|auto-2|<tuple|1|1>>
 
349
    <associate|auto-3|<tuple|2|2>>
 
350
    <associate|auto-4|<tuple|2|2>>
 
351
    <associate|auto-5|<tuple|3|3>>
 
352
    <associate|auto-6|<tuple|3|?>>
 
353
    <associate|auto-7|<tuple|4|?>>
 
354
    <associate|auto-8|<tuple|4|?>>
 
355
    <associate|auto-9|<tuple|A|?>>
 
356
    <associate|footnote-1|<tuple|1|?>>
 
357
    <associate|footnr-1|<tuple|1|?>>
 
358
  </collection>
 
359
</references>
 
360
 
 
361
<\auxiliary>
 
362
  <\collection>
 
363
    <\associate|figure>
 
364
      <tuple|normal|Spirale de Fibonacci construite � partir des 6 premiers
 
365
      termes de la suite.|<pageref|auto-2>>
 
366
 
 
367
      <tuple|normal|Construction des deux arcs initiaux de la
 
368
      spirale|<pageref|auto-4>>
 
369
 
 
370
      <tuple|normal|Construction des brins pour
 
371
      <with|mode|<quote|math>|f<rsub|3> et f<rsub|4>.>|<pageref|auto-6>>
 
372
 
 
373
      <tuple|normal|Une spirale d�formable interactivement|<pageref|auto-7>>
 
374
    </associate>
 
375
    <\associate|toc>
 
376
      <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|1<space|2spc>Introduction>
 
377
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
 
378
      <no-break><pageref|auto-1><vspace|0.5fn>
 
379
 
 
380
      <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|2<space|2spc>L'amorce>
 
381
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
 
382
      <no-break><pageref|auto-3><vspace|0.5fn>
 
383
 
 
384
      <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|3<space|2spc>Encore
 
385
      une transformation> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
 
386
      <no-break><pageref|auto-5><vspace|0.5fn>
 
387
 
 
388
      <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|4<space|2spc>Conclusion>
 
389
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
 
390
      <no-break><pageref|auto-8><vspace|0.5fn>
 
391
 
 
392
      <vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|5<space|2spc>Annexe>
 
393
      <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
 
394
      <no-break><pageref|auto-9><vspace|0.5fn>
 
395
    </associate>
 
396
  </collection>
 
397
</auxiliary>
 
 
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