L'Approximation polygonale : bilans et perspectives
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(12) Q?AM E'6`D'D/ +aL =?'D++?'`R 7 'b:'6L7'b(* B?"P'6/ '^=?'D+c(9'D+ '6:'6 7'D+!W 7&+T%7d
(13) Nb/ 'DR + '6 ?DO 7&+M !+ &+M=e
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(15) f7 ' '6R '6$ A'Z"'k"A% $=?'Z"NB(9& ; ' Jml`'D+b(* D'6/ 'D+H+ ?^U&%+'DR +H+ 7H"'D+H % &+b=e
(16) 'DR (6`ME7nV/ "NB=?:' '6_=?'o+. BB'8=?'D+M'DR (61+[J < pX 7&+MB ?% &++ 7>=?'q EU'67?h'*'6B?"'D+6OX"P
(17) '6R '6; M=?'g 'g:C(:9'S&@1! >7? (9'D+E(:"N ++,-T%7'D+>r/ "Nr2sN+kL N+@0/ L N+E=e
(18) BH'6R * \2]+k UW 'D(* \2]+[Od'*"N+ET 7'5"P
(19) L N &(*'0'6 %1 7S +T%7&$ ' Oe &+3^T%7'BL%-+BM/ L%N+G=?'(* D'6/ 'D+_+.7UW,'D(*.t2P+G=?'B'D+.&'D(*8=?'V"P
(20) ?2s : g$ '6R F'6R NT%7' 'D(:9'61(9H'DR +H'*"uT%7'G'DR + '6Lv >=?'D+_ $"'D+H 7M &+ '6 &+3U?\"'BR 7@U:7?AJ. w@x [yDz{&|y. } "#?$ &" Y ? r-+Z:9'81 &+32s% @ 2 "t ~ 'D=0'D=?$ 'E! X >5+ 'DT 7'6 &(*'52a"\ ' + '6$ B'6 ?1+6JP l` B7:'6_XN+3 dO} "A#?$ &v" Y @N+Z+ * &=1=r1 + ~e?bN+X'6L '6 S7 &L =U?"'G\2`$ '6 5'6 N(G(9& 1 (*'6 N+ .-(6+X2 UW 'D(*1+cE7&+ bU&'E(* &+3N=?'6'D=eJ 3 F9'B&*+ E&8 2_9'M&&'6DO H'M'D+ '6 ?=%\m'6:'6 B(* '6 NO + %B'6 B'D+V &(* &+3N+ :'6 BA:9?A 9'6+ '*"L 'D+[O`b9?N(:9h:'@7&+ 'D= h} "A#?$ &v" Y ?AM d2s7:9'6B ' O H'>+ 7L%'6# 9'r&'*"N=F2 'D+ '6 ?bB'69=+6J H9'6 dO?H'b !+ '_k '6 (:9BU& + 'D=5 B:9'_E ?ED @ 2 B'6 '6$ #v"A% $89'X"\A ~%'D=M'D=?$ ' & ?1+6J H9?N+Z'6 '6$ #MN+ZU& + 'D=0 09'8ME7=%-+.1 &(*'EU&'6 H'6'6 S9'G"\ '+ '6$ 5'6 1+Z &=r9'V"t ~ 'D='D=?$ ' & ?1+Z &=M @9'E+ 72 9'D+ '8=%N+ 1 &(*'D+6J g'r\"t"7&+ :1' OHH9 #F'*&B?"'D+6OH9'r '6:'D+ 28 7 (:99: 7$ 9%UW,'D(*.AL%'):'D+ 1+ =?'6B &+.1 $V' Jf$&J L N &(*'Z M 1.A% B H9@G%+ ~&a &=B9: 7$ 9+ 7UW,'D(* L 'X'D+ 1+c+ 9H $ $ '6 B'6: N(G+ 9&&'V'D+ '6L + 7&(:9> +b $"'D+*H &=@9'Z ?&7'6 &(*'E2 N+ ' J.
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(25) L N &(*'87 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 J J
(26) ,'DR (:9'*"\"A< ' 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 J >J = E 1 '6"-51 &+3"N 7 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 J J m'G +T%7&$ '87 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 J>= e'D+Z(* D'6/ :'D+^+.7UW,'D(*.t2P@ + 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 >J =J lc : ; "'6c"]
(27) 'DR (6HvB" 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 >J =>J = }'DR +.'6L '6 "'D+Z $"'DC + 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 >J =J }'DR +.'6L '6 "'D+Z=?'DD+ 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 , r ? Gy FIH-Ci. J.K'LN[N{ M&?{ x 0-C , { G| Hddz x dz J } .A &(:!' 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 >J = Sb7&"\'DR +Z=?'Z"P
(28) Q? T 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 J 'K U@(6 (:C@ ' R 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 J l` &(:"7&+3 V7 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 , r ? Gy FIH-CW -d XdY LZHJ J } .A &(:!' 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 >J =
(29) Q &"#C+ 'E+ #? 1vNT%7' 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 J e'D+Z7'D+ '6R 9=?'D+]7 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 J l` &(:"7&+3 V7 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 , r ? Gy FIH-CW -d/ - C G| H3 _N{ M& J } .A &(:!' 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 >J = Sb7&"\'DR +Z=?'Z"P
(30) Q? 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 J K U@(6 (:C@ ' ' R 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 J l` &(:"7&+3 V 7 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 , b { XdY LZHJBccd Je/ JeHde Ke 0f0-).{ _'_ Yz Hdg| Fe } 'DR + '6 ?1 D 7 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 \ J l`9\)=e
(31) f7 >(*.AD'6/ '8=e
(32) '6R '6$' 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 \ >J =
(33) ,'DR (6:C 7 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 \ >J =J m'G^'6R >'6/ h ' 7 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 \ >J =>J = B+ 7 2P (*i ' 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 \ >J =J l` &(:"7&+3 V 7 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 7 797 7 7:7 7 797 7 7:7 7 797 797 7 7 \ J ,. 4 ; ; ? ? A A. +PO +RQ. +P[ Y\ Y\ ? A E` =Ra =Ra =R= =R= EO = = = =R = \ R= A.
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(37) 'DR (6 H?AMT" 7 7 797 7 797 7 7:7 7 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 Y J e'D+XB'D+ 7:'D+b(* B&* L 'D+6O?"'D+X'D+ 1+c'*d'D(*7H'DR + 7 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 Y J Y &"#C+.'o=?'D+XC'DR + 7?"1 1+ 7:7 7 797 7 797 7 7:7 7 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 Y J J pb EU'8=?'8+.'6$ B'6 ?1+H'6_+ 7.2] (*' 7:7 7 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 Y J >J =
(38) L N &(*' 7 7:7 7 797 7 797 7 7:7 7 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 Y >J e'D+X'DR + 7?"11+c'6 @ $ 'D + 7 7 797 7 797 7 7:7 7 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 w J'Je d Hd/ _d0- 'Ly / - 0-{ Gy FeH-d/ _ z HI_'H ? y6z / L J{Yy LZHJ - 0 1 |{&zy@ ){ 'L4 S.{ 0cy - 0-{FdYz X3{&| l_J '6R '6E & >=?'k"P
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(40) ,'DR (6: 797 7 7:7 7 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 l_>J = '6R '6E & >=?'k"NB+ 7 2P (*]' 797 7 797 7 7:7 7 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 l_J 'DR + 7F' R 7 7 7:7 797 7 7:7 7 797 7 797 7 7:7 7 797 7:7 7 797 7 797 7 7:7 7 797 7 7:7 797 . yDz%m| ymz/ -d -H JdJ ? C L x 0fLZH.Mz. { _ F3L- 4. HJ R0. O ` O O. a a. _ ?. ^ 4 ^ 4 ^ R? R? RA RA. [ \. [3E [ O.
(41) ;. . * . W . %. . pb%7&+BU&%1=? &+B= &+5(*'6''6R :7&=?'@7 F U?"]'6/ B'>(:"N +:+3NT 7'R5b(*'*"7?8=?'M"]
(42) F&"#?$ &"' J
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(45) ?24 g+6
(46) Q (6(* 5&$ '8$ '6R H'6R *"'6B'6 =?'o=?'67?)Lv 1 $ 'D+c'D++ '6 ? '*"-+ 5 m=?'D'b+E$=? M H'6 B'6R 'D'D+6+ J &Y (*'Z F'5'6R 5 &=%N(6R' 56 "P\
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(49) f'_ *L%=?"'>7B=?'' Aga = &+H"'E(6 =?'8=e
(50) f7 'E=?'G +b?"\N(6 & +
(51) GD ?RAPJ ! m'@ $*+b F=e
(52) f'67 F 'o' U(:9&(6 ; (: '8' R &Ou =b 7 & >+B =? '@E U E'GU'DR '6=?7&7?+ 'D_+B=? '8?."tANi(6A..AA%L% &'D+@+b'D(*+ BA &?=%"'*NC+ !'D+['6O &+"NSU?"'6' J 'DR + '6 * F=?'D+ < K @24 &(* )=?7g(* ?'*'o=?'k"P
(53) Q?"\N(6 dOa=e
(54) 7'D+cBH'6R 1 \2P+_+.^'DR (:\T 7'D+ZL%'6 '6 8+[
(55) QW 7'6DJ } H'*C'65?"A' O!= &+c"'8(6 =?'8=e
(56) f7 '8 ?"tN(6.A% )=?'8=c'DR (*%7&'Z &=?7&+ '*"\"'B=?'G?]'D/ (*'D+b=?'G N++ 7&+[O "'D+cB ^'6R 1 \2]+ + 7?L *+`=?L '6 ?G'6; '`.-+c'6 (*%BR' 5"P
(57) Q? B 'Z=?`& + '6B?6'6R '6`+ 7 "NV+ 7 2P (*' =?'c"]
(58) UW '6a'6 "'D+ (:97'D+ =?'H N++.7&+ + 7 2P (*'`.-+.'^'6 B=?'69 *+ =?'`"P
(59) f%UW,'6[m=?L '6 ?Z'6; :' E ?EN+'6R 'D+6J &+ +Z9d'6/ B'D+b=?'E'D(:9'61(9' Oe7 'B=?'D+G?"\N(6 &+k L \"6'6R $ '6R 'D+G(* &(*'6 '(*% &(*'6 'V"-M:'D(* &N++ &(*' =e
(60) f UW '6b'6Z?"7&+Z& N(*7?"\]'6/ '6B'6 ?Z"NBi-+.'o'6 S(* 'D+.& &= &(*'E'6 ?'V7 >B='*/ "'8$ '6R F'6R NT%7'I=c'*R & ? &_=?'D+Z+ '6$ B'6 ?1+H=?'o=?:'G'6H"NB$ '6R F'6R '_=?'D+Z=? H'6R 'D+[J &+G(*'@(6 =?' Om\"^ 7&+V+ '6EU?"A'M'D++ '6 ? '*"_=?'=c'*R & ?B(:"N'6B'6 ?V"A'D+V(* D'6/ :'D+8T%7?+ ?G$ '6R ^'6R 1"'6 B'6 ?b'D(:9'61(9H'DR +6J} 7b(*'*"NO 7&+b(:"N +:+3\& &+_(*'D+X(* ['6/ 'D+c'6 S=?'67?r(6'6R $ .A'D+[O"'D+_(*.AD'6/ 'D+c UW 'D(* \2P+ ?Lv N &(*' C^'6H"'D+Z(* D'6/ :'D+^+.7UW,'D(*.t2P+Z+ 7L '6 ?b'*"N \2P+8V/ "P
(61) Q?"\N(6 dJ pb%R' 5 (*'6'>'6R 7&=?'b'D+.`\"\"7&+ '6R '8=?'I+:(9H'6R +`T%7?e2s% H&1; :'I+3E7?"1 H'6R B'6 c"NE(9& ; '8=?'G! *+ '6^+ % ?AM dJ 8(:9&<; '_'D+ `v"A%1+ '6'DR + '6 ?'6R 'H& <7 M1vA`(*% ?7v"A%1+ T 7'X< "'D+`+ '6$%B'6 *+ + ?b'6'DR + '6 ?C'DR +&b7 >:1H'6 >& A ? \"\" ' R J. @
(62) [ \ _ 6 "!N !/#%$&('*) [+\ _ h-,.0/ 1@}: }/[ . &+m"A'b(* ?'*'`=?'c"Nb'D(*% &N++ &(*'b=e
(63) f UW,'61+t"'D+ &=%-+.&'6 &+U?"'8=?'H(* &+3N=`'6R '6"'c2] T 7'"NbEN+ ' '6 g(* 'D+ ! &= &(*'E'6 ?'V"'o5C=e'*/ "A'V'6Z"'D+G=? ^'6R 'D+X 'E&'678+ 'k2]'B+ &+b'6 &=?:'o'6 g(* 5'B(*'6 1 'D+ 1 &+32s% &+[J 2b 'X1 &+324 M 8(* :'D+ & &=eO& a'*'6B?"' OZ/ 7 B(:9& $ '6B'6 ?u=e
(64) 'DR (:9'*"t"' J 2b (*.AD'6/ 'M'D++ '6 ? '*"_'6E UW 'D(* \2I! 7 '6R L"7'6E"'D+E&'6 24 M &(*'D+B=e
(65) f7 '>:D? F(* &+3N+ :' / & 7L%^ ++.7'6`T 7'"A'D+c'DR + 7?"11+m24 7 ?N+`+ A'6 ? ?Lv N ?1&+ VT 7'*"NT%7'I+.'6 c7 B'6 &+ '6EU?"'I=?'H1 &+ 2s% &+X=`'*R & ?'D+_V .]J e'D+i1 &+324 M &+GT%7'@ 7&+V'6 &=? &+E'6 F(* B:'>+ ?G"'D+E?"7&+B(:"N ++3NT%7'D+6O \"I+6
(66) $o" *+ =?72]%(*'67B=e
(67) ,'DR (:9'*"\"A' Oc=?'M"-0%1 '6B=?'M"-0* &+3"N F &+3IT%7d
(68) f7 '@1 &+32s% q1'6B'6 ? N+ 'B'6 g(* B:'iT%7'B 7&+G &'*" &+Z"'BM +T%7&$ ' Jl`'D+Z1 &+,2s : &+b+. G'*?"\N(*C'6R 'D+Z'6 =c'6R 1\" (: PD'D/ +[J + 3 +3 + , 1 |RFeN0 0- d@=%N+ 1 &(*'M=?'8"P
(69) f%UW,'6G%7>& 24N+G+M1vt"\"'B'D+ 8(*% 7'B=?'V2] (*4 0A5C'DR (:N+ ' Je]"`'D+ 8=? &(V ^'DR (*'D++:' =?'8'6 &=?:'8'6 >(* B:'G7 '8Lv N >!++3U?"'B=?'G"P
(70) 'DR (9'*"\"'G" 1+X=?'G"NE'D(* &v-+:+ &(*' J.
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