13

Metodo padovan

Embed Size (px)

Citation preview

Page 1: Metodo padovan

!"#!$%&'(%)'*&+&",!#-,&)'#&%.++/+01234++516789:+;%<#=%&+

>.6+?@06+AB0+C1DD6+EF1+1D+G@AC81+HF1I1+1JH189A14768+10+D@+A907189@0@K++"076+1A@?9L4+MF4I6A1476DN+01+

14?F14786+14+D6+

869:+I1+7@I6+?914?96+O+I1+7@I@+6871PK+++++%K+"9407194K+

++

+

Q6CD681A@0+I1+?@060+AFO+014?9DD60+O+?@4@?9I60+H@8+7@I@0K++R@4+014?9DD60+H@8EFS+H187141?14+6+D6+

467F86D1:6+O+D60+?@4@?1A@0+64?10786DA1471K+

R9+HD6476A@0+F46+01A9DD6+I1+TFIU6+14+1D+0979@+6I1?F6I@N+06C81A@0+I1+6471A64@+D@+EF1+H6068B+V+

218A9468BN+?81?18B+?@4+0F0+H8@H960+?686?718U079?60+O+H8@IF?98B+TFI960+EF1+14+0F+947189@8+714I8B4+01A9DD60+

01A1T64710+6+D60+EF1+HD6476A@0K+W@I@+107@+@?F881+H@8EFS+?6I6+01A9DD6+H@011+F4+H8@286A6+214S79?@+

C914+H81?90@K++"4+?6I6+018+X9X@+10+D@+A90A@K+

<1+D6+A90A6+A64186+EF1+06C81A@0+EF1+H6068B+IF86471+1D+I10688@DD@+I1+D6+TFIU6N+14+1D+018+GFA64@+

H6068B+D@+A90A@V+?F64I@+46?1+F4+C1CS+O6+06C1A@0+EF1+714I8B+D60+?686?718U079?60+I1+F4+6IFD7@N+G@AC81+

@+AFT18K++W@I@+107@+4@0+H681?1+764+467F86D+/+M@8A6+H6871+I1+D6+467F86D1:6+Y+EF1+O6+4@+G6?1A@0+?60@+I1+

D@0+A9D628@0+EF1+0F?1I64+I1D6471+4F1078@V++F4+?6HFDD@+EF1+01+6C81N+F4+HBT68@+EF1+?@4078FO1+0F+49I@N+F4+

49Z@+EF1+9471476+64I68NKKK+"D+018+X9X@+107B+?@4794F6A1471+?6AC964I@K+

"D+G@AC81+?6AC96+76AC9S4+I10I1+1D+A90A@+A@A147@+I1+0F+?@4?1H?9L4+G6076+1D+94076471+I1+0F+AF1871K++

"07@+10+D@+EF1+DD6A6A@0+I10688@DD@K++"071+I10688@DD@+HF1I1+018+A@789:N+I1+D142F6T1N+9471D1?7F6D+@+

1A@?9@46DN+94I9079476A1471K++W@I@+10+I10688@DD@K++&F10786+H180@46D9I6I+76AC9S4+?6AC96+01234+4F107860+

1JH18914?960+O+4F1078@0+6H814I9:6T10K++"D+G1?G@+I1+018+6IFD7@0+4@+09249M9?6+EF1+I1T1A@0+I1+

I10688@DD684@0KKK+R91AH81+1076A@0+?6AC964I@N+634EF1+4@+D@+EF186A@0N+286?960+6+D60+06C960+D1O10+I1+D6+

467F86D1:6K+

+

%&<%!+Y+Q%5.%!+Y+;"&R%!+

"D+I10688@DD@+I1D+018+GFA64@+D@+H@I1A@0+6C@8I68+I1+I9M1814710+A641860K++;686+!FI@DM+R719418+D6+81D6?9L4+

EF1+1J9071+14781+1D+64I68N+D6+H6D6C86+O+1D+H1406A9147@+10+H89A@8I96D+H686+D6+?@AH81409L4+O+D6+6HD9?6?9L4+

I1478@+I1+D6+1IF?6?9L4+ON+H@8+1J71409L4N+92F6DA1471+14+D@0+H8@?10@0+7186HSF79?@0K++"D+6M98A6+EF1+10760+

7810+6?79X9I6I10+I1M9414+6D+018+GFA64@+?@A@+76DV+>1D+G@AC81+10+1D+018+EF1+64I6+I181?G@N+EF1+F79D9:6+F4+

D142F6T1+?@I9M9?6I@+O+EF1+1D6C@86+9I160+@+016+EF1+H91406PK++"0+9AH@876471+14714I18+?@A@+!K+R719418+

?686?7189:6+?6I6+F46+I1+10760+6?79X9I6I10K+

%&<%!++4@+10+764+0@D@+I10HD6:6801K++;@41801+I1+H91+O+64I68+10+D6+01Z6D+AB0+X909CD1+I1+F4+H8@?10@+AF?G@+

AB0+6AHD9@+O+?@AHD1T@K++"0+F4+H8@?10@+1X@DF79X@+EF1+G6?1+EF1+1D+49Z@+H601+I1+F46+H@09?9L4+G@89:@476D+6+

F46+X1879?6DK++W14I8B+EF1+X14?18+D6+MF18:6+I1+D6+286X1I6IN+O+097F68+0F+?F18H@+14+1D+10H6?9@+?@4+1EF9D9C89@+

O+68A@4U6N+I@A9464I@+7@I60+D60+I981??9@410K++%4710+I1+H@I18+62F6476801+I1+H91N+1D+49Z@+H606+H@8+

I9M1814710+M6010V++X@D7168N+86078168N+267168+O+64I68K++"07@+H606+?F64I@+1D+H1EF1Z@+1X@DF?9@46+

4@8A6DA1471K++;18@+10+H@09CD1+EF1+10760+M6010+4@+01+G6O64+816D9:6I@+@+C914+01+G6O64+G1?G@+I1+A64186+

94?@AHD176K++"4+1071+?60@+H@8+1T1AHD@+I1?9A@0+V+01+G6+>06D76I@P+1D+2671@K++;18@++[H@8+EFS+I1?9A@0+

Page 2: Metodo padovan

EF1+01+G6+>06D76I@P+F46+176H6+\++;F10+H@8EFS+64?10786DA1471+4@0@78@0+06C1A@0+EF1+10+467F86D+EF1+

26711K++W@I60+10760+176H60+0@4+10H1?UM9?60+I1+D6+467F86D1:6+GFA646+O+107B4+9AHDU?9760+14+D@0+9AHFD0@0+I1D+

@826490A@K++R9+10760+176H60+107B4+H8@286A6I60+214S79?6A1471+14+1D+G@AC81N+107@+EF9181+I1?98+EF1+

467F86DA1471+0@4+9AH@8764710+H686+1D+I10688@DD@+I1D+49Z@K+

+

Q%5.%!+4@+0LD@+EF9181+I1?98+I1+A64186+810789?79X6+1D+D142F6T1+@86DN+094L+EF1+94?DFO1+7@I60+D60+M@8A60+I1+

?@AF49?6?9L4K++Q6O+I9M1814710+79H@0+I1+D142F6T1V++2107F6DN+AUA9?@N+10?897@N+A671AB79?@N+AF09?6DN+

?@I9M9?6I@N+O+@78@0K++R1234+;1I8@+5D@?GN+14++)6468960+1J9071+F46+A64186+I1+?@AF49?6801+H@8+09DC9I@0N+O+

H681?1+EF1+634+01+F79D9:6+14+D6+92D1096+H686+D118+D@0+06DA@0K++;@I1A@0+X18+EF1+D@0+49Z@0+01+?@AF49?64+I1+

I9M1814710+A641860+O+EF1+0F+H89A186+?@AF49?6?9L4+10+0F+H8@H9@+?F18H@K+)F64I@+107986+D@0+C86:@0+H686+

EF1+D@+?@T64N+107@+O6+10+?@AF49?6?9L4K++)@A@+I9?1+%DC187+5@6I1DD6+V+>94?DF0@+1D+09D14?9@+6C0@DF7@+4@0+I9?1+

?@060+I1+F46+H180@46K++"0+9AH@09CD1+EF1+1D+94I9X9IF@+4@+HF1I6+?@AF49?68PK+

+

;"&R%!++4@+D@+7141A@0+EF1+14714I18+349?6A1471+?@A@+D6+0@D6+H@09C9D9I6I+I1+?8168+9I160N+094L+?@A@+D60+

?6H6?9I6I10+I1+6H814I18+O+6I6H76801+6+0F+H8@H9@+A1I9@K+,4+1T1AHD@+I1+107@+10+D6+G907@896+I1D+49Z@+D@C@+

I1+%X1O8@4N+14+-864?96+V++>)F64I@+D1+14?@4786A@0+186+6I@D10?1471+O+0F+?@AH@876A9147@+01+H681?96+6D+I1+

D@0+D@C@0N+26716C6N+D6AU6+1D+62F6+1J6?76A1471+92F6D+EF1+D@+G6?14+D@0+649A6D10N+6FDD6C6+?@A@+D@0+D@C@0+

]186+0F+D142F6T1^K++"07@+09249M9?6+EF1+609A9DL+O+01+6I6H7L+6D+A1I9@+I@4I1+D1+7@?L+X9X98K++;18@+09+?@21A@0+

F4+26797@+O+D@+?896A@0+690D6I@+I1+0F+10H1?91N+0LD@+?@4+G@AC810N+?F64I@+01+G68B+6IFD7@+01+?@AH@8768B+

1J6?76A1471+92F6D+EF1+D@0+@78@0+267@0V+267168B+]4@+64I68B+I181?G@+?@A@+D6+H180@46+EF1+D@+G6+?896I@^N+

A6FDD68B+]4@+G6CD68B^N+714I8B+D60+A90A60+816??9@410+O+?@AH@876A9147@0+EF1+0F0+G18A64@0N+?@A@+09+

091AH81+GFC9101+X9X9I@+?@4+1DD@0K++[;@8+EFS+1D+G@AC81+]1D+49Z@+D@C@^+H681?1+G6C18+H18I9I@+0F+9I1479I6I+@+

0F0+?686?718U079?60+I1+G@AC81+]267164I@N+6FDD64I@N+17?KKK^+O+1D+267@+G6+2F68I6I@+D60+0FO60+I1+267@\++;F10+

H@8EFS+1D+018+GFA64@+79141+D6+?6H6?9I6I+I1+6I6H76801+O+6H814I18+O+10760+I@0+?686?718U079?60+M@8A64+

H6871+I1+SD+O+10+D@+EF1+!K+R719418+4@AC86+H1406A9147@K+

G77HV__```KX9X6D6X9I6K@82+/+X9X6D6X9I6+/+#071@H67U6+59@14182S79?6+)1DFD68+/+#K+5K+)K+/+;@`181I+CO+a6AC@+

#H14+R@F8?1+$1418671IV+b+<1?1AC18N+cdeeN+efVgb++

$14186DA1471+D@0+649A6D10+107B4+H8@286A6I@0+H686+?FAHD98+0F+H@714?96D+214S79?@N+094+H@I18D@+

A@I9M9?68K++"D+G@AC81+10+I9M181471K++W6AC9S4+H@011+0F+H8@286A6+214S79?@N+H18@+41?10976+I1+F4+6AC91471+

6I1?F6I@N+H686+G6?18D@++1M1?79X@K++$D@C6DA1471+012F98B+0F+H8@?10@+I1+I10688@DD@N+EF1+10+92F6D+H686+7@I@0+

]H187141?1+6D+H8@286A6+214S79?@^N+6H814I18+6+64I68N+G6CD68+O+6+H14068K++;18@+6I1AB0+?6I6+F4@+HF1I1+

I10688@DD68+0F0+H8@H960+?6H6?9I6I10K++%D2F4@0+D@+G68B4+?@4+0F0+?6H6?9I6I10+A@789?10N+EF1+107B4+AB0+

D926I60+6D+64I68N+@78@0+I10688@DD68B4+AB0+D6+H6D6C86N+O+@78@0+0F+?6H6?9I6I+9471D1?7F6D+@+016+1D+

H1406A9147@K++R9+7@I@+107@+10+H@09CD1+10+286?960+6+EF1+1D+018+GFA64@+79141+D6+H@09C9D9I6I+I1+H@I18+

10?@218N+H@011+1D+>D9C81+6DC1I8U@P++h"0+1D+H@I18+I1D+H1406A9147@+h+++"D+G@AC81+10+1D+349?@+EF1+79141+1076+

A686X9DD@06+?6H6?9I6I+I1+H1406A9147@+O+EF1+D@+I907942F1+I1+D@0+649A6D10K++.6+H6D6C86+O+1D+H1406A9147@+

X64+AFO+D926I@0+N+10+I9MU?9D+01H6868+EFS+H187141?1+6+F4@+O+EFS+6D+@78@N+?F64I@+01+78676+I1+6?79X9I6I10+

9471D1?7F6D10K+

+

Page 3: Metodo padovan

!".%)'#&"R+"&W!"+%&<%!N+Q%5.%!+i+;"&R%!+

R91AH81+G6O+F4+0924@+EF1+?686?7189:6+?6I6+F46+I1+10760+6?79X9I6I10K++)F64I@+F4+49Z@+01+H@41+I181?G@+O+

01+I10HD6:6+X1879?6DA1471N+O+107@+H606+G6?96+1D+6Z@N+I1?9A@0+EF1+1AH91:6+6+64I68K++"4781+F4+6Z@+O+

A1I9@+O+I@0+6Z@0+H@I1A@0+I1?98+EF1+1D+49Z@+1AH91:6+6+?@AF49?6801+?@4+1D+D142F6T1+@86DK++[)FB4I@+

H@I81A@0+I1?98+EF1+1D+49Z@+1AH91:6+6+I10?FC898+0F+?6H6?9I6I+I1+H14068N+I1+?8168+9I160+\++;686+!K+R719418+

N+107@+DD126+G6?96+D@0+7810+6Z@0N+14+1D+A@A147@+EF1+SD+I9?1+>i#PN+?F64I@+G6CD6+I1+09+A90A@K+

"0760+7810+6?79X9I6I10+107B4+D926I60N+0@4+94718I1H14I914710+O+01+I10688@DD64+H686D1D6A14/+

+71N+6F4EF1+01234+D6+1I6I+F46+H81I@A941+AB0+EF1+D6+@786N+O+G6O6+F4+@8I14+H686+D6+6IEF909?9L4+O+

A649M1076?9L4+I1+D60+?686?718U079?60+AB0+9AH@8764710+I1+?6I6+F46K+

)@A@+6?6C6A@0+I1+I1?98N+1D+49Z@+1AH91:6+6+64I68+G6?96+1D+6Z@N+6+G6CD68+G6?96+D@0+I@0+O+6+H14068+G6?96+

D@0+7810K++<F86471+1076+01?F14?96N+R719418+I9?1+EF1+G6O+F46+?91876+I1H14I14?96+14781+F46+6?79X9I6I+O+D6+

@786K++%M98A6V++>"D+?F18H@+GFA64@N+H@8+F4+H8@?10@+A907189@0@N+6H814I1+6+64I68N+6+@891476801+14+1D+

10H6?9@N+6+I10HD6:6801+I1+F4+0979@+6+@78@N+1D+G1?G@+I1+64I68+01+1JH8106+?@A@+F4+D142F6T1PK+

+

"076+6M98A6?9L4+4@0+HF1I1+H681?18+AFO+1J786Z6N+H18@+1D+2864+M@496786+68214794@+jF98L0N+76AC9S4+6IA971+

EF1+7@I@+1D+?F18H@N+7@I@+1D+RK&K)K+7@A6+H6871+14+1D+H8@?10@+I1+D6+H6D6C86V+>"0+I9MU?9D+14?@47868+F46+H6871+

I1D+RK&K)K+EF1+4@+HF1I6+71418+81D6?9L4+?@4+D6+?@AF49?6?9L4+@+1D+D142F6T1K++'4?DF0@+D6+ASIFD6+10H946DN+EF1+

H@I8U6+H681?18+4@+10768+81D6?9@46I6+?@4+10760+MF4?9@410+1014?96D10N+?@4789CFO1+I1+A64186+AFO+

9AH@876471+94M@8A64I@+6D+?L871J+?181C86D+I1+D6+H@07F86N+I1+D@0+A@X9A9147@0+I1+D60+1J781A9I6I10+O+I1+D60+

@7860+H68710+I1+?F18H@K++"07@+H18A971+6+D6+H180@46+I1+H@I18+I90H@418+I1+7@I@+0F+?F18H@+H686+?6H768+@+

1A9798+0924@0+O+0UAC@D@0+H686+D6+?@AF49?6?9L4+?@4+0F0+?@42S41810K++&@0@78@0+816M98A6A@0+EF1+7@I@+1D+

RK&K)K+H6879?9H6+14+1D+D142F6T1PK+

+

;96217+?@A@+jF98L0+N+76AC9S4+I6+81M1814?96+I1+D6+?@41J9L4+14781+10760+7810+6?79X9I6I10+I10?89760+H@8+

R719418+V++.6+9471D9214?96+0140@89@A@789:+]@+016+1D+64I68^+EF1+H81?1I1+6D+D142F6T1N+H81H686+0@C81+1D+

718814@+D6+6??9L4+1D1A1476DN+D@+EF1+AB0+768I1+01+78640M@8A68B+14+H1406A9147@+81MD1J9@46I@K++;96217+

76AC9S4+6M98A6+EF1+I1C1+1J90798+F4+HF1471+14781+D6+9471D9214?96+0140@89@A@789:+O+1D+H1406A9147@+

81MD1J9@46I@N+I9?1V++>KKK+10+1D+D142F6T1+EF1+01+I10688@DD6+092F914I@+F4+@8I14+I1M949I@+O+EF1+01+

78640M@8A68B+14+H1406A9147@+0LD@+?F64I@+016+6H7@+H686+I1T6801+78640M@8A68PK+

+[jFS+EF9181+I1?98+107@\++jF1+H686+EF1+107@+01+A649M91071+7@I@+I1H14I1+I1+F46+A6IF86?9L4+

41F8@DL29?6K++;96217+O+R719418+I9?14+D@+A90A@+?@4+I9M1814710+H6D6C860K++,4@+G6CD6+I1+64I68N+I1+G6CD68+O+

I1+H14068+N+;96217+I1+9471D9214?96+0140@89@A@789:N+D142F6T1+O++H1406A9147@+81MD1J9@46I@K++#78@0+6F7@810+

786764+1D+71A6+?@4+7S8A94@0+I9M1814710+H18@+EF1+EF91814+I1?98+D@+A90A@K++=92@70k9N+.F896+O+.1@4791X+G64+

HFCD9?6I@+F4+D9C8@+797FD6I@+V+>.142F6T1N+I10688@DD@+O+6H814I9:6T1PK++jF98L0+O+R?G86218+G64+10?897@+V++

>.142F6T1N+6H814I9:6T1+O+H09?@A@789?9I6IPK++W@I@0+786764+1D+A90A@+71A6N+@+016+D60+81D6?9@410+I1+D60+7810+

6?79X9I6I10++EF1+?@40797FO14+D6+I1M949?9L4+H8@H96+I1D+018+GFA64@+V++64I68N+G6CD68+O+H14068K++<1+D6+A90A6+

A64186+EF1+4@+H@I1A@0+I9X9I98+6D+G@AC81N+6+1DD60+76AH@?@+D60+H@I1A@0+01H6868K+

<1+A64186+EF1+D6+H6D6C86+01+I10688@DD6+6+H68798+I1D+64I68N+1D+H1406A9147@+01+I10688@DD6+6+H68798+I1+D6+

1X@DF?9L4+I1D+D142F6T1K++;@8+F4+D6I@+D6+H6D6C86+10+1D+X1GU?FD@+EF1+78640A971+1D+H1406A9147@+O+H@8+@78@+

D6I@+4@+H@I1A@0+H14068+094+D142F6T1N++"D+ASI9?@+EF1+01+@?FH6C6+I1D+49Z@+D@C@+I1+%X1O8@4N+D1+I1?U6+6D+

Page 4: Metodo padovan

14M18A18@+EF1+D1+6OFI6C6+V++>Q6:D1+G6CD68N+EF1+60U+06C81A@0+09+HF1I1+H14068PK+++!@:1476D+?F64I@+01+

81M9181+6D+6F790A@+6M98A6V++>"D+G1?G@+I1+4@+G6CD68+94?@8I96+1X9I1471A1471+1D+I10688@DD@+I1+D60+@7860+

M6?FD76I10+9471D1?7F6D10N+?@A@+1D+H1406A9147@+6C0786?7@N+D6+M@8A6?9L4+I1+?@4?1H7@0+@+1D+H1406A9147@+

?8U79?@N+EF1+I1H14I14+I1D+I10688@DD@+I1+D60+M6?FD76I10+X18C6D10+>K+

%46D9:64I@+7@I60+10760+?@409I186?9@410+A1+?@4X14?U+EF1+4@+018XU6+I1+46I6+H@418+6+F46+H180@46+I1D6471+

I1+F4+10H1T@+H686+1401Z68D1+6+G6CD68+@+6+?@881298+6D234+I1M1?7@+I1+6879?FD6?9L4K++W6AH@?@+A1+018XU6+

F79D9:68+D@0+TF12@0+AB0+I9X180@0+I1+M92F89760+?@4+D@0+4@AC810+10?897@0+?@4+D@0+A90A@0+M@41A60K+

RFH1+I1+D6+?@4M1814?96+I1+R719418+0@C81+1D+64I68+N+G6CD68+O+H14068N+TF07@+64710+I1+718A9468+1D+?F80@+I1+

-@4@6FI9@D@2U6K+"071+?F80@+D@+718A94S+9406790M1?G6N+4@+H@8+D6+H6871+71L89?6+O+?9147UM9?6+]+EF1+186+CF146N+

?@4+H8@M10@810+?@AH1714710+O+F4+H8@286A6+C914+1D129I@^N+094L+H@8+D6+H6871+H8B?79?6+O+7186HSF79?6K++i@+4@+

EF18U6+786768+D@0+0U47@A60N+094L+0F0+?6F060N+@+D@+EF1+H81?1I1+6+D6+?6F06K+

G77HV__```KX9X6D6X9I6K@82+/+X9X6D6X9I6+/+#071@H67U6+59@14182S79?6+)1DFD68+/+#K+5K+)K+/+;@`181I+CO+a6AC@+

#H14+R@F8?1+$1418671IV+b+<1?1AC18N+cdeeN+efVgb++

#!$%&'(%)'#&+&",!#.#$')%+/++W1AHD1+-6O+

i@+?81U6+14+D@+EF1+R719418+I1?U6N+EF1+1D+H8@?10@+I1+64I68+10+D@+EF1+4@0+DD1X6+6+G6CD68K++%G@86+M6D76C6+

I10?FC898+?LA@K+

+WFX1+D6+2864+0F1871+I1+?@4@?18+1D+786C6T@+I1+W1AHD1+-6O+O+0F0+I90?UHFD@0+)68D+<1D6?67@N+$D144+<@A64N++

!69AF4I@+=1860N+"I`68I+.1+l944+O+@78@0K+

"D+H8@?10@+467F86D+I1D+?@4@?9A9147@+GFA64@+10+1D+6H@O@+?@4794F@+0@C81+1D+?@4@?9A9147@+I1+4F1078@0+

H81I1?10@810+O+H81H6868+1D+?6A94@+I1+D@0+EF1+X91414+I178B0K++.6+GFA649I6I+MF4?9@46+I1+1076+A64186+14+

F46+1X@DF?9L4+?@4076471+I1+0F+?@4@?9A9147@K++)F64I@+81I6?76A@0+F4+786C6T@+?9147UM9?@N+F46+71090N+17?K+

&@0+1J9214+?9760+C9CD9@28BM9?60K++"07@+816DA1471+09249M9?6+EF1+D60+9I160+4F1X60+01+C6064+0@C81+

?@4@?9A9147@0+647189@810K++.6+?914?96+M@8A6+F46+X18I6I186+H98BA9I1+I@4I1+?6I6+F4@+H@41+1D+H91+0@C81+

D6+10H6DI6+I1+D@0+I1+6C6T@+O+714I896A@0+EF1+10768+I90HF107@0+6+?1I18+D6+10H6DI6+H686+EF1+D6+H98BA9I1+

?@4794F1K++"0+AFO+9AH@876471+018+GFA9DI10+O+X18+EF1+D@+H@?@+EF1+G1A@0+?@4012F9I@+10+F46+?@4789CF?9L4+

H686+6C898+@78@0+?6A94@0K++i+0@C81+7@I@+4@+@DX9I684@0+I1+D@0+EF1+4@0+G64+@M81?9I@+0F0+10H6DI60K+

%+X1?10+EF914+4@0+G6+H18A979I@+6X64:68N+49+SD+A90A@+D@+06C1N+H@8EFS+6D2F4@0+EF1+4@0+G64+I1T6I@+0F0+

?@4@?9A9147@0+N+0F0+?816?9@410N+0F0+94I9?6?9@410NKKK+O6+4@+1J90714K++<1+M@8A6+H6879?FD68+O+094?186+EF918@+

G6?18+F4+014?9DD@+G@A146T1+6+7@I@0+D@0+6F7@810+EF1+G1+?976I@N+10H1?96DA1471+!K+R719418+O+W1AHD1+-6ON+

H@8+0F0+M9D@0@M960+O+?@4@?9A9147@0+EF1+A1+G64+H18A979I@+786768+6+AF?G6+21471+EF1+G6+X149I@+6+X18A1+

H686+6D9X968+@+1D9A9468+0F0+I9M9?FD76I10K+

W1AHD1+-6ON+41F8@?98FT64@+6A189?64@N+X9X9L+O+0FM89L+D6+012F4I6+2F1886+AF4I96DK++)@4+0F0+?@D6C@86I@810N++

0@C81+7@I@+<@A64+O+<1D6?67@N+HFI918@4+816D9:68+107FI9@0+O+1JH18914?960+0@C81+1D+I10688@DD@+I1D+018+

GFA64@N+I10M964I@+7@I@0+D@0+AS7@I@0+H86?79?6I@0+14+106+SH@?6K++%I1AB0+I1+0F0+H8@H960+1JH18914?960+

F79D9:68@4+1D+786C6T@+A@4FA1476D+I1+$101DD+0@C81+1D+I10688@DD@+I1+D@0+49Z@0+4@8A6D10K++;18@+10768U6+MF186+

I1+DF268+EF1818+?@4768+7@I6+D6+G907@896+I1+D@0+786C6T@0+I1+W1AHD1+-6ON+@+016+EF1+0LD@+?9768S+D@0+?@4?1H7@0+

EF1+D1+098X918@4+I1+C601+H686+I10688@DD68+0F+AS7@I@K++RF+H89A186+H81A906+186+EF1+D6+#47@2S41090+

]I10688@DD@+I1+?6I6+94I9X9IF@^+810FA1+14+6D2F4@0+60H1?7@0+D6+-9D@2S41090+]D6+1X@DF?9L4+I1+D60+10H1?910^K++

"071+I10688@DD@+EF1+G6?1+EF1+1D+G@AC81+H601+I1+D6+H@09?9L4+G@89:@476DN+6+D6+X1879?6D+O+6+64I68N+SD+D6+

4@AC8L+#82649:6?9L4+&1F8@DL29?6+]EF1+01+H8@IF?1+H@8+A1I9@+I1D+H8@H9@+I10688@DD@+@47@214S79?@^K+

+

Page 5: Metodo padovan

<1D6?67@+D6+I1M941+60UV++>.6+#82649:6?9L4+&1F8@DL29?6+10+1D+810FD76I@+I1+F4+I10688@DD@+418X9@0@+

@47@214S79?@+?@4794F@N+10+D6+A1T@8+?@4I9?9L4+M909@DL29?6+EF1+0LD@+01+M946D9:6+14+1D+G@AC81K++"071+

I10688@DD@+810FA1+D6+1X@DF?9L4+M9D@214S79?6++I1D+G@AC81m+1AH91:6+14+1D+718?18+A10+I1+1AC686:@+O+

4@8A6DA1471+718A946+G6?96+D@0+0190+6Z@0+O+A1I9@K++"07@+EF1+01+H8@IF?1+14+7@I@0+D@0+A6AUM18@0N+14+1D+

G@AC81+H8@28106+X1879?6DA1471+H@8+D6+ASIFD6+10H946D+O+H@8+7@I60+D60+8129@410+I1D+R&)N+G6076+1D+49X1D+I1D+

?L871JK++"D+I10688@DD@+M946D+10H1?UM9?@+I1D+G@AC81+01+816D9:6+14+1D+?L871J+O+01+D67186D9:6+]I1+9:EF918I6+6++

I181?G6+@+I1+I181?G6+6+9:EF918I6^PK++W6AC9S4+6M98A6+EF1+V++>;686+018+?@AHD176A1471+GFA64@N+1D+

G@AC81+79141+EF1+018+?6H6:+I1+F79D9:68+1D+D142F6T1K++"D+D142F6T1+10+1D+810FD76I@+I1D+I10688@DD@+M9D@214S79?@+

I1D+09071A6+418X9@0@K++"D+D142F6T1+10+1D+810FD76I@+I1D+I10688@DD@+O+I1+D6+@82649:6?9L4+I1+0F+09071A6+

418X9@0@PK+

;@4I81A@0+AF?G6+6714?9L4+14+1076+3D79A6+6M98A6?9L4+EF1+14+810FA14+EF9181+I1?98V+>+"D+D142F6T1+4@+01+

HF1I1+I10688@DD68+094L+G6O+H81X96A1471+F46+C601+I1+@82649:6?9L4+41F8@DL29?6+6I1?F6I6K++i+D6+

@82649:6?9L4+41F8@DL29?6+10+I10?8976+?@A@+1D+I10688@nDD@+@47@214S79?@N+@+016+D60+176H60+EF1+1D+49Z@+

79141+EF1+H6068+G6076+H@41801+I1+H91+O+I10HD6:6801N+6D718464I@+1D+6X64?1+I1+D@0+H910+@+64I68PK++)F64I@+

O@+?@AH814IU+EF1+G6CU6+I10?FC9187@+D6+I10?89H?9L4+I1+D@+EF1+!K++R719418+4@AC86+1D+H8@?10@+I1+64I68N+

MF1+?@A@+09+GFC9186+I10?FC9187@+1D+;68690@+H18I9I@K+

+

!"#!$%&'(%)'#&+&",!#.#$')%+

W1AHD1+-6O+O+0F0+?@AH6Z18@0+@C018X68@4+EF1+D@0+49Z@0+4@8A6D10+I1+?F6DEF918+?9X9D9:6?9L4+I1D+AF4I@N+

IF86471+0F+?81?9A9147@N+7@I@0+G6?964+091AH81+D@0+A90A@0+2107@0+107181@79H6I@0+O+D@0+4@AC868@4+

>H678@410P+K++W6AC9S4+HFI918@4+@C018X68+EF1+D@0+49Z@0+EF1+H8101476C64+D109@410+?181C86D10+4@+H@I964+

G6?18+107@0+A@X9A9147@0K++)@4+107@+H14068@4V+>R9+G9?9101A@0+G6?18+107@0+A@X9A9147@0+@+H678@410+6+D@0+

H6?914710N+6F4EF1+MF186+H609X6A1471N+[H@I8U6+018+H@09CD1+EF1+0F+09071A6+418X9@0@+6H814I9186++O+AB0+

768I1+D@+G9?9186+H@8+14?682@\++i+60U+D@+G9?9A@0N+O+HFI9A@0+@C018X68+EF1+816DA1471+1D+49Z@+G6?U6+107@0+

A@X9A9147@0PK+++

;18@+6I1AB0+01+I918@4+?F1476+EF1+6+X1?10+1D+I10688@DD@+01+G6?U6+4@8A6DA1471+?@A@+09+01+GFC9186+

EF976I@+F4+CD@EF1@K++<10HFS0+I1+D@0+>H678@410P+N+MF18@4+94?DFO14I@+D@0+@78@0+A@X9A9147@0+EF1+

?@8810H@4I14+6D+I10688@DD@+467F86D+I1+D@0+49Z@0N+?@A@+8@I68N+86078168N+267168N+17?K++.@0+810FD76I@0+MF18@4+

D@0+A90A@0K++%+1071+H8@?1I9A9147@+D@+4@AC868@4+D6+!1@82649:6?9L4+&1F8@DL29?6N+?@4+107@+01+147914I1+D6+

81?6H97FD6?9L4+I1D+I10688@DD@+@47@214S79?@N+176H6+H@8+176H6N+092F914I@+D6+A90A6+01?F14?96+EF1+14+1D+

I10688@DD@+4@8A6DK+

;686+A9+EF1+186+D@2@H1I6+O+EF1+CF0?6C6+F46+7186H96+?6H6:+I1+H81?1I18+6+D@0+0U47@A60N+107@+MF1+F4+2864+

I10?FC89A9147@K++%?@8IB4I@A1+I1+D@+EF1+G6CU6+I9?G@+R719418N+EF1+1D+H8@?10@+I1+64I68+?@4IF?U6+6+D6+

H6D6C86+]H@8+107@+14714I1A@0+?F6DEF918+79H@+I1+D142F6T1^+A1+?@4X14?U+I1+G6C18+14?@4786I@+A9+?6A94@K++

"AH1?S+6+6HD9?68+1076+7186H96+6+F4@0+49Z@0+O+6+@78@0+4@K++a1+I9+?F1476+I1+EF1+D@0+EF1+01+G6C964+

C141M9?96I@+I1+D6+!#&+]!1@82649:6?9L4+41F8@DL29?6^+G6C964+A1T@86I@+I1+A64186+AB0+8BH9I6+O+1M1?79X6K++

.6+F79D9?S+H686+7@I@0+D@0+?60@0+I1+786407@84@0+I1+D6+H6D6C86+O+I1D+D142F6T1+?@4+810FD76I@0+AFO+H@0979X@0K++

.6+!#&+786C6T6+1D+?F18H@N+O+S071+10+1D+H81?F80@8+I1D+D142F6T1+@86DN+I1D++G77HV__```KX9X6D6X9I6K@82+/+

X9X6D6X9I6+/+#071@H67U6+59@14182S79?6+)1DFD68+/+#K+5K+)K+/+;@`181I+CO+a6AC@+#H14+R@F8?1+$1418671IV+b+

<1?1AC18N+cdeeN+efVgb6H814I9:6T1+I1+D6+D1?7F86+O+I1+D6+10?897F86K++"D+D142F6T1+2107F6D+O+D6+AUA9?6N+

6H681?14+AF?G@+AB0+71AH864@+EF1+D6++H6D6C86+6879?FD6I6K++"0+9AH@876471+6?D6868+EF1+D6+!#&+4@+10+1D+

Page 6: Metodo padovan

F49?@+H8@?1I9A9147@+EF1+4@0@78@0+F79D9:6A@0+IF86471+D6+7186H96K++.6+!#&+4@0+098X1+I1+C601+H686+7@I@0+

D@0+?60@0N+H18@+76AC9S4+H86?79?6A@0+@78@0+1T18?9?9@0+01234+?6I6+H187F8C6?9L4+@+D60+41?109I6I10+

10H1?UM9?60K+

)F64I@+MF9+?@40?91471+I1+D@+EF1+H686+A9+186+F4+2864+I10?FC89A9147@N+1D+G1?G@+I1+14?@47868+1071+?6A94@+

H@8+1D+EF1+0147U+AF?G6+6M949I6IN+H140S+EF1+018U6+C141M9?9@0@+78640A9798+1071+AS7@I@+6+A90+?@D1260K++i+A1+

EF1IS+AFO+0@8H814I9I6+6D+X18+?@A@+186+?8979?6I6K++.@+EF1+AB0+A1+9AH@876C6+1864+D@0+810FD76I@0+764+

H@0979X@0+EF1+714964+A90+H6?914710N+O+?@A@+1076C6+?@4X14?9I6+I1+0F+X6D9I1:+N+012FU+A9+?6A94@K++"AH1?S+6+

107FI968+41F8@D@2U6N+HF10+O@+EF18U6+06C18+H@8+EFS+F4+AS7@I@+764+014?9DD@N+714U6+764+CF14@0+810FD76I@0K+

&@+7142@+791AH@+6EFU+I1+1JHD9?68@0+7@I@+D@+EF1+6H814IUN+H18@+?6I6+I96+1076C6+AB0+?@4X14?9I6+EF1+1071+

AS7@I@+186+XBD9I@N+O+A1+I6C64+AF?G6+H146+D60+H180@460+EF1+D@+?8979?6C64K++)@4794FS+107FI964I@+O+634+

?@4794F@+107FI964I@N+O+?F647@+AB0+107FI9@+AB0+A1+I@O+?F1476+I1+EF1+107@O+14+1D+CF14+?6A94@K+

+

-,&)'#&"R+&",!#="$"W%W'=%R+

)@A@+D@2@H1I6N+A1+H681?U6+EF1+6D+AS7@I@+?816I@+H@8+W1AHD1+-6O+D1+M6D76C6+6D2@+H686+?@AHD1768D@K++

<1478@+I1+0F+M9D@0@MU6N+SD+6M98A6+EF1+09+F4+49Z@+4@+?@4092F1+?@AHD1768+F46+6?79X9I6IN+H@8+1T1AHD@+267168N+

4@+01+D1+79141+EF1+14781468+6+G6?18D@N+094L+EF1+10+A1T@8+786C6T68+D60+6?79X9I6I10+H81?1I14710+6D+2671@K+

R6C914I@+EF1+D60+-F4?9@410+81MD1T@/X1217679X60+]810H986?9L4N+0F??9L4N+A6079?6?9L4+O+I12DF79?9L4^+0@4+

?@4@?9I60+?@A@+MF4?9@410+H81/D942oU079?60N+@+016+EF1+H81H6864+D6+41F8@/AF0?FD67F86+H686+EF1+016+

H@09CD1+D6+6879?FD6?9L4+I1+D@0+M@41A60N+I1+D60+H6D6C860N+I1+D6+H6D6C86+2D@C6Dm+1AH1?S+6+@C018X68+EF1+D@0+

49Z@0+EF1+H8101476C64+H8@CD1A60+I1+H6D6C86+]H894?9H6DA1471+H68BD9090+?181C86D^+714964+10760+MF4?9@410+

AFO+1078@H16I160+O+EF1+D@0+6MB09?@0+D60+H18I964K++R92F914I@+1D+A90A@+86:@46A9147@+M9D@0LM9?@+I1+WK+-6ON+

14+X1:+I1+94714768+?@881298+D6+H6D6C86+O+D6+6879?FD6?9L4+H8@H96A1471+I9?G6N+1AH1?S+6+786C6T68++

10H1?UM9?6A1471+D60+MF4?9@410+1014?96D10N+H81/D942oU079?60K++.@0+810FD76I@0+MF18@4+764+H8@A171I@810+EF1+

10760+6?79X9I6I10+M@8A68@4+H6871+I1+>A9+!#&PK+

i6+06C1A@0+EF1+0@4+D@0+H8@H9@?1H7@810N+EF1+A1I96471+7@I@+1D+09071A6+418X9@0@+?@4IF?14+6D+?L871J+D@0+

107UAFD@0+O+D60+94M@8A6?9@410+H686+EF1+1D+G@A34?FD@+I1+;14M91DI+01+9I1479M9EF1N+O+H8@X@?64I@+?@A@+

?@401?F14?96+D@+EF1+?@4@?1A@0+?@A@+1D+"0EF1A6+)@8H@86D+K++"0+1D+H8@?1I9A9147@+467F86D+I1+A6IF81:+

EF1+G68B+EF1+D60+1078F?7F860+41F8@DL29?60+0164+@H186?9@46D10K++"D+94I9X9IF@+EF1+79141+0F+Q@A34?FD@+C914+

9AH81246I@+@+016+0F+10EF1A6+?@8H@86D+A6IF8@N+HF1I1+816D9:68+?F6DEF918+A@X9A9147@+?@4+0F+?F18H@+O+

76AC9S4+D@0+A@X9A9147@0+H686+G6CD68K++W@I@0+D@0+A@X9A9147@0+G1?G@0+IF86471+D@0+1T18?9?9@0+I1+D6+!#&+

M@8A64+H6871+I1D+H@714?96D+214S79?@+GFA64@+O+?@4IF?14+6+D6+H8@H9@?1H?9L4+I1+D@0+A30?FD@0+]G6:+

41F8@AF0?FD68^N+I1+D@0+714I@410+]L8264@0+41F8@714I94@0@0^N+O+I1+D60+6879?FD6?9@410+]81?1H7@810+I1+D60+

?BH0FD60+6879?FD6810^K++W@I@0+107@0+H8@H9@?1H7@810+76AC9S4+01+14?F147864+14+D6+:@46+CF?6DN+O+76AC9S4++

4@8A64+H6871+I1D+H@714?96D+214S79?@+GFA64@K++<1+A64186+EF1N+D6+94?@8H@86?9L4+I1+D@0+1T18?9?9@0+I1+D60+

-F4?9@410+&1F8@X1217679X60N+H9140@+EF1+?@AHD176+I1+A64186+09249M9?679X6+1D+AS7@I@+@892946D+I1+!#&K+

;@8+@786+H6871+A1+2F0768U6+I1T68+?D68@+EF1+A9+AS7@I@+7186HSF79?@+79141+I9X180@0+60H1?7@0+I9M1814710+6+

D@0+H8@HF107@0++H@8+<@A64+O+<1D6?67@K++i@+786C6T@+?@4+@786+@891476?9L4N+0@C817@I@+H@8EFS+14+1D+M@4I@+

I1+D@+EF1+O@+G62@+107B+D6+M9D@0@MU6+6478@H@0LM9?6+I1+!FI@DM+R719418K+

"D+AS7@I@+H1I62L29?@+I1+R719418+H81?@49:6+EF1+D6+6DM6C179:6?9L4++I6+?@A914:@+0LD@+?F64I@+1D+49Z@+

1AH91:6+6+?6AC968+D@0+I914710K++"4+1071+A@A147@+1D+09071A6+418X9@0@+10+1X9I1471A1471+A6IF8@+O+107@+

H18A971+I1+A64186+467F86D+1D+6H814I9:6T1+I1+D6+D1?7F86+O+D6+10?897F86K++R1234+1076+H1I62@2U6+N+7@I@+01+

Page 7: Metodo padovan

G6?1+14+1D+A@A147@+I1+A6IF86?9L4+6I1?F6I@+H686+?6I6+6?79X9I6IN+46I6+01+6479?9H6K++)6I6+X1:+EF1+

H@I1A@0+I1?98+EF1+F4+49Z@+10+6H7@+@+A6IF8@+H686+816D9:68+F46+6??9L4+?@4?8176N+107@+EF9181+I1?98+EF1+G6+

6IEF989I@+D6+A6IF81:+I1+1076+H@09C9D9I6I+14+0F+R&)N+14+0F+?L871JK++&@+7141A@0+EF1+EF1818+1401Z68+6+

D118+6+F4+49Z@+09+1D+?1478@+@??9H976D+]I1+D6+X9076+^+4@+01+G6+I10688@DD6I@N+I1+D6+A90A6+A64186+EF1+4@+

H@I1A@0+94714768+G6?18+?6A9468+F4+49Z@+I1+p+A1010K++R91AH81+I1C1A@0++810H1768+D6+A6IF81:+

41F8@DL29?6N+O+H@8+1076+86:L4+10+764+9AH@876471+?@4@?18+D60+I9M1814710+176H60+1X@DF79X60K++Q6O+AF?G@0+

6F7@810+EF1+G6CD64+I1+1071+71A6N+H18@+H180@46DA1471+H9140@+EF1+D6+94M@8A6?9L4+AB0+?@AHD176+X9141+

I1D+786C6T@+I1+$101DDK+

#786+I9M1814?96+10+D6+01?F14?96+I1+1T18?9?9@0K++"4+1D+AS7@I@+4@AC86I@+<@A64+Y+<1D6?67@N+O+EF1+

6?7F6DA1471+01+?@4@?1+?@A@P+aS7@I@+H686+1D+I10688@DD@+I1D+H@714?96D+GFA64@PN+01+G6?1++F4+C6D64?1+I1D+

H6?91471+H686+I171849468+0F+49X1D+I1+A6IF86?9L4N+O+D@0+1T18?9?9@0+1AH91:64+6+H68798+I1+6EFUK+

=@4+51k10O+G6CD64I@+I1D+R&)+I9?1V+>+"D+R&)+10+F46+6D6AC86I6+?@AHD1T6+I1+?98?F97@0+I1+6D9A1476?9L4K++

<64I@+D@0+9AHFD0@0+AB0+H89A689@0N+D@0+?6A94@0+01+6C814+O+@78@0+?98?F97@0+4F1X@0+01+HF1I14+M@8A68PK+++

;@8+1071+A@79X@+O@+091AH81+1AH91:@+H@8+D@0+1T18?9?9@0+AB0+H89A689@0N+?@4794F6A@0+O+012F9A@0+14+?6I6+

0109L4+7@I60+D60+176H60++467F86D10+I1+D6+1X@DF?9L4K+

.@0+I@0+AS7@I@0+?6AC964+14+D6+9471409I6I+O+14+D6+M81?F14?96+I1+D@0+1T18?9?9@0K++"4+1D+AS7@I@+;6I@X64+D60+

0109@410+IF864+214186DA1471+pg+A94F7@0N+I@0+X1?10+H@8+01A646K++"076+M81?F14?96+D6+6FA1476A@0+0LD@+

H686+D@0+?60@0+AB0+286X10K++)6I6+1T18?9?9@+01+81H971+X68960+X1?10N+01234+D60+H@09C9D9I6I10+MU09?60+@+D60+

41?109I6I10+I1+?6I6+H6?91471+@+I1+G77HV__```KX9X6D6X9I6K@82+/+X9X6D6X9I6+/+#071@H67U6+59@14182S79?6+

)1DFD68+/+#K+5K+)K+/+;@`181I+CO+a6AC@+#H14+R@F8?1+$1418671IV+b+<1?1AC18N+cdeeN+efVgb?6I6+

786407@84@N+94714764I@+1X9768+6D+ABJ9A@+1D+?64064?9@+AF0?FD68K++#786+I9M1814?96+10+H@8+1D+G1?G@+I1+D6+

H81014?96+I1+D@0+H6I810+IF86471+D60+7186H960K++)81@+EF1+D@0+H6I810++0@4+9AH@8764710+H686+D6+7186H96+I1+

0F0+G9T@0N+H18@+0LD@+?@A@+H6I810N+EF1+@C018X14N+6?@AH6Z14+1+94M@8A14+I1+D@0+H8@CD1A60+O+I1+D@0+

?6AC9@0+EF1+DD1264+6+0F0+G9T@0K++&@+10+MB?9D+71418+I@0+MF4?9@410+TF4760+V+1D+I1+H6I81+O+1D+I1+7186H1F76K++

)@A@+D60+I@0+MF4?9@410+0@4+764+9AH@8764710N+O@+091AH81+H9I@+EF1+F4@+I1+D@0+I@0+H6I810+]4@8A6DA1471+

10+D6+A6I81^+6090764+6+7@I60+D60+0109@410K++RF+H81014?96+7864EF9D9:6+6D+49Z@N+O+1D+H6I81+@+D6+A6I81+791414+D6+

@?609L4+I1+06C18+D@+EF1+D1+H606K++'4?DF0@+6+X1?10+H686+01234+EFS+1T18?9?9@0N+H@I8B4+6OFI68+6D+7186H1F76K+

+

.#R+"q"!)')'#R+<".+a"W#<#+++++++++++

#0+D@0+I10?89C98S+I1+A64186+C81X1N+H@8EFS+A9+94714?9L4+10+0LD@+78640A9798@0+F46+9I16+I1+EFS+10+1D+

aS7@I@+;6I@X64+I1+!1@82649:6?9L4+&1F8@MF4?9@46DK++"0768U6+MF186+I1+DF268+EF1818+1401Z68+F4+AS7@I@+

14+?F678@+DU4160N+]6F4EF1+016+014?9DD@+H18@+I1+6HD9?6?9L4+I9MU?9D^N+HF10+D@0+1T18?9?9@0+791414+EF1+018+

H18M1?7@0+H686+EF1+1D+R&)+0LD@+81?9C6+D60+94M@8A6?9@410+?@881?760K+

;678L4+G@A@D67186D+/++R1+G6?1+14+I1?3C97@+X14786D+]?@4+D6+C688926+14+1D+0F1D@^N+D6+?686+2986I6+G6?96+1D+D6I@+

I@4I1+D@0+A91AC8@0+0FH189@810+1+94M189@810+107B4+MD1J9@46I@0K++.@0+A91AC8@0+I1D+@78@+D6I@+107B4+

107986I@0+G6?96+6C6T@+7@?64I@+1D+?F18H@K++R1+X64+6D718464I@+D@0+D6I@0K+

;678L4+?8F:6I@+Y+W6AC9S4+14+I1?3C97@+X14786DK++.6+?6C1:6+?@4794F6+2986I6+G6?96+1D+C86:@+EF1+107B+

I@CD6I@K++"D+@78@+C86:@+H@41+D6+A64@+I178B0+I1+D6+10H6DI6+O+D6+H91846+I1+1071+D6I@+01+MD1J9@46+A9147860+

EF1+D6+@786+H91846+01+EF1I6+107986I6K++#+016+EF1+1D+C86:@+O+D6+H91846+14+MD1J9L4+01+14?F147864+@HF107@0K++

"076+H@09?9L4+76AC9S4+01+X6+6D718464I@K++

Page 8: Metodo padovan

Q6O+?F678@+1T18?9?9@0+AB0+EF1+H81?1I14+6+107@0+I@0+H678@410+H18@+EF1+4@+D@0+I10?89C98S+6EFU+H@8EFS+

41?109768U6+I1A6096I@+10H6?9@K++R94+1AC682@N+D@0+I@0+1T18?9?9@0+EF1+H@I1A@0+?@409I1868+AB0+

9AH@8764710+0@4+D@0+H678@410+EF1+@0+6?6C@+I1+I10?89C98K+

<10HFS0+I1+D@0+H678@410N+H86?79?681A@0+D60+6?79X9I6I10+10H1?UM9?60+I1D+I10688@DD@+467F86D+O+4@8A6D+I1+

7@I@0+D@0+94I9X9IF@0K++R1+786C6T6+?@4+7@I@0+D@0+79H@0+I1+D@?@A@?9L4+I1D+49Z@N+091AH81+092F914I@+1D+@8I14+

467F86D+I1D+I10688@DD@K+

++

!@I68+Y+10+764+467F86D+EF1+4@+G6?1+M6D76+4942F46+1JHD9?6?9L4K+

+

!60781@+G@A@D67186D+Y+01+G6?1+14+D6+A90A6+H@09?9L4+EF1+D6+EF1+G1A@0+F79D9:6I@+H686+1D+H678L4+

G@A@D67186DK+"D+H6?91471+01+I6+F4+9AHFD0@+G6?96+6I1D6471+?@4+1D+I1I@+2@8I@+I1+D6+H91846+MD1J9@46I6+O+

?@4+D6+A64@+I1D+C86:@+MDD1J9@46I@K++R91AH81+6D718464I@+D@0+I@0+D6I@0K+

+

!60781@+?8F:6I@+Y+?@4+D6+10H6DI6+AB0+14I181:6I6N+I1T6A@0+EF1+1D+H6?91471+8607811+467F86DA1471K++R9+4@+

?@4092F1+G6?18+1D+A@X9A9147@+?8F:6I@+]A64@+I181?G6+?@4+D6+H91846+9:EF918I6+O+X9?1X1806^N+01+D@+I1T6A@0+

G6?18+?@A@+EF9186N+O+O6+X181A@0+EF1+?@4+1D+791AH@N+?F64I@+G6O6+A1T@86I@+D@0+1T18?9?9@0+I1D+H678L4+

?8F:6I@N+D@+?@4012F98B+0@D@K+

++

$671@+Y+4@+41?10976+494234+?@A147689@K+

+

"T18?9?9@+I1D+A6?6?@+Y+64I68+6+?F678@+H6760+?@4+D60+H918460+107986I60K++)@4+1071+1T18?9?9@+01+786C6T6+

AF?G@+D6+MF18:6+I1+D@0+C86:@0K++"0+AFO+9AH@876471+H686+D@0+I9028BM9?@0K+

+

%26?G6801+O+D1X6476801+Y+7@I6+D6+HD6476+I1+D@0+H910+791414+EF1+7@?68+6D+0F1D@+]H@I8190+@C018X68+EF1+G6O+

F46+176H6+I1+1X@DF?9L4+14+D@0+49Z@0+EF1+01+107B4+AF?G@+867@+626?G6I@0+TF264I@^K+

+

a68?G6+?8F:6I6+Y+H686+1079AFD68+A1T@8+D@0+H8@H9@?1H7@810N+D6+A68?G6+01+79141+EF1+G6?18+?@4+

A@X9A9147@0+1J62186I@0K++,46+A64@+2@DH16+D6+H91846+@HF1076+EF1+79141+EF1+10768+MD1J9@46I6+O+G6?96+

6889C6K++"076+6?79X9I6I+0LD@+D6+H86?79?6A@0+?@4+D@0+49Z@0+I1+AB0+I1+7810+6Z@0+O+4@+?@4+6EF1DD@0+H6?914710+

EF1+6+H1068+I1+F46+1I6I+?8@4@DL29?6+0FH189@8+6+7810+6Z@0+N+634+4@+G64+6IEF989I@+D6+A6IF81:+41F8@DL29?6+

?@881H@4I91471+6+D@0+7810+6Z@0K+

+

&@76V+107@0+1T18?9?9@0+01+791414+EF1+1T1?F768+14+1D+A90A@+@8I14+EF1+G64+09I@+1JHF107@0K++;@I8190+X18+

EF1+?@4+107@0+1T18?9?9@0+@+6?79X9I6I10N+1D+H6?91471+H606+286IF6DA1471+I1+D6+H@09?9L4+G@89:@476D+6+D6+

X1879?6DN+I1+D6+A90A6+A64186+EF1+IF86471+1D+I10688@DD@+4@8A6DK+

+

Page 9: Metodo padovan

=@D718176+Y+467F86DA1471+0LD@+D6+G6?1A@0+?@4+D@0+H6?914710+EF1+D6+HF1I14+816D9:68+094+EF1+D10+HF1I6+

H18TFI9?68+MU09?6A1471K++;686+D@0+H6?914710+?@4+7890@AU6+ceN+D6+X@D718176+0LD@+D6+G6?14+?@4+D6+6F7@89:6?9L4+

I1D+ASI9?@+EF1+D@+DD1X6N+0@C817@I@+6+?6F06+I1D+H8@CD1A6+I1D+67D60K+

+

R9DD6/G6A6?6+29867@896+Y+G1A@0+I1+71418+H81?6F?9L4+O+4@+H86?79?68+107@0+1T18?9?9@0+?@4+D60+H180@460+EF1+

791414+4BF0160K++"4+1071+?60@+6D+?6C@+I1+I@0+@+7810+A1010+D@+981A@0+94?@8H@864I@+H8@28109X6A1471+O+60U+

01+H@I8B+C141M9?968+094+0FM898K++"071+1T18?9?9@+10+AFO+9AH@876471+H686+D6+1079AFD6?9L4+I1D+X107UCFD@+

6FI979X@K+

+

"T18?9?9@0+I1+D60+A64@0+Y+0@4+F46+01891+AFO+6AHD96+EF1+092F1+76AC9S4+D6+1X@DF?9L4+A6IF8679X6+I1+D60+

A64@0K+

+

"T18?9?9@0+I1+D6+X9076+Y+0@4+F46+01891+I1+1T18?9?9@0+EF1+092F14+1D+I10688@DD@+4@8A6D+O+EF1+H8@X@?64+F4@0+

107UAFD@0+DD6A6I@0+81MD1T@/@H7@/A@789?10K++R@4+A@4@+O+C94@?FD6810K+++

+

"T18?9?9@0+I1+?@@8I946?9L4+@?FD@/A64F6D+Y+I10HFS0+I1+D@0+1T18?9?9@0+X90F6D10+O+A64F6D10N+H@I1A@0+G6?18+

@78@0+79H@0+I1+TF12@0+I9M1814710+?@4+D6+H1D@76K+

+

R6D768+6+D6+?@AC6+Y+10+F4+1T18?9?9@+AFO+9AH@876471+H686+D6+@891476?9L4+71AH@8@/10H6?96DK++R1234+1D+

H6?91471+01+G68B+I1+I9M1814710+A641860K+

+

W6AC9S4+1J90714+@78@0+1T18?9?9@0+?@A@+06D768+6+H91+?@T@N+G6?18+06D797@0N+64I68+G6?914I@+06D797@0+O+

092F914I@+1D+897A@N+17?K+++

G77HV__```KX9X6D6X9I6K@82+/+X9X6D6X9I6+/+#071@H67U6+59@14182S79?6+)1DFD68+/+#K+5K+)K+/+;@`181I+CO+a6AC@+

#H14+R@F8?1+$1418671IV+b+<1?1AC18N+cdeeN+efVgbW6AC9S4+D1+H@I1A@0+94?DF98+I9M1814710+TF12@0+

94M6479D10N+EF1+214186DA1471+0@4+F49X1806D10+O+M@8A64+H6871+I1+0F+I10688@DD@+467F86DK++%EFU+4@+7141A@0+

10H6?9@+H686+I10?89C98D@0K+

+

,46+X1:+718A946I@0+107@0+1T18?9?9@0+?@8H@86D10+N+H86?79?681A@0+D@0+I1+D60+MF4?9@410+81MD1T@/X1217679X60+V++

810H986?9L4N+0F??9L4N+A6079?6?9L4+O+I12DF79?9L4K++<10HFS0+786C6T681A@0+D6+A64186+I1+097F68+D@0+M@41A60+

?@4+@78@0+1T18?9?9@0+10H1?UM9?@0K+

;@1A60+Y+1D+7186H1F76+6?@AH6Z6+7@I@0+D@0+1T18?9?9@0+81?9764I@+H@1A60K++;8@?F864I@+EF1+D@0+X180@0+

714264+F46+6D97186?9L4+I1+D@0+M@41A60+O+0@C817@I@+I1+D@0+EF1+1D+H6?91471+79141+I9M9?FD76I+14+H8@4F4?968++

]+I1+1076+A64186+D6+1079AFD6?9L4+01+G6?1+?@4+A@I1D@0+?@881?7@0^K++.@0+H@1A60+G64+I1+71418+F4+CF14+

A1406T1+H686+6FA14768+1D+X@?6CFD689@+O+1079AFD68+1D+86:@46A9147@K++W6AC9S4+0@4+9AH@8764710+H686+I68+

897A@+6+D6+21471+EF1+4@+79141+O+6I1AB0+D@0+A30?FD@0+810H@4I14+A1T@8+?@4+A@X9A9147@0+8U7A9?@0K++.@0+

Page 10: Metodo padovan

H@1A60+0@4+AFO+1079AFD64710+H@8EFS+2F0764+6+7@I@0++

[%+EF9S4+01+D1+HF1I1+6HD9?68+1071+AS7@I@\++)@A@+D@2@H1I60N+1071+AS7@I@+D@+6HD9?6A@0+6+H6?914710+EF1+

791414+H8@CD1A60+I1+1D@?F?9L4+O_@+D142F6T1K++;@8+@78@+D6I@+D6+21471+EF1+CF0?6+1071+78676A9147@+79141+

214186DA1471+107@0+786407@84@0N+EF1+01+HF1I14+H81014768+4@+0LD@+14+D@0+EF1+791414+F4+I1M9?914?96+

]?@A@+0U4I8@A1+I1+<@`4N+H686D9090+?181C86DN+6F790A@N+I1M9?914?96+A1476DN+KKK^+094L+76AC9S4+14+H180@460+

4@8A6D10+1+9471D9214710+]I90D6D960+014?9DD60+@+C914+I9M9?FD76I10+I1+6H814I9:6T1+I1+D6+D1?7F86+@+D6+10?897F86^K++

;686+W1AHD1+-6ON+D@0+H8@CD1A60+I1+1D@?F?9L4+O+I1+D142F6T1+>4@+0@4+H8@CD1A60+I9M1814710N+094@+

I9M1814710+286I@0+I1D+A90A@+H8@CD1A6P+N+@+016+EF1+1D+@89214+10+1D+A90A@N+F4+I10@8I14+I1D+I10688@DD@+@+

I1+D6+@82649:6?9L4+I1D+R&)K++R9+D6+?6F06+10+D6+A90A6N+1D+78676A9147@+79141+EF1+018+1D+A90A@N+6I6H76801+6+D6+

286X1I6I+I1D+786407@84@N+O+10+107@+D@+EF1+G6?1A@0+14+4F107860+7186H960K+

++

)#&).,R'#&+

)@A@+H@I1A@0+?@4076768N+1071+AS7@I@+?@409071+14+1T18?9?9@0+AFO+014?9DD@0+EF1+H187141?14+6+D6+

467F86D1:6+GFA646K++"07@0+A@X9A9147@0+4@+G64+09I@+?816I@0+6879M9?96D1A741+49+94X1476I@0K++R@4+764+

014?9DD@0+EF1+G6O+EF9S4+HF1I6+IFI68+I1+0F+1M9?6?96K++.6+467F86D1:6+10+014?9DD6K++%EFU+7141A@0+0F0+D1O10+6+

I90H@09?9L4+I1+6EF1DD@0+EF1+0@4+?6H6?10+I1+81?@4@?18D60N+I1+?6H768D60N+I1+09071A679:68D60N+H686+H@I18D60+

F79D9:68+?@4X1491471A1471K++)@A@+"9407194+I1?U6V+>4@+1J9071+494234+?6A94@+DL29?@+H686+I10?FC898+D60+

D1O10+1D1A1476D10+I1D+,49X180@N+1D+349?@+?6A94@+10+D6+947F9?9L4K++"D+A1?6490A@+I1D+I10?FC89A9147@+4@+10+

49+DL29?@+49+9471D1?7F6DN+10+F46+9DFA946?9L4+81H147946N+?609+F4+SJ76090K++;18@+10+?9187@+EF1+I10HFS0+

9471D9214?96+646D9:6+O+EF1+D6+1JH18914?96+?@4M98A6+D6+947F9?9L4PK+

!FI@DM+R719418+O+W1AHD1+-6O+7FX918@4+1D+H89X9D129@+I1+71418+D6+947F9?9L4+O+D6+9471D9214?96+H686+?@4M98A68+

1076+947F9?9L4+H@8+D6+1JH18914?96K++a9+0F1871+G6+09I@+?@4@?18+0F0+786C6T@0+O+H@I18+C141M9?968A1+I1+1DD@0K+

=@DX914I@+6+D6+M8601+I1+"9407194+EF1+G1+?976I@+6D+H894?9H9@+I1+1071+687U?FD@N+A1+2F0768U6+6Z6I98+EF1+O@+4@+

0S+09+786C6T@+?@4+D6+?914?96+@+?@4+1D+6871K++.@+EF1+09+0S+10+EF1+7647@+1D+R9071A6+&18X9@0@+?@A@+1D+Q@AC81+

634+0@4+F4+A907189@+H686+4F1078@0+ISC9D10+?@4@?9A9147@0K++"D+6871+D@+F79D9:@+F4+H@?@+?F64I@+81?97@+D@0+

H@1A60+EF1+6?@AH6Z64+6+D@0+1T18?9?9@0K++.6+?914?96+76AC9S4+N+HF10+107FI964I@+1D+R9071A6+&18X9@0@+

6H814I@+4@X1I6I10+?9147UM9?60N+EF1+A1+9DFA9464N+?@A@+D6+1J90714?96+I1+D6+;D6079?9I6I+&1F8@DL29?6+O+I1+

D@0+-6?7@810+&1F8@78LM9?@0N+EF1+TF079M9?64+HD146A1471+1D+786C6T@+EF1+G62@K++&@+@0+G6CD68S+I1+1071+71A6N+

O6+D@+G6+G1?G@+1D+<8K+&1D0@4+%44F4?967@N+I@?7@8+14+?914?960+41F8@DL29?60+O+AB0+?6H6?976I@+EF1+O@K+

!1H97@+EF1+1071+AS7@I@+10+AFO+014?9DD@N+764+014?9DD@+?@A@+D6+467F86D1:6K++i+O@+H9140@+EF1+1D+EF1+092F1+

D60+1401Z64:60+I1+D6+467F86D1:6N+O+6+0F+TF9?9@N+79141+A14@0+H@09C9D9I6I10+I1+1EF9X@?6801K+%879?FD@+

786IF?9I@+H@8V++W18106+-1D9FV+7M1D9FC60rO6G@@K10+W186H1F76+I1+81@82649:6?9L4+41F8@MF4?9@46DN+H1I62@26+

O+D@2@H1I6+

)_K+"071X1+568642SN+cp++CJK+e6K+

dsppd+)%!<"<",+

W1DK+9+M6JV++nt+spp+pp+gp+

G77HV__```KX9X6D6X9I6K@82+/+X9X6D6X9I6+/+#071@H67U6+59@14182S79?6+)1DFD68+/+#K+5K+)K+/+;@`181I+CO+a6AC@+

#H14+R@F8?1+$+

+

+

Page 11: Metodo padovan
Page 12: Metodo padovan
Page 13: Metodo padovan

+