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Colegiul Naional IENCHI VCRESCU

PROIECT:Numrul de aur Mihalahe Mariana Cla!a a I"#a E

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7/25/2019 Proiect Mate . Nr de Aur

2/7

7/25/2019 Proiect Mate . Nr de Aur

3/7

1aloarea e!act a lui pn la cea de*a dou mia ecimal apare ncartea "Seciunea de 0ur2oestea lui 2hi, cel mai uimitor numr" de3ario 4iio

1,

$#%&' '5%%6 75%57 %7%8& 79%$% '7'$9 $'%## 668&' &5#65%&96$- cea de-a cincizecea zecimal8%$8# '977% $886& 98$&7 $8%#% 5&877 56&68 &68&7 #%5'5##'67- cea de-a o suta zecimal

%7697 &%%&6 9'%$% 5#698 #8$$' '%$88 8'9'$ 5'#65 '#%&&$&6$$68$'9 77''' %5&%$ 9595' 59%85 &9$'% '88$$ #'#55 8%85&8$6%%&$698 &%6$$ %589& #6##$ 5$8&6 &'888 #&7'8 #$8$5 97%$8$85$'- cea de-a dou sute cincizecea zecimal#'$#7 7'%#7 569%6 X& '7&%& 9%%65 97797 67587 $#%9$

59'$7%$777 587#& 77'8& 66#'7 7576& 759$9 %7$6% %9&5% 67''57788#8977% 66&$$ 76%&5 #9%%7 $&675 5%%6# 87&&6 $98#6 &969#656%%'7#$$ 89$87 57&69 %5&$5 6&7&& &8%#8 #&786 $8#66 ###666%&9'

#9'#6 #7# #6&7$ $$955 #7$$5 65%6' #6$#' 9$&&$ 6&%67%&6#&- cea de-a cinci suta zecimal

#'#65 98'$% 57869 8#57% 7'9'& 9$6%' &&88% 6%9$5 56%8566%'76%79% 6%88% 5##&5 6$89& &'&8$ 5$#9$ #6&&8 9&7$7 ''%87'66$7%$#&8 %'%'# 8$%'' &'687 858$6 98$'# #$9'' 5876' #$6## #8##9

%%#%$ '%9#' '#$8& '%7&& 9888# $965# 8%$$6 9857$ 975&$ %##'#6#955 '7'8' 956'7 575%9 &5&7& 576$8 #'888 5%# 68$#&

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7/25/2019 Proiect Mate . Nr de Aur

4/7

6&95$##$79 $855& 5%#$8 5&999 8&%98 765&' 987&$ &8 8655676#69'7866 69586 6%$89 $#57' 8&%86 9&9#' #8#%# 9$8%9 9#888

7%&5'576#8 '7#79 #6&88 '6'9% &9668 6%$#$ &&%$% %'%85 98'&7958$76%6%& #6%%5 58#55 &86&6 6$5&' %59'8 #5$%# 5%$#9 #7'6%&'#75567## &$58$ &%%$6 785$8 8$696 9$&98 '#686 6698& '9'$#'5'$8- cea de-a o mia zecimal

#&6$6 '%5'6 $799$ &$&$& 958#$ 9%57$ $6959 9#5&& 7&&9995&%59&885 9'&57 8'#87 %8'99 8#88# 87#97 77&&$ 76&'7 &9$96'7656$$'56 8'575 7557$ 9%796 %%6'& '5$8' &5&'6 9&''5 5'%9$8#&878'$5& 89#'% $%&7# 79665 59$5% #8877 9676# 6%&'7 #6'#8

$79'88&7#$ '568' 8#'7& 77775 7%6'& 8'#97 #6$6$ %5'69 8#&'&$%6'6%%&'7 7#6&& 5'597 7&5$8 6599% 5%6$% 68'8& 59#87 8$%5'996'&56&79 &5959 $%77& #6999 #5%%# 58#%& 8&$7& 985&9 9#%5'75769

58$&& 6'7%9 88%8# &%% #57$7 79778 88'#% %5#'# 5857$%5$88&&8'& #77'6 6&8$5 58'&& 6%&'& %98$# #%&69 79#58 %%66&9&8#&5$%78 75'$8 6#'95 89#%6 $&666 %%7$$ 9%'$# 9&8'% 5#'75''''#

88'#& 9''58 '8#'$ 87'#5 8$'68 %5#&$ 6&9&' '558% 88$98$'99$8&5&8 565%$ 78768 69566 89$99 &%$#9 7%697 '967% 8$76#

7/25/2019 Proiect Mate . Nr de Aur

5/7

7/25/2019 Proiect Mate . Nr de Aur

6/7

nici o repetiie sau regularitate a pricinuit o aderat crifiloofic. @nele surse susin chiar c pitagoreicii au sacrificat #&&de oi din caua numrului. Aotui acest lucru pare e!trem deimproail deoarece ei erau egetarieni strici. 2itagoreicii erau

nendoielnic conini c e!istena unor numere precum era att denfricotoare nct ea treuia s repreinte un fel de eroarecosmic, o informaie care ar treui suprimat i inut secret.Baptul c e!ist numere iraionale a implicat i descoperireaincomensurailitii. ?n lucrarea sa "Cespre iaa lui 2itagora" (cca.'&& .

7/25/2019 Proiect Mate . Nr de Aur

7/7

#./aportul dintre numrul alinelor i al ondarilor din orice colonieeste 2 #&&& E &.$#%, deci 2