8-Raz\303\243o MaravilhosaUma explora\303\247\303\243o da raz\303\243o maravilhosa. Ela \303\251 derivada de diferentes maneiras, e aplicada a ret\303\242ngulos comuns.<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Inicializa\303\247\303\243o</Font></Text-field>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JSFHJSFHJSFHJSFH<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8"> 1. Solu\303\247\303\243o de uma Equa\303\247\303\243o Quadr\303\241tica</Font></Text-field>JSFHN\303\263s come\303\247amos nossa jornada com essa equa\303\247\303\243o quadr\303\241tica desfavor\303\241vel, que tem coeficientes de 1 ou -1, e solucionamos.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 duas solu\303\247\303\265es, mas a raiz positiva \303\251 chamada de raz\303\243o \303\241urea - por raz\303\265es que ainda n\303\243o s\303\243o evidentes. Este \303\251 um n\303\272mero irracional estimado pelos gregos antigos, e supostamente usado na arquitetura do Parthanon.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 n\303\263s veremos, esse n\303\272mero especial aparece em v\303\241rios lugares - embora existam mais do que n\303\263s possamos verificar. Esse n\303\272mero \303\251 algumas vezes simbolizado por phi , depois do escultor grego Phidias, no entanto, n\303\263s usaremos g, para "n\303\272mero \303\241ureo", aqui apenas por conveni\303\252ncia.JSFH<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8"> 2. Ret\303\242ngulos Similares Infinitos</Font></Text-field>JSFHImagine que n\303\263s temos um ret\303\242ngulo comum de dimens\303\265es de base x, e altura 1.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O lado de altura 1, \303\251 menor do que a maior largura do lado x, assim n\303\263s podemos medir 1 unidade na base, e criar uma unidade quadrada, dentro desse ret\303\242ngulo.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JSFHJSFHJSFHEsse procedimento pode funcionar em qualquer ret\303\242ngulo com base maior do que altura. No entanto, suponha que n\303\263s coloquemos uma condi\303\247\303\243o adicional. O ret\303\242ngulo vermelho a direita \303\251 semelhante ao ret\303\242ngulo original - como tri\303\242ngulos similares. Isto \303\251, a raz\303\243o desta largura para esta altura \303\251 igual a raz\303\243o da largura para altura do tri\303\242ngulo original. Isso n\303\243o \303\251 verdade. No entanto, \303\251 verdade apenas o n\303\272mero x a direita.
Vamos encontrar x - escrevendo esta equa\303\247\303\243o de raz\303\265es e solucionando. Olhe atentamente para o diagrama acima, e encontre a largura e altura dos dois ret\303\242ngulos.
Lado Menor Lado Maior
Ret\303\242ngulo Original 1 x
Ret\303\242ngulo Menor x - 1 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 aqui est\303\241. A solu\303\247\303\243o positiva \303\251 a raz\303\243o \303\241urea. (Obviamente, que a solu\303\247\303\243o negativa n\303\243o deve ser jogada fora, porque n\303\263s podemos fazer uma medida negativa dos lados.) A raz\303\243o \303\241urea, ou n\303\272mero maravilhoso, \303\251 o comprimento do lado que torna isso proporcionalmente verdadeiro - e este \303\251 o \303\272nico n\303\272mero que faz isso.
J\303\241 que o ret\303\242ngulo menor \303\251 uma c\303\263pia menor do original, n\303\263s podemos fazer a mesma cois com ele - fa\303\247a um quadrado com o lado menor, e corte o quadrado para sobrar um ret\303\242ngulo ainda menor.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JSFHAgora esse terceiro ret\303\242ngulo \303\251 similar ao segundo, e portanto ao original tamb\303\251m ! Vamos agora fazer um quadrado da sua base. N\303\263s podemos continuar esse processo ... infinitamente! Cada ret\303\242ngulo \303\251 similar ao original. 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 voc\303\252 pode ver, n\303\243o existe final para esse processo. Isso acontece porque a similaridade dos primeiros dois ret\303\242ngulos \303\251 cont\303\255nua.
Observe que o ret\303\242ngulo original est\303\241 sendo gradualmente coberto por uma s\303\251rie de quadrados. O comprimento desses lados desses quadrados s\303\243o ... 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 n\303\263s adicionarmos as \303\241reas desses ret\303\242ngulos, que s\303\243o as somas dos quadrados desses n\303\272meros, n\303\263s obteremos um n\303\272mero muito pr\303\263ximo ao n\303\272mero \303\241ureo, g. Se n\303\263s continuarmos infinitamnete, n\303\263s obteremos exatamente isso, j\303\241 que a \303\241rea do tri\303\242ngulo original tamb\303\251m \303\251 g.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRitGK0YrRitGK0YrRitGK0YrRistSSNtaUdGJDYlUSJnRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYsNi1RIjtGJ0YvRjIvRjZGTEY3RjlGO0Y9Rj9GQS9GRVEsMC4yNzc3Nzc4ZW1GJy8lK2V4ZWN1dGFibGVHRjRGLw==JSFH<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">3. A Propor\303\247\303\243o Mais Bonita</Font></Text-field>JSFHFoi dito que a raz\303\243o \303\241urea \303\251 a mais bonita das raz\303\265es. Em v\303\241rios tipos de arte e arquitetura, ele \303\251 supostramente a vis\303\243o mais natural. Ele foi chamado de "raz\303\243o divina" por Leonardo Da Vinci, e alguns dizem que a face da Mona Lisa se adapta ao ret\303\242ngulo. Segundo o que dizem, \303\251 a raz\303\243o da altura pela largura do Parthenon Grego, uma \303\241rea famosa de Atenas constru\303\255da em 447 a.c., e chamada de "o mais perfeito poema do mundo feito em pedra" por um autor franc\303\252s.
Vamos compar\303\241-la a alguns ret\303\242ngulos comuns que n\303\263s vemos todo dia. Aqui est\303\243o alguns ret\303\242ngulos comuns, seguidos pela sua raz\303\243o, e o percentual de compara\303\247\303\243o ao n\303\272mero maravilhoso.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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JSFHOutra aplica\303\247\303\243o da raz\303\243o maravilhosa s\303\243o as pir\303\242mides eg\303\255pcias. A grande pir\303\242mide em Giza ascende em um \303\242ngulo de 51 graus, 54 minutos. Qual a medida de um tri\303\242ngulo ret\303\242ngulo (formado pelo desenho diagonal do ret\303\242ngulo maravilhoso).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 isto n\303\243o est\303\241 terminado. No entanto, se voc\303\252 criar uma tri\303\242ngulo onde a hipotenusa \303\251 g, e a base \303\251 1, voc\303\252 obt\303\251m o \303\242ngulo...que \303\251 mais pr\303\263ximo a issoLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Isso significa que o comprimento da face da pir\303\242mide \303\251 mais ou menos g vezes a base. Os eg\303\255pcios tinham esse prop\303\263sito?
JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">4-N\303\272meros Fibonacci</Font></Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Se n\303\263s retir\303\241ssemos nossa aten\303\247\303\243o da geometria e a coloc\303\241ssemos para uma simples sequ\303\252ncia recursiva de n\303\272meros, os n\303\272meros Fibonnaci, n\303\263s encontraremos uma conex\303\243o totalmente inesperada. Os n\303\272meros Fibonnaci s\303\243o definidos por duas sementes, os dois primeiros elementos s\303\243o 0 e 1. Ent\303\243o voc\303\252 obt\303\251m o pr\303\263ximo, e os membros subsequentes da lista adicionando os dois anteriores.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E se n\303\263s peg\303\241ssemos a raz\303\243o de n\303\272meros Fibonacci consecutivos? Isto \303\251 pegar um n\303\272mero e dividir pelo anterior, e ent\303\243o o pr\303\263ximo n\303\272mero, e dividir pelo seu anterior. O que acontecer\303\241 a essas raz\303\265es?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Esses n\303\272meros parecem similares ao n\303\272mero maravilhoso. Poderiam ser?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Vamos ver qu\303\243o perto esses n\303\272meros chegam da raz\303\243o maravilhosa. Se n\303\263s dividirmos cada um deles por g, e multiplicarmos por 100, iremos obter a percentagem desses n\303\272meros que est\303\241 de acordo com o n\303\272mero maravilhoso.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Isso \303\251 muito interessante porque essas raz\303\265es Fibonacci ficam um pouco maiores do que um pouco menores que g, mas pelo 20th, elas est\303\243o de acordo com 1 d\303\251cima-mil\303\251sima parte de uma percentagem! Se n\303\263s a favorecermos ela pode ser mais precisa..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 chegamos a 100%! Iremos provar que esses n\303\272meros convergem para a raz\303\243o maravilhosa ration na pr\303\263xima se\303\247\303\243o.
Por falar nisso, aqui est\303\241 F[50]/F[49], apenas para mostrar qu\303\243o grandes os n\303\272meros podem ser.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1GIzYmLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUkjbW5HRiQ2JFEjNDBGJy9GOFEnbm9ybWFsRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0ZDRkMvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGRUZDLUYjNiZGMC1GOzYmLUYjNiUtRkA2JFEjMzlGJ0ZDRjRGN0ZDRkhGS0Y0RjcvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmZuLyUpYmV2ZWxsZWRHRkdGRUZDLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">5. Fra\303\247\303\265es Cont\303\255nuas </Font></Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Aqui est\303\241 outro lugar onde a raz\303\243o maravilhosa aparece. Vamos recordar o que g ae sua aproxima\303\247\303\243o decimal s\303\243o.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZFLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRitGK0YrRitGK0YrRitGK0YrRistSSNtaUdGJDYlUSJnRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRistRiw2LVEqJmNvbG9uZXE7RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjI3Nzc3NzhlbUYnL0ZFRlNGKy1JKG1mZW5jZWRHRiQ2JC1GIzYqLUkjbW5HRiQ2JFEiMUYnRi9GKy1GLDYtUSIrRidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjIyMjIyMjJlbUYnL0ZFRlxvRistRkc2JVElc3FydEYnL0ZLRjRGLy1GVjYkLUYjNiUtRmVuNiRRIjVGJ0YvLyUrZXhlY3V0YWJsZUdGNEYvRi9GaW9GL0YvLUYsNi1RIi9GJ0YvRjJGNS9GOEZMRjlGO0Y9Rj8vRkJRLDAuMTY2NjY2N2VtRicvRkVGYHAtRmVuNiRRIjJGJ0YvLUYsNi1RIjtGJ0YvRjIvRjZGTEY3RjlGO0Y9Rj9GQUZULUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRkMvJSZkZXB0aEdGXnEvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRmpwNiZGXHFGX3FGYXEvRmRxUSVhdXRvRidGRkYrRk9GKy1GRzYlUSZldmFsZkYnRkpGTS1GVjYkLUYjNigtRkc2JVEiJUYnRkpGTS1GLDYtUSIsRidGL0YyRmhwRjdGOUY7Rj1GP0ZBL0ZFUSwwLjMzMzMzMzNlbUYnRistRmVuNiRRIzI1RidGL0Zpb0YvRi9GZXBGaXBGZnFGaXBGZnEtRkc2I1EhRidGaW9GLw==Agora n\303\263s formamos uma s\303\251rie de fra\303\247\303\265es complexas com total 1, que s\303\243o muito mais complicadas :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N\303\263s podemos reconhecer esses n\303\272meros como n\303\272meros Fibonnaci....que tendem para o n\303\272mero maravilhoso!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 ver se n\303\263s podemos provar que esses n\303\272meros tendem para o n\303\272mero maravilhoso. Observe que uma fra\303\247\303\243o complexa infinita desse tipo tem uma certa similaridade - por causa da natureza infinita dessa lista de radicais embutidos. Uma vez que infinito \303\251 ainda infinito!!Se solucionarmos a equa\303\247\303\243o, veremos qual valor poderia ser de uma express\303\243o desse tipo com um n\303\272mero infinito de 1's inclu\303\255do.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 n\303\272meros parecem familiares!LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=<Text-field style="Heading 1" layout="Heading 1">6. Radicais Infinitos </Text-field>JSFHAqui est\303\241 outro lugar onde a raz\303\243o maravilhosa aparece. Vamos recordar o valor de g e sua aproxima\303\247\303\243o decimal 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 n\303\263s formamos uma s\303\251rie de radicais com total 1.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 n\303\263s calcularmos essas express\303\265es numericamente, 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Curioso. Aqueles n\303\272meros parecem similares \303\240 raz\303\243o maravilhosa. Vamos ter alguma id\303\251ia de qu\303\243o pr\303\263ximos aqueles n\303\272meros est\303\243o do n\303\272mero maravilhoso, ao dividirmos cada um por g, e depois multiplicarmos por 100 para expressar como 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Parece que esses n\303\272meros chegam REALMENTE perto de ser o mesmo que g. Podemos provar? Observe que um radical infinito desse tipo tem uma certa similaridade - por causa da natureza infinita dessa lista de radicais inclu\303\255dos. Dessa observa\303\247\303\243o, n\303\263s podemos obter essas equa\303\247\303\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 n\303\263s pegarmos o primeiro exemplo como uma equa\303\247\303\243o, e resolvendo-a, n\303\263s saberemos que valor poderia ser o de uma express\303\243o desse tipo com um n\303\272mero infinito de termos dentro.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSIlRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI7RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYnRj1GQA==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! Verificada!LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=