M\303\263dulos de Segundo Grau > Geometria por Gregory A. Moore
A Raz\303\243o Maravilhosa
Uma explora\303\247\303\243o da raz\303\243o maravilhosa. Ela \303\251 derivada de diferentes maneiras, e aplicada a ret\303\242ngulos comuns.
[Dire\303\247\303\265es : Execute primeiramente a se\303\247\303\243o Code Resource. Embora n\303\243o haja output imediato, essas defini\303\247\303\265es ser\303\243o usadas posteriormente nessa worksheet.]
0. C\303\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. Solu\303\247\303\243o de uma Equa\303\247\303\243o Quadr\303\241tica
N\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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
Existem duas solu\303\247\303\265es, mas a ra\303\255z positiva \303\251 chamada de raz\303\243o maravilhosa ratio - 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 \317\206 , depois do escultor grego Phidias, no entanto, n\303\263s usaremos g, para "n\303\272mero maravilhoso", aqui apenas por conveni\303\252ncia.2. Ret\303\242ngulos Similares Infinitos
Imagine 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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Esse 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 1
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 aqui est\303\241. A solu\303\247\303\243o positiva \303\251 a raz\303\243o maravilhosa ratio. (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 maravilhosa ratio, 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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Agora 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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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY+LUkjbWlHRiQ2JVEjZzdGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSJ+RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkwtRjY2LVEq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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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Se 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 maravilhoso, 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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 3. A Propor\303\247\303\243o Mais Bonita
Foi dito que a raz\303\243o maravilhosa ratio \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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Outra aplica\303\247\303\243o da raz\303\243o maravilhosa ratio 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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Bem isto n\303\243o est\303\241 terminado. No entanto, se voc\303\252 criar uma tri\303\242nguloonde 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 isso
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
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?
4. N\303\272meros Fibonacci
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 od 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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 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 ratio. 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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
Quase 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 F50/F49, apenas para mostrar qu\303\243o grandes os n\303\272meros podem ser.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 5. Fra\303\247\303\265es Cont\303\255nuas
Aqui est\303\241 outro lugar onde a raz\303\243o maravilhosa ratio aparece. Vamos recordar o que g ae sua aproxima\303\247\303\243o decimal s\303\243o.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 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 :
1, 1+1/1 , 1+1/(1+1/1) , 1+1/(1+1/(1+1/1)) , 1+1/(1+1/(1+1/(1+1/1))) , 1+1/(1+1/(1+1/(1+1/(1+1/1)))) , ...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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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Vamos 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 x = 1+1/(1+1/(1+1/(1+1/(1+1/`...`))))Portanto n\303\263s temos esses tipos de rela\303\247\303\243o
x = 1+1/xSe solucionarmos essa 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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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSIlRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI7RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYnRj1GQA==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
Esses n\303\272meros parecem familiares! 6. Radicais Infinitos
Aqui est\303\241 outro lugar onde a raz\303\243o maravilhosa ratio aparece. Vamos recordar o que g e sua aproxima\303\247\303\243o decimal s\303\243o.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Agora n\303\263s formamos uma s\303\251rie de radicais com total 1.
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Se n\303\263s calcularmos numericamente, obteremos.
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Hmmm. Curioso. Aqueles n\303\272meros paracem similares a raz\303\243o maravilhosa ratio. 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. Se n\303\263s dividirmos cada um por g, e depois multiplicarmos por 100 para expressar como percentagem...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 qe esses n\303\272meros chegam REALMENTE perto de ser o mesmo que g. Podemos provar it? 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\265es ...
x = sqrt(1+sqrt(1*sqrt(1+sqrt(1+sqrt(1+`...`)))))
x = sqrt(1+x)Se 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\243odesse tipo com um n\303\272mero infinito de termos dentro.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Esses n\303\272meros parecem familiares!