Pol\303\255gonos Regulares & Estrelas
Uma explora\303\247\303\243o de pol\303\255gonos reguares e suas caracter\303\255sticas - incluindo gr\303\241ficos de diferentes tipos de eixos de simetria, e as estrelas do mundo da geometria.
[Dire\303\247\303\265es : Execute primeiramente a se\303\247\303\243o Code Resource. Embora n\303\243o haja nenhum output imediato, essas defini\303\247\303\265es ser\303\243o usadas posteriormente em outro this worksheet.
0. C\303\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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZfcC1JI21vR0YkNi1RIn5GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZ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Pol\303\255gonos
Um pol\303\255gono \303\251 qualquer forma simples e fechada formados com segmentos de linha.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Alguns pol\303\255gonos familiares incluem tri\303\242ngulos ...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Quadrados e ret\303\242ngulos ....LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYyLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRitGK0YrRitGK0YrRitGK0YrRistSSNtaUdGJDYlUShkaXNwbGF5RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNmhuRistRkc2JVElcGxvdEYnRkpGTS1GUDYkLUYjNipGKy1GUDYmLUYjNi5GKy1GUDYmLUYjNictSSNtbkdGJDYkUSIzRidGLy1GLDYtUSIsRidGL0YyL0Y2RkxGN0Y5RjtGPUY/RkEvRkVRLDAuMzMzMzMzM2VtRictRl5vNiRRIjBGJ0YvLyUrZXhlY3V0YWJsZUdGNEYvRi8vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGYW8tRlA2Ji1GIzYnLUZebzYkUSI3RidGL0Zhb0Znb0Zqb0YvRi9GXHBGX3BGYW8tRlA2Ji1GIzYnRmZwRmFvLUZebzYkUSI2RidGL0Zqb0YvRi9GXHBGX3BGYW8tRlA2Ji1GIzYnRl1vRmFvRl1xRmpvRi9GL0ZccEZfcEZhb0ZpbkZqb0YvRi9GXHBGX3BGYW9GKy1GRzYlUSRzZ3lGJ0ZKRk1GK0Zqb0YvRi9GYW8tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGQy8lJmRlcHRoR0Zcci8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GaHE2JkZqcUZdckZfci9GYnJRJWF1dG9GJ0YrRitGK0YrRitGK0YrRitGK0ZULUZQNiQtRiM2KkYrLUZQNiYtRiM2LkYrLUZQNiYtRiM2KC1GLDYtUSomdW1pbnVzMDtGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMjIyMjIyMmVtRicvRkVGaHMtRl5vNiRRIjVGJ0YvRmFvLUZebzYkUSIxRidGL0Zqb0YvRi9GXHBGX3BGYW8tRlA2Ji1GIzYnRmpzRmFvRl10RmpvRi9GL0ZccEZfcEZhby1GUDYmLUYjNidGanNGYW9GXW9Gam9GL0YvRlxwRl9wRmFvLUZQNiYtRiM2KEZkc0Zqc0Zhb0Zdb0Zqb0YvRi9GXHBGX3BGYW9GYHNGam9GL0YvRlxwRl9wRmFvRistRkc2JVEkc2duRidGSkZNRitGam9GL0YvRmFvRmdxRmRyRitGK0YrRitGK0YrRitGK0YrRlQtRlA2JC1GIzYqRistRlA2Ji1GIzYuRistRlA2Ji1GIzYnLUZebzYkUSIyRidGL0Zhb0ZbdkZqb0YvRi9GXHBGX3BGYW8tRlA2Ji1GIzYnLUZebzYkUSI0RidGL0Zhb0ZbdkZqb0YvRi9GXHBGX3BGYW8tRlA2Ji1GIzYnRmJ2RmFvRmJ2RmpvRi9GL0ZccEZfcEZhby1GUDYmLUYjNidGW3ZGYW9GYnZGam9GL0YvRlxwRl9wRmFvRmd1RmpvRi9GL0ZccEZfcEZhb0YrLUZHNiVRJHNvckYnRkpGTUYrRmpvRi9GL0Zhb0ZncUZkckYrRitGK0YrRitGK0YrRitGK0ZULUZQNiQtRiM2KkYrLUZQNiYtRiM2LkYrLUZQNiYtRiM2KEZkc0ZmcEZhb0Zqc0Zqb0YvRi9GXHBGX3BGYW8tRlA2Ji1GIzYoRmRzRmZwRmFvRlt2RmpvRi9GL0ZccEZfcEZhby1GUDYmLUYjNihGZHNGW3ZGYW9GW3ZGam9GL0YvRlxwRl9wRmFvLUZQNiYtRiM2KEZkc0ZbdkZhb0Zqc0Zqb0YvRi9GXHBGX3BGYW9GaHdGam9GL0YvRlxwRl9wRmFvRistRkc2JVEkc2JlRidGSkZNRitGam9GL0YvLUZHNiNRIUYnRmdxRmRyRitGK0YrRitGK0YrRitGK0YrRitGam9GL0YvLUYsNi1RIjtGJ0YvRjJGZG9GN0Y5RjtGPUY/RkEvRkVRLDAuMjc3Nzc3OGVtRidGam9GLw==Mais existem mais!
2. Pol\303\255gonos Regulares
Pol\303\255gonos regulares s\303\243o pol\303\255gonos onde todos os lados s\303\243o iguais e todos os \303\242ngulos interiores s\303\243o iguais. Um pol\303\255gono regular de cinco lados \303\251 chamado pent\303\241gono.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Todos os pol\303\255gonos regulares se adaptam a c\303\255rculos.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Aqui est\303\243o os detalhes desse pent\303\241gono.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEnZGV0YWlsRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEoUmVnUG9seUYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUkjbW9HRiQ2LVEiO0YnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0ZWLyUmZGVwdGhHRmluLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZlbjYmRmduRmpuRlxvL0Zfb1ElYXV0b0YnLUYsNiNRIUYnRj1GQA==Embora ele requeira alguma tradu\303\247\303\243o, o que ele est\303\241 dizendo \303\251 que o interior dos \303\242ngulos s\303\243o estes v\303\241rios graus.
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 est\303\243o alguns outros pol\303\255gonos regulares. Voc\303\252 pode nome\303\241-los?
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Aqui est\303\241 um pol\303\255gono regular de 17 lados, o qual tem alguma signific\303\242ncia hist\303\263rica (depois de encontrar a primeira constru\303\247\303\243o de tal pol\303\255gono, um jovem Gauss decidiu sua vida na matem\303\241tica). Observe como ele est\303\241 perto do c\303\255rculo que o 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Se n\303\263s desenh\303\241ssemos um n\303\272mero de pol\303\255gonos regulares no mesmo diagrama n\303\263s podemos ver seu progresso. Aqui est\303\243o pol\303\255gonos regulares com 3 a 10 lados, e xdepois 3 a 30 lados. Eles parecem preencher o c\303\255rculo mais e mais.
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N\303\263s sabemos que a soma dos \303\242ngulos de um tri\303\242ngulo \303\251 180 graus, e ret\303\242ngulo (ou qualquer pol\303\255gono de quatro lados) \303\251 360 graus.
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Se existisse um pol\303\255gono regular com 10 lados, e cada lado \303\251 3 p\303\251s maior, o per\303\255metro \303\251 f\303\241cil de calcular.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEjMTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIqRidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjE2NjY2NjdlbUYnLyUncnNwYWNlR0ZHLUYsNiRRIjNGJ0YvLUYzNi1RIjtGJ0YvRjYvRjpRJXRydWVGJ0Y7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y4Ri8=
Por outro lado, se n\303\263s tiv\303\251ssemos um pol\303\255gono regular com 7 lados, e a dist\303\242ncia do centro para qualquer dos v\303\251rtices \303\251 5 p\303\251s, qual \303\251 o per\303\255metro? Esse \303\251 um problema que n\303\243o pode ser respondido adequadamente at\303\251 que voc\303\252 fa\303\247a trigonometria, mas n\303\263s podemos usar o Maple para encontrar a resposta.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5. \303\201rea de Pol\303\255gonos Regulares
Um pol\303\255gono regular com n lados pode ser dividido em n tri\303\242ngulos is\303\263sceles.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZKLUkjbWlHRiQ2JVEvUmVndWxhclBvbHlnb25GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2LS1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUS1GLDYlUShSZWdQb2x5RidGL0YyRjotRjs2LVEiLEYnRj5GQC9GREYxRkVGR0ZJRktGTUZPL0ZTUSwwLjMzMzMzMzNlbUYnLUkjbW5HRiQ2JFEiN0YnRj5GVy1GLDYlUSJvRidGL0YyRlctRmhuNiRRIjFGJ0Y+LyUrZXhlY3V0YWJsZUdGQkY+Rj4tRjs2LVEiOkYnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yNzc3Nzc4ZW1GJy9GU0Znby1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0ZRLyUmZGVwdGhHRl5wLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZqbzYmRlxwRl9wRmFwL0ZkcFElYXV0b0YnLUYsNiVRJnBvaW50RidGL0YyLUY2NiQtRiM2Jy1GLDYlUSJBRidGL0YyRlctRjY2Ji1GIzYqLUYsNiVRJGNvc0YnL0YwRkJGPi1GNjYkLUYjNiktRmhuNiRRIjJGJ0Y+LUY7Ni1RIipGJ0Y+RkBGQ0ZFRkdGSUZLRk0vRlBRLDAuMTY2NjY2N2VtRicvRlNGZ3ItRiw2JVEjUGlGJ0ZbckY+LUY7Ni1RIi9GJ0Y+RkBGQy9GRkYxRkdGSUZLRk1GZnJGaHJGZ25GYW9GPkY+RldGOi1GLDYlUSRzaW5GJ0ZbckY+RlxyRmFvRj5GPi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zhb0Y+Rj4tRjs2LVEiO0YnRj5GQEZaRkVGR0ZJRktGTUZPRmhvRmlvRmZwRmpwLUY2NiQtRiM2Jy1GLDYlUSJCRidGL0YyRlctRjY2Ji1GIzYqRmhxLUY2NiQtRiM2KS1GaG42JFEiNEYnRj5GY3JGaXJGXHNGZ25GYW9GPkY+RldGOkZgc0ZndEZhb0Y+Rj5GY3NGZnNGYW9GPkY+RmlzRmlvRmZwRmpwLUY2NiQtRiM2Jy1GLDYlUSJDRidGL0YyRlctRjY2Ji1GIzYwRmhxLUY2NiQtRiM2KS1GaG42JFEiM0YnRj5GY3JGaXJGXHNGZ25GYW9GPkY+RmNyRmhxLUY2NiQtRiM2J0ZpckZcc0ZnbkZhb0Y+Rj5GV0Y6RmBzRml1RmNyRmhxRmB2RmFvRj5GPkZjc0Zmc0Zhb0Y+Rj5GaXNGaW9GZnAtRiw2JVEoc2VnbWVudEYnRi9GMi1GNjYkLUYjNilGOi1GLDYlUSVyYWQxRidGL0YyRldGOi1GNjYmLUYjNihGW29GV0Y6RmFxRmFvRj5GPkZjc0Zmc0Zhb0Y+Rj5GaXNGaW9GZnBGZHYtRjY2JC1GIzYpRjotRiw2JVElcmFkMkYnRi9GMkZXRjotRjY2Ji1GIzYoRltvRldGOkZgdEZhb0Y+Rj5GY3NGZnNGYW9GPkY+RmlzRmlvRmZwRmR2LUY2NiQtRiM2KUY6LUYsNiVRImhGJ0YvRjJGV0Y6LUY2NiYtRiM2KEZbb0ZXRjpGYnVGYW9GPkY+RmNzRmZzRmFvRj5GPkZpc0Zpb0ZmcEZkdi1GNjYkLUYjNilGOi1GLDYlUSVzaWRlRidGL0YyRldGOi1GNjYmLUYjNidGYXFGV0ZgdEZhb0Y+Rj5GY3NGZnNGYW9GPkY+RmlzRmFvRj4=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoZGlzcGxheUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzY5LUkjbW9HRiQ2LVEifkYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUYsNiVRJWRyYXdGJ0YvRjItRjY2JC1GIzYyLUYsNiNRIUYnLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRlEvJSZkZXB0aEdGXW8vJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRmluNiZGW29GXm9GYG8vRmNvUSVhdXRvRidGOkY6RjpGOkY6RjpGOkY6RjpGOi1GNjYmLUYjNmZwRjotRiw2JVEjVUNGJ0YvRjItRjY2JC1GIzYpLUYsNiVRKnRoaWNrbmVzc0YnRi9GMi1GOzYtUSI9RidGPkZARkNGRUZHRklGS0ZNL0ZQUSwwLjI3Nzc3NzhlbUYnL0ZTRltxLUkjbW5HRiQ2JFEiMUYnRj4tRjs2LVEiLEYnRj5GQC9GREYxRkVGR0ZJRktGTUZPL0ZTUSwwLjMzMzMzMzNlbUYnLUYsNiVRJGNiZUYnRi9GMi8lK2V4ZWN1dGFibGVHRkJGPkY+RmFxRjotRiw2JVEoUmVnUG9seUYnRi9GMi1GNjYkLUYjNilGZHBGZ3AtRl5xNiRRIjJGJ0Y+RmFxLUYsNiVRJGNnbkYnRi9GMkZqcUY+Rj5GYXFGaG5GZW9GOkY6RjpGOkY6RjpGOkY6RjpGOkY6RjotRiw2JVElcmFkMUYnRi9GMi1GNjYkLUYjNi0tRiw2JVEmY29sb3JGJ0YvRjJGZ3AtRiw2JVEkcmVkRidGL0YyRmFxRmRwRjpGZ3BGOkZjckZqcUY+Rj5GYXFGaG5GZW9GOkY6RjpGOkY6RjpGOkY6RjpGOkY6RjotRiw2JVElcmFkMkYnRi9GMi1GNjYkLUYjNi5GYHNGZ3AtRiw2JVElZ29sZEYnRi9GMkZhcUY6LUYsNiVRKmxpbmVzdHlsZUYnRi9GMkY6RmdwRjotRl5xNiRRIjNGJ0Y+RmpxRj5GPkZhcUZobkZlb0Y6RjpGOkY6RjpGOkY6RjpGOkY6RjpGOi1GLDYlUSJoRidGL0YyLUY2NiQtRiM2MEZkcEY6RmdwRjpGY3JGYXFGOkZgc0Y6RmdwRjotRiw2JVEmY29yYWxGJ0YvRjJGanFGPkY+RmFxRmhuRmVvRjpGOkY6RjpGOkY6RjpGOkY6RjpGOkY6LUYsNiVRJXNpZGVGJ0YvRjItRjY2JC1GIzYwRmRwRjpGZ3BGOkZjdEZhcUY6RmBzRjpGZ3BGOi1GLDYlUSZncmVlbkYnRi9GMkZqcUY+Rj5GZW5GaG5GZW9GOkY6RjpGOkY6RjpGOkY6RjpGOkZqcUY+Rj4vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGanFGPkY+RmFxRjotRiw2JVElYXhlc0YnRi9GMkZncC1GLDYlUSVub25lRidGL0YyRmFxRjotRiw2JVEoc2NhbGluZ0YnRi9GMkZncC1GLDYlUSxjb25zdHJhaW5lZEYnRi9GMkY6RjpGOkY6RjpGOkY6RjpGanFGPkY+LUY7Ni1RIjtGJ0Y+RkBGZHFGRUZHRklGS0ZNRk9GXHFGanFGPg==Voc\303\252 precisa de tr\303\252s partes de informa\303\247\303\243o :
1. n, o n\303\272mero de lados
2. a altura de cada tri\303\242ngulo (a linha s\303\263lida amarelo/laranja no meio do tri\303\242ngulo)
3. o comprimento de um lado do pol\303\255gono.
N\303\263s podemos obter isto atrav\303\251s do comando detail ....LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEnZGV0YWlsRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEoUmVnUG9seUYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUkjbW9HRiQ2LVEiO0YnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0ZWLyUmZGVwdGhHRmluLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZlbjYmRmduRmpuRlxvL0Zfb1ElYXV0b0YnLUYsNiNRIUYnRj1GQA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY3LUkjbWlHRiQ2JVElQXJlYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORlNGNS1JI21uR0YkNiRRIjdGJ0Y5LUY2Ni1RIipGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMTY2NjY2N2VtRicvRk5GZ24tRiw2JVEkc2luRicvRjBGPUY5LUkobWZlbmNlZEdGJDYkLUYjNictRiw2JVEjUGlGJ0Zcb0Y5LUY2Ni1RIi9GJ0Y5RjtGPi9GQUYxRkJGREZGRkhGZm5GaG5GVS8lK2V4ZWN1dGFibGVHRj1GOUY5RlktRiw2JVEkY29zRidGXG9GOUZdby1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRlJGVEY1LUYsNiVRJmV2YWxmRidGL0YyLUZebzYkLUYjNigtRiw2JVEiJUYnRi9GMi1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRkovRk5RLDAuMzMzMzMzM2VtRidGNS1GVjYkUSM1MEYnRjlGaW9GOUY5LUY2Ni1RIjtGJ0Y5RjtGXnFGQEZCRkRGRkZIRkpGVC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0ZMLyUmZGVwdGhHRlxyLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZocTYmRmpxRl1yRl9yL0ZiclElYXV0b0YnLUYsNiNRIUYnRmlvRjk=
6. Estrelas
Outro tipo de pol\303\255gono, que n\303\243o \303\251 "regular", mas \303\251 sim\303\251trico, \303\251 uma "estrela" - uma forma geralmente n\303\243o estudada nos livros de geometria, mas certamente comum em ilustra\303\247\303\265es.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Observe que uma estrela se adapta dentro de um pol\303\255gono regular. Uma estrela de 5 lados se adapta dentro de um pol\303\255gono de 5 lados. Assim, se voc\303\252 cortar os cinco pontos como v\303\251rtices perto do centro, voc\303\252 ver\303\241 que existe outro pent\303\241gono dentro da estrela tamb\303\251m!
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