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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,神奇的莫比乌斯圈,瓯海实验小学 金海跃,4条边2个面,2条边2个面,4条边2个面,1条边1个面,一端不变,另一端拧180度,两端对接粘贴。,这个神奇的纸环叫莫比乌斯带,它是德国数学家莫比乌斯于1858年发现的,所以就以它的名字命名。因为它有许多看起来不可思议的运用,所以很多人也通俗地称它为“怪圈”。,莫比乌斯带,中国科技馆内的三叶扭结,应用,“莫比乌斯圈”国家图书馆,应用,克莱因瓶,应用,机器上的传动带,应用,应用,应用,过山车,日本人的专利不用翻动音乐磁带,应用,变化,变化,我的纸圈,创造提示:,将纸条拧360度、 540度会如何呢?,将纸条平均分成四等分,五等分,沿等分线剪会如何呢?,课堂梳理,这节课你有什么收获?,对于数学,你有什么新的感受?,(POMLKIHGEDCBzyxvutrqpnmljihfedca98654210-)(&%$#ZYWVUTRQPNMLJIHFEDBAzxwvusrqonmkjigfecba8765321+-)*&%!#ZXWVTSRQONMKJIGFECBAyxwutsrponlkjhgfdcb98754320+-(*&$!#YXWUTSQPONLKJHGFDCBzyxvutrqpomlkihgedca98654210+)(*%$!ZYXVUTRQPNMLKIHGEDCAzywvusrqonmljihfedba9765321+-)*&%$#ZYWVUSRQONMKJIGFEDBAzxwvtsrponlkjhgfecba8764320+-(*&$!#ZXWVTSRPONLKJHGFDCBAyxwutsqpomlkihgedcb98754310+)(*%$!ZYXWUTSQPOMLKIHGEDCAzyxvutrqpnmljihfedba98654210-)(&%$#ZYWVUTRQPNMLJIHFEDBAzxwvusrqonmkjigfecba8764321+-)*&%!#ZXWVTSRPONMKJIGFECBAyxwutsqponlkjhgfdcb98754310+-(*&$!#YXWUTSQPOMLKJHGFDCBzyxvutrqpnmlkihgedca98654210-)(*%$!ZYXVUTRQPNMLJIHGEDCAzywvusrqonmkjihfedba9765321+-)*&%$#ZYWVUSRQONMKJIGFEDBAzxwvtsrponlkjhgfdcba8764320+-(*&$!#YXWVTSRPONLKJHGFDCBzyxwutsqpomlkihgedca98754310+)(*%$!ZYXVUTSQPOMLKIHGEDCAzywvutrqpnmljihfedba97654210-)(&%$#ZYWVUSRQPNMLJIHFEDBAzxwvtsrqonmkjigfecba8764321+-)*&%!#ZXWVTSRPONMKJIGFECBAyxwutsqpomlkjhgfdcb98754310+)(*&$!#YXWUTSQPOMLKIHGFDCBzyxvutrqpnmljihgedca98654210-)(&%$!ZYXVUTRQPNMLJIHFEDCAzywvusrqonmkjigfedba9765321+-)*&%!#ZYWVUSRQONMKJIGFECBAzxwvtsrponlkjhgfdcba8764320+-(*&$!#YXWVTSRPONLKJHGFDCBzyxvutsqpomlkihgedca98654310+)(*%$!ZYXVUTRQPOMLKIHGEDCAzywvusrqpnmljihfedba97653210-)(&%$#ZYWVUSRQONMLJIHFEDBAzxwvtsrponmkjigfecba8764320+-)*&%!#ZXWVTSRPONLKJIGFECBAyxwutsqpomlkjhgfdcb98754310+)(*&$!#YXWUTSQPOMLKIHGEDCBzyxvutrqpnmljihfedca98654210-)(&%$#ZYXVUTRQPNMLJIHFEDBAzywvusrqonmkjigfecba9765321+-)*&%!#ZXWVUSRQONMKJIGFECBAyxwvtsrponlkjhgfdcb98764320+-(*&$!#YXWUTSRPONLKJHGFDCBzyxvutsqpomlkihgedca98654310+)(*%$!ZYXVUTRQPNMLKIHGEDCAzywvusrqonmljihfedba9765321+-)(&%$#ZYWVUSRQONMKJIHFEDBAzxwvtsrponlkjigfecba8764320+-(*&%!#ZXWVTSRPONLKJHGFECBAyxwutsqpomlkihgfdcb98754310+)(*%$!#YXWUTSQPOMLKIHGEDCBzyxvutrqpnmljihfedca98654210-)(&%$#ZYWVUTRQPNMLJIHFEDBAzxwvusrqonmkjigfecba8765321+-)*&%!#ZXWVTSRQONMKJIGFECBAyxwutsrponlkjhgfdcb98754320+-(*&$!#YXWUTSQPONLKJHGFDCBzyxvutrqpomlkihgedca98654210+)(*%$!ZYXVUTRQPNMLKIHGEDCAzywvusrqonmljihfedba9765321+-)*&%$#ZYWVUSRQONMKJIGFEDBAzxwvtsrponlkjhgfecba8764320+-(*&$!#ZXWVTSRPONLKJHGFDCBAyxwutsqpomlkihgedcb98754310+)(*%$!ZYXWUTSQPOMLKIHGEDCAzyxvutrqpnmljihfedba98654210-)(&%$#ZYWVUTRQPNMLJIHFEDBAzxwvusrqonmkjigfecba8764321+-)*&%!#ZXWVTSRPONMKJIGFECBAyxwutsqponlkjhgfdcb98754310+-(*&$!#YXWUTSQPOMLKJHGFDCBzyxvutrqpnmlkihgedca98654210-)(*%$!ZYXVUTRQPNMLJIHGEDCAzywvusrqonmkjihfedba9765321+-)*&%$#ZYWVUSRQONMKJIGFEDBAzxwvtsrponlkjhgfdcba8764320+-(*&$!#YXWVTSRPONLKJHGFDCBzyxwutsqpomlkihgedca98754310+)(*%$!ZYXVUTSQPOMLKIHGEDCAzywvutrqpnmljihfedba97654210-)(&%$#ZYWVUSRQPNMLJIHFEDBAzxwvtsrqonmkjigfecba8764321+-)*&%!#ZXWVTSRPONMKJIGFECBAyxrqpnmljihfedba97654210-)(&%$#ZYWVUSRQPNMLJIHFEDBAzxwvtsrqonmkjigfecba8764321+-)*&%!#ZXWVTSRPONMKJIGFECBAyxwutsqponlkjhgfdcb98754310+-(*&$!#YXWUTSQPOMLKJHGFDCBzyxvutrqpnmlkihgedca98654210-)(*%$!ZYXVUTRQPNMLJIHFEDCAzywvusrqonmkjigfedba9765321+-)*&%!#ZYWVUSRQONMKJIGFECBAzxwvtsrponlkjhgfdcba8764320+-(*&$!#YXWVTSRPONLKJHGFDCBzyxwutsqpomlkihgedca98754310+)(*%$!ZYXVUTSQPOMLKIHGEDCAzywvutrqpnmljihfedba97654210-)(&%$#ZYWVUSRQONMLJIHFEDBAzxwvtsrponmkjigfecba8764320+-)*&%!#ZXWVTSRPONLKJIGFECBAyxwutsqpomlkjhgfdcb98754310+)(*&$!#YXWUTSQPOMLKIHGFDCBzyxvutrqpnmljihgedca98654210-)(&%$!ZYXVUTRQPNMLJIHFEDCAzywvusrqonmkjigfedba9765321+-)*&%!#ZYWVUSRQONMKJIGFECBAyxwvtsrponlkjhgfdcb98764320+-(*&$!#YXWUTSRPONLKJHGFDCBzyxvutsqpomlkihgedca98654310+)(*%$!ZYXVUTRQPOMLKIHGEDCAzywvusrqpnmljihfedba97653210-)(&%$#ZYWVUSRQONMLJIHFEDBAzxwvtsrponmkjigfecba8764320+-)*&%!#ZXWVTSRPONLKJHGFECBAyxwutsqpomlkihgfdcb98754310+)(*%$!#YXWUTSQPOMLKIHGEDCBzyxvutrqpnmljihfedca98654210-)(&%$#ZYXVUTRQPNMLJIHFEDBAzywvusrqonmkjigfecba9765321+-)*&%!#ZXWVUSRQONMKJIGFECBAyxwvtsrponlkjhgfdcb98764320+-(*&$!#YXWUTSQPONLKJHGFDCBzyxvutrqpomlkihgedca98654210+)(*%$!ZYXVUTRQPNMLKIHGEDCAzywvusrqonmljihfedba9765321+-)(&%$#ZYWVUSRQONMKJIHFEDBAzxwvtsrponlkjigfecba8764320+-(*&%!#ZXWVTSRPONLKJHGFECBAyxwutsqpomlkihgfdcb98754310+)(*%$!ZYXWUTSQPOMLKIHGEDCAzyxvutrqpnmljihfedba98654210-)(&%$#ZYWVUTRQPNMLJIHFEDBAzxwvusrqonmkjigfecba8765321+-)*&%!#ZXWVTSRQONMKJIGFECBAyxwutsrponlkjhgfdcb98754320+-(*&$!#YXWUTSQPONLKJHGFDCBzusrqonmkjigfecba8765321+-)*&%!#ZXWVTSRQONMKJIGFECBAyxwutsrponlkjhgfdcb98754320+-(*&$!#YXWUTSQPONLKJHGFDCBzyxvutrqpomlkihgedca98654210+)(*%$!ZYXVUTRQPNMLKIHGEDCAzywvusrqonmljihfedba9765321+-)(&%$#ZYWVUSRQONMKJIHFEDBAzxwvtsrponlkjhgfecba8764320+-(*&$!#ZXWVTSRPONLKJHGFDCBAyxwutsqpomlkihgedcb98754310+)(*%$!ZYXWUTSQPOMLKIHGEDCAzyxvutrqpnmljihfedba98654210-)(&%$#ZYWVUTRQPNMLJIHFEDBAzxwvusrqonmkjigfecba8765321+-)*&%!#ZXWVTSRQONMKJIGFECBAyxwutsqponlkjhgfdcb98754310+-(*&$!#YXWUTSQPOMLKJHGFDCBzyxvutrqpnmlkihgedca98654210-)(*%$!ZYXVUTRQPNMLJIHGEDCAzywvusrqonmkjihfedba9765321+-)*&%$#ZYWVUSRQONMKJIGFEDBAzxwvtsrponlkjhgfecba8764320+-(*&$!#ZXWVTSRPONLKJHGFDCBzyxwutsqpomlkihgedca98754310+)(*%$!ZYXVUTSQPOMLKIHGEDCAzywvutrqpnmljihfedba97654210-)(&%$#ZYWVUSRQPNMLJIHFEDBAzxwvtsrqonmkjigfecba8764321+-)*&%!#ZXWVTSRPONMKJIGFECBAyxwutsqponlkjhgfdcb98754310+-(*&$!#YXWUTSQPOMLKIHGFDCBzyx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