奇妙的图形密铺教师：卢颖单位：良乡三小.ppt

奇妙的图形密鋪 教师： 卢 颖 单位：良乡三小 探究提示： 1、操作：组长分工，选择完全相同的平面图 形进行拼接： 如果能密铺，请把密铺的图案粘在 彩纸上； 2、讨论：如果不能密铺，分析为什么？ （提示：观察拼接点处有几个角， 它们有什么关系呢？） 2 14 3 2 14 3 2 14 3 2 14 3 2 2 2 2 2 2 1 1 1 1 1 1 3 3 3 3 3 3 1 3 4 2 3 41 2 3 41 2 1 3 4 2 60 60 60 60 6060 120 120 120 36 108108 108 用你掌握的知识来判断下面 正多边形能否密铺. 正八边形(一个内角是135度) 正九边形(一个内角是140度) 正十边形(一个内角是144度) 不能密铺 不能密铺 不能密铺 密铺的历史 1619年数学家奇柏（J.Kepler） 第一个利用正多边形密铺平面。 1891年苏联物理学家费德洛（E.S.Fedorov） 发现了十七种不同的密铺平面的对称图案。 1924年数学家波利亚（Polya）和尼格利（Nigele） 重新发现这个事实。 荷兰艺术家埃舍尔（M.C.Escher） 他创作的艺术作品，结合数学与艺术，给人留下深刻印象， 更让人感受到数学的独特魅力。 天与水 日与夜 日与月 自由 脱变 越來越小 fQiUlXo#s%v(y0B3E6I9LdOgRjVmYp!t&w-z1C4G7JaMePhTkWnZr$u*x+A2E5H8KcNfQiUlXp#s%v)y0B3F6IaLdOgSjVmYq!t*w-z1D4G7JbMePhTkWoZr$u(x+A2E5H9KcNfRiUlXp#s&v)y0C3F6IaLdPgSjVnYq!t*w-A1D4G8JbMeQhTlWoZr%u(x+B2E6H9KcOfRiUmXp!s&v)z0C3F7IaLdPgSkVnYq$t*w-A1D5G8JbNeQhTlWo#r%u(y+B2E6H9LcOfRjUmXp!s&w)z0C4F7IaMdPhSkVnZq$t*x-A2D5G8KbNeQiTlWo#r%v(y+B3E6H9LcOgRjUmYp!s&w)z1C4F7JaMdPhSkWnZq$u*x- 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