帮你认识2~(1/2)

• 作 者: 陆剑鸣
• 机 构: 中国人民大学附属中学 100080
• 出 处: 中学生数学
• 发表日期: 2004年期
• 关键词: 算术平方根 阴影部分 无限不循环小数 几何意义 平方数 角向 不等于 二忍 证明过程 连分数

你认识2~(1/2)吗?1.2~(1/2)的代数意义:2~(1/2)是2的算术平方根;2.2~(1/2)的几何意义:将边长为4的正方形纸片的四个角向中心对折,如右图.阴影部分的正方形的面积为2.由此得到:2~(1/2)是面积为2的正方形的边长;是边长为1的正方形的对角线.3.2~(1/2)的值是多少呢?我们做如下的探讨.(1)因为12=1,22=4,32=9,…,平方数越来越大,所以2~(1/2)大于1而小于2;

Do you know 2 ~ (1/2)? 1.2 ~ (1/2) of the algebraic meaning: 2 ~ (1/2) is the arithmetic square root of 2; 2.2 ~ (1/2) of the geometric meaning: the side length is The four corners of the four squares of paper are folded in half toward the center, as shown in the right. The area of ​​the square in the shaded part is 2. This gives: 2~(1/2) is the side length of a square with an area of ​​2; it is the side length. What is the value of the 3.2-1/2 1/2 diagonal of the square? We discuss as follows. (1) Because 12=1, 22=4, 32=9,..., the number of squares is increasing The larger, so 2 ~ (1/2) is greater than 1 and less than 2;