三角形的外接圆半径不小于其内切圆直径,即R≥2r,这就是简约而有用的欧拉不等式.如果存在满足不等式R≥K≥2r的几何量K,则称K为欧拉不等式的一个隔离.欧拉不等式因其在初等几何中的重要地位而备受关注,其各式各样的隔离也是异彩纷呈.但是,也有一些隔离或稍嫌复杂,或略显造作.刘绍学先生在其主编的数学教科书[1]中曾说:数学是有用的,数学是自然的.斯言诚哉.为追求难能可贵的数学品格,人们致力于寻找各种简单而自然的欧拉不等式的隔离,贵刊文[2]便是一例.在三角形的基本元素及其生成元素中,就 The radius of the circumscribed circle of the triangle is not less than the diameter of its inscribed circle, ie R≥2r, which is a simple and useful Euler’s inequality. If there exists a geometric quantity K that satisfies the inequality R≥K≥2r, then K is called Euler’s inequality One Isolation Euler’s inequality has drawn much attention because of its importance in elementary geometry, and its various kinds of isolation are colorful, but there are also some isolated or somewhat complicated or slightly complicated works in which Mr. Liu Shaoxue The mathematical textbook edited by [1] once said that mathematics is useful, and mathematics is natural.Sincerely, in pursuit of the commendable mathematical character, people are devoted to searching for simple and natural Euler’s inequality isolation An example of an article [2] is found in the basic elements of the triangle and its generated elements