球是我们日常生活中十分熟悉的一种几何体,球的影子连小朋友们也见得多,似乎不屑一顾,但用数学的眼光去作一番观察,却能激发同学们思考的兴趣,会发现它能编织出立几、解几和三角基础知识交汇点上的富有价值的应用问题,是同学们课外进行研究性学习的一个实践课题.下面证明几个简单的命题,并解答几个常见的实例,供同学们学习参考. The ball is a kind of geometry that we are very familiar with in our daily life. The shadow of the ball is even more visible to the children. It seems to be dismissive, but using mathematics to make an observation can inspire students’ interest in thinking. It can weave valuable application problems on the intersection of several points, solutions, and basic knowledge of triangles. It is a practical topic for students to carry out research studies outside class. The following proves several simple propositions and answers several common ones. Examples for students to learn reference.