用两片不同颜色的面包,中间夹一片火腿,做成一个火腿三明治.问只切一刀就将这个三明治的三层同时分成等体积的两半,这个切法一定存在吗? 我们先来看平面上的一个简单情形. 对于平面上的一个任意形状的封闭图形,用一条直线将它平分为面积相等的两半,这样的直线一定存在吗?若存在,有多少条? 特殊地,如果这个图形是圆,那么很容易得到,通过圆心的任意一条直线,都将该圆平分为等积的两半(两部分不仅面积相等,而且 Use two pieces of bread of different colors with a ham sandwiched between them to make a ham sandwich. Ask only one knife to divide the three layers of the sandwich into two equal volumes. Is this cut must exist? Let’s look at the plane first. A simple case above. For a closed shape of an arbitrary shape on a plane, use a straight line to divide it into two halves of equal area. Is such a line necessarily present? If so, how many are there? Specially, if this figure It is a circle, so it is easy to get. Through any straight line of the circle, it divides the circle into two equal parts. (The two parts are not only equal in area but also