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让高中学生做些作截面的练习,对发展他们的空间想象能力有一定的帮助。学生练习作多而体的截面时,可从作正方体的截面开始。本文从简单到复杂介绍作正方体截面的若干例子,以供参考。在棱长为α的正方体上给出确定截面的条件一定可以作出截面。因为正方体的各个面都是平面,所以用平面去截它所得的截面必是多边形。由于截面至少与正方体的三个面相交,至多与6个面相交,所以截面的形状只能是三角形、四边形、五边形、六边形四种。截面与正方体每一个面的交线由两个公共点决定,所以只要找到截面与正方体某个面的两个公共点,就能作出截面与该面的交线。
Allowing high school students to do cross-sectional exercises will help to develop their spatial imagination. When students practice a multi-body cross-section, start with a cross-section that is a cube. This article from simple to complex as a number of examples of cube cross section, for reference. The condition of determining the cross-section on a cube with an edge length of α must be able to make a cross-section. Because all faces of the cube are planes, the section taken with the plane must be polygonal. As the cross-section at least intersects the three faces of the cube, intersecting at most six faces, the shape of the cross-section can only be triangular, quadrangular, pentagonal, hexagonal. The intersection of the cross section and each cube of the cube is determined by two common points so that the intersection of the cross section and the plane can be made by simply finding two common points between the cross section and one of the faces of the cube.