论文部分内容阅读
立体几何中的“公理六”(即祖(日桓)原理),课本中很少涉及它的应用。除了柱、锥体积公式推导外,仅有球的体积公式用祖(日桓)原理推导。因此,到高三时,大多数学生对这一原理仅有模糊的印象,更谈不上掌握及应用了。为了使学生能更好掌握这个原理,我们通过将解析几何中椭圆、双曲线、抛物线绕对称轴旋转后,所得到几何体体积计算来加深对祖(日桓)原理的认识。祖(日桓)原理:夹在两个平行平面间的两个几何体,被平行于这两个平面的任意平面所截,
The “Axiom 6” (ie the ancestral (Japanese) principle) in solid geometry is rarely used in textbooks. In addition to the derivation of the column and cone volume formulas, only the volume formula of the sphere is deduced using the ancestral (Sun) principle. Therefore, by the third year, most students have only a vague impression of this principle, let alone control and application. In order to enable students to better grasp this principle, we have deepened our knowledge of the ancestral (Japanese sundial) principle by calculating the geometry volume obtained by rotating the ellipse, hyperbola, and parabola around the axis of symmetry in analytic geometry. The principle of the ancestral (japanese): Two geometries sandwiched between two parallel planes are truncated by any plane parallel to the two planes.