Mathematically, solid geometry is the traditional name of three-dimensional Euclidean space geometry-because in fact, this is roughly the space in which we live. Generally as a follow-up course of plane geometry. Stereo measurement involves volume measurement of different shapes: cylinder, cone, frustum, sphere, prism, wedge, bottle cap and so on.

Pythagoras School studied spheres and regular polyhedrons, but before Plato School began to study them, people knew little about pyramids, prisms, cones and cylinders. Eudoxus established their measuring method and proved that the volume of a cone is one third of that of a cylinder with equal bottom and equal height, and may be the first person to prove that the volume of a sphere is proportional to the cube of its radius.

Beginners will find solid geometry difficult, but as long as you lay a good foundation, solid geometry will become easy. The key to learn solid geometry well is to establish a solid model, transform the solid into a plane, and use plane knowledge to solve problems. Solid geometry will definitely cause big problems in the college entrance examination, so it is very important to learn solid well.

conversion method

The dihedral angle is generally at the intersection of two planes, and appropriate points, usually endpoints and midpoints, are taken. After this point, make the perpendicular lines of the intersection line on two planes respectively, and then put these two perpendicular lines into a triangle to consider. Sometimes, two parallel lines perpendicular to each other are often made into a more ideal triangle.

The plane angle of dihedral angle is directly obtained by the formula s projection =S inclined plane cosθ. The key to using this method is to find out the inclined polygons and their projections on the relevant planes from the graphics, and their areas are easy to obtain.

You can also use analytic geometry to find the coordinates of the normal vector N 1 and N2 of two planes. Then according to n1N2 = | n1| N2 | cos α, θ = α is the included angle between two planes. It should be noted here that if both normal vectors are vertical planes and point to two planes, the included angle θ = π-α of the two planes is found.