Mathematics Zhejiang liberal arts dihedral angle
There are six common methods to make the plane angle of dihedral angle: 1. Define method 2. Vertical plane method 3. Projection theorem 4. Three vertical theorems 5. Vector method 6. The dihedral angle of transformation method is generally on the intersection line of two planes, and appropriate points are taken, which are often endpoints and midpoints. 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 related planes from the graphics, and their areas are easy to get. The coordinates of the normal vector N 1 and N2 of two planes can also be obtained by analytic geometry. 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, then the usual solution of dihedral angle with included angle θ = π-α is: (1) The plane angle of dihedral angle is determined by definition; (2) As a vertical plane of dihedral angle, the angle formed by the intersection of vertical plane and dihedral angle is the plane angle of dihedral angle; (3) Making the plane angle of dihedral angle by using the three perpendicular theorem (inverse theorem); (4) Find the dihedral angle in the space coordinates. Among them, points (1) and (2) mainly calculate the plane angle of dihedral angle according to the definition, and then use the sine and cosine theorem of triangle to solve the triangle. The basic steps to calculate dihedral angle (1) are to make the plane angle of dihedral angle: a) take the midpoint of the base of isosceles triangle as the plane angle; B: Use the vertical line of the plane (three vertical lines theorem or its inverse theorem) as the plane angle; C, a straight line perpendicular to the edge passes through the vertical plane of the edge to form a plane angle; D: Use two parallel lines with dihedral angles without edges as plane angles. (2) Prove that the angle is a plane angle; (3) Inducing into a triangle to find the angle. In addition, it can also be obtained by using space vectors.