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平面夹角计算

平面夹角计算
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2019-01-30 08:54
向量立体几何几何作图
①本范例演示了如何计算两个平面之间的夹角；②涉及的核心数学概念包括向量点积、法向量、余弦定理；③作图要点——从下方『构造摘要』提炼用到了Segment, Circle, Point, Angle, Vector, Polygon, Ray, Intersect等GeoGebra命令/对象；④适合高中立体几何教学和几何作图练习。

GeoGebra 命令及参数

  1. Segment(rotateLRc, rotateLR0) → a
  2. Circle(rotateLRc, rotateLR0) → c
  3. Point(c) → rotateLR
  4. Angle(rotateLR0, rotateLRc, rotateLR) → α
  5. Segment(rotateLRc, rotateLR) → b
  6. Circle(rotateUDc, rotateUD0) → d
  7. Point(d) → rotateUD
  8. Angle(rotateUD0, rotateUDc, rotateUD) → β
  9. Segment(rotateUDc, rotateUD0) → e
  10. Segment(rotateUDc, rotateUD) → f
  11. Vector(O, O + (0, sin(β))) → Oz
  12. Vector(O, O + (cos(α), (sin(α) * cos(β)))) → Ox
  13. Vector(O, O + ((-1 * sin(α)), (cos(α) * cos(β)))) → Oy
  14. Polygon(A1, A3, A4, A6) → poly1, a1, a3, a4, a6
  15. Polygon(A10, A12, A13, A15) → poly2, a10, a12, a13, a15
  16. Angle(A14, P, A2) → θ_1
  17. Ray(P, A14) → i
  18. Ray(P, A2) → j
  19. Point(j) → C
  20. Point(i) → R
  21. Circle(P, 4) → k
  22. Intersect(k, j, 1) → Q
  23. Segment(A, B) → l
  24. Segment(A16, A18) → m
  25. Segment(A18, A17) → n
  26. Segment(A19, A21) → p
  27. Segment(A21, A20) → q