方位角动态演示 by Tim Brzezinski

方位角动态演示 by Tim Brzezinski
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2017-08-26 11:52
该范例演示从点A到点B,再到点C的方位角和距离。涉及的核心数学概念包括角度、向量和三角函数。使用了Circle, Intersect, Rotate, Dilate, Segment, Angle, Textfield等GeoGebra命令。适合初中及以上学生学习方位角和向量的相关知识。

GeoGebra 命令及参数

  1. Circle(A, a) → c
  2. Intersect(c, f, 1) → B
  3. Rotate(B, ((-b) * π / 180), A) → B'
  4. Circle(B', d) → e
  5. Intersect(e, h, 1) → C
  6. Rotate(C, ((-j) * π / 180), B') → C'
  7. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], B) → A'
  8. Segment(A, A') → l
  9. Angle(B', A, B) → α
  10. Angle(C', B', C) → β
  11. Rotate(B, If[1 < k ≤ 2, ((-(k - 1)) * α), (-α)], A) → B'_1
  12. Angle(B'_1, A, B) → γ
  13. Segment(A, B'_1) → m
  14. Dilate(B', If[2 < k ≤ 3, 3 - k, 0], C) → B''
  15. Segment(B', B'') → n
  16. Rotate(C, If[3 < k ≤ 4, ((-(k - 3)) * β), (-β)], B') → C'_1
  17. Angle(C'_1, B', C) → δ
  18. Segment(B', C'_1) → p
  19. Segment(A, C') → q
  20. Angle(C', A, B) → ε
  21. Textfield(a) → InputBox1
  22. Textfield(b) → InputBox2
  23. Textfield(d) → InputBox3
  24. Textfield(j) → InputBox4
  25. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C'_1) → A'_1
  26. Segment(A, A'_1) → r
  27. Circle(A, C') → s
  28. Intersect(s, f) → D, E
  29. Rotate(D, If[1 < o ≤ 2, ((-(o - 1)) * ε), (-ε)], A) → D'
  30. Angle(D', A, D) → η