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六分仪

六分仪
几何画板及绘图内容加载中，请稍等……
2014-02-18 01:19
角三角函数解析几何
通过调整六分仪，使太阳的像与地平线的像重合。红角表示仰角，此范例演示了仰角与地平线的关系，涉及三角函数和角度概念。使用了交点、圆、旋转、角度、圆弧、线段、线、中点、向量等GeoGebra命令。适合初中及以上学生学习三角函数和几何作图。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, R) → sextantCircle
  3. Point(sextantCircle) → zeroDegrees
  4. Rotate(zeroDegrees, 30*°, O) → zeroDegrees'_1
  5. Angle(zeroDegrees, O, zeroDegrees'_1) → thirtyDegrees2
  6. Rotate(zeroDegrees, 330*°, O) → zeroDegrees'
  7. Angle(zeroDegrees', O, zeroDegrees) → thirtyDegrees1
  8. CircleArc(O, zeroDegrees', zeroDegrees'_1) → sixtantArc
  9. Segment(O, zeroDegrees') → sixtantSegment1
  10. Point(sixtantArc) → A
  11. Segment(O, A) → sixtantSegment2
  12. Point(sixtantArc) → MovablePoint
  13. Point(sixtantSegment1) → mirrorBase
  14. Circle(mirrorBase, r) → c
  15. Line(mirrorBase, yAxis) → verticalMirrorLine
  16. Intersect(c, verticalMirrorLine, 2) → verticalIntersectPoint
  17. Rotate(verticalIntersectPoint, mirrorAngle, mirrorBase) → verticalIntersectPoint'
  18. Angle(verticalIntersectPoint, mirrorBase, verticalIntersectPoint') → mAngle
  19. Circle(O, r / 2) → d
  20. Segment(mirrorBase, verticalIntersectPoint') → mirror1
  21. Midpoint(mirrorBase, verticalIntersectPoint') → mirrorCentre
  22. Line(mirrorCentre, xAxis) → horizonLine
  23. Segment(O, mirrorCentre) → b
  24. Midpoint(O, mirrorCentre) → B
  25. Vector(O, B) → u
  26. OrthogonalLine(mirrorCentre, mirror1) → mirrorNormal
  27. Intersect(c, mirrorNormal, 1) → C
  28. Angle(C, mirrorCentre, O) → angleToNormal
  29. Angle(MovablePoint, O, zeroDegrees'_1) → angleMovable
  30. Point(d) → D
  31. Rotate(D, mirrorAngle - angleMovable, O) → M1
  32. Angle(D, O, M1) → α
  33. Line(M1, O) → e
  34. Intersect(d, e, 2) → M2
  35. Segment(M2, M1) → mirror2
  36. OrthogonalLine(O, mirror2) → mirror2Normal
  37. Intersect(d, mirror2Normal, 2) → E
  38. Angle(E, O, mirrorCentre) → β
  39. Rotate(E, (-β), O) → E'
  40. Angle(E', O, E) → γ
  41. Ray(O, E') → f
  42. Segment(O, MovablePoint) → g
  43. Intersect(d, g, 1) → F
  44. Segment(F, MovablePoint) → h
  45. Point(horizonLine) → HorizonPoint
  46. Line(HorizonPoint, yAxis) → a
  47. Ray(G, H) → i
  48. Point(i) → SunPoint
  49. Point(f) → I
  50. Point(f) → J
  51. Vector(I, J) → v
  52. Point(horizonLine) → K
  53. Circle(SunPoint, r) → k
  54. Segment(SunPoint, O) → j
  55. Intersect(k, j, 1) → L
  56. Mirror(HorizonPoint, yAxis) → HorizonPoint'
  57. Line(HorizonPoint', yAxis) → m
  58. Point(horizonLine) → N
  59. Vector(mirrorCentre, N) → z
  60. Point(horizonLine) → P
  61. Intersect(f, i) → Q
  62. Vector(SunPoint, Q) → p
  63. Translate(HorizonPoint', Vector[(-p)]) → HorizonPoint''
  64. Vector(HorizonPoint', HorizonPoint'') → q
  65. Point(horizonLine) → S
  66. Point(horizonLine) → T
  67. Point(horizonLine) → U
  68. Point(horizonLine) → V
  69. Vector(U, P) → n
  70. Point(horizonLine) → M
  71. Vector(M, K) → w
  72. Segment(K, S) → l
  73. Segment(N, T) → s
  74. Segment(P, V) → t
  75. Rotate(zeroDegrees'_1, 350*°, O) → W
  76. Angle(W, O, zeroDegrees'_1) → δ
  77. Rotate(W, 350*°, O) → W'
  78. Angle(W', O, W) → ε
  79. Rotate(W', 350*°, O) → W''
  80. Angle(W'', O, W') → ζ
  81. Rotate(W'', 350*°, O) → W'''
  82. Angle(W''', O, W'') → η
  83. Rotate(W''', 350*°, O) → Z
  84. Angle(Z, O, W''') → θ
  85. Segment(W, O) → a_1
  86. Segment(W', O) → b_1
  87. Segment(W'', O) → c_1
  88. Segment(W''', O) → d_1
  89. Segment(Z, O) → e_1
  90. Point(xAxis) → A_1
  91. Angle(SunPoint, O, A_1) → ι
  92. Circle(MovablePoint, 1.5) → f_1
  93. Line(O, MovablePoint) → g_1
  94. Intersect(f_1, g_1, 2) → textPoint