五分钟计时器

五分钟计时器
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2017-01-23 14:32
①本范例演示如何通过 GeoGebra 构建一个五分钟计时器;②涉及的核心数学概念包括角度、时间计算、几何变换;③作图要点:使用了 Random, If, Circle, Rotate, Tangent, Intersect, Dilate, Polygon, Semicircle, Line, OrthogonalLine, Midpoint, Textfield, Ellipse, Sequence 等命令和对象;④适合初中数学教学,用于理解时间与角度的关系及几何作图技巧。

GeoGebra 命令及参数

  1. Random(0, 11) → A16
  2. If(counterlevel < 6, (Random[0, 3] * 15), (Random[0, 11] * 5)) → B16
  3. Circle(A, 0.05) → r6
  4. Rotate(C, (-C17), A) → C'
  5. Tangent(C', r6) → t7, t1
  6. Intersect(r6, t7) → Z
  7. Dilate(Z, 1.15, C') → F
  8. Intersect(r6, t1) → X
  9. Dilate(X, 1.15, C') → E
  10. Circle(A, 0.15) → r7
  11. Rotate(D, (-B17), A) → D'
  12. Tangent(D', r7) → t3, t6
  13. Intersect(r7, t3) → J
  14. Dilate(J, 1.1, D') → M
  15. Intersect(r7, t6) → H
  16. Dilate(H, 1.1, D') → N
  17. Circle(A, 5) → r1
  18. Circle(A, 4.3) → r2
  19. Polygon(F, E, C') → tg1, d10, d11, d13
  20. Polygon(D', N, M) → tg2, d4, d6, d3
  21. Circle(A, 0.2) → r8
  22. Rotate(B, (-A17), A) → B'
  23. Tangent(B', r8) → t8, t2
  24. Intersect(r8, t8) → K
  25. Intersect(r8, t2) → L
  26. Dilate(K, 1.12, B') → G
  27. Dilate(L, 1.12, B') → I
  28. Polygon(I, G, B') → tg3, d7, d2, d1
  29. Rotate(D, 30°, A) → DA
  30. Rotate(DA, 30°, A) → DB
  31. Rotate(DB, 30°, A) → DC
  32. Rotate(DC, 30°, A) → DD
  33. Rotate(DD, 30°, A) → DE
  34. Rotate(DE, 30°, A) → DF
  35. Rotate(DF, 30°, A) → DG
  36. Rotate(DG, 30°, A) → DH
  37. Rotate(DH, 30°, A) → DI
  38. Rotate(DI, 30°, A) → DJ
  39. Rotate(DJ, 30°, A) → DK
  40. Circle(A, 5.1) → r3
  41. Semicircle(I, G) → z1
  42. Semicircle(I, G) → z2
  43. Intersect(r3, r2) → O, , ,
  44. Line(D, DF) → t4
  45. Intersect(r3, t4) → P, Q
  46. OrthogonalLine(Q, t4) → t5
  47. Midpoint(T, R) → V
  48. Midpoint(U, S) → W
  49. Circle(V, R) → r4
  50. Circle(W, S) → r5
  51. Polygon(T, R, S, U) → tg4, d9, d5, d8, d12
  52. Semicircle(T, R) → z3
  53. Semicircle(S, U) → z4
  54. If(A16 < 10, "0" + A16, "" + A16) → A18
  55. If(B16 < 10, "0" + B16, "" + B16) → B18
  56. If(C16 < 10, "0" + C16, "" + C16) → C18
  57. Textfield(userinputhour) → InputBox1
  58. Textfield(userinputminute) → InputBox2
  59. If(useranswerhour ≟ A16, true, false) → answerhourcorrect
  60. If(useranswerminute ≟ B16, true, false) → answerminutecorrect
  61. Polygon(D', N, M) → tg2_{err}, m_1, d', n
  62. Polygon(I, G, B') → tg3_{err}, b', i, g
  63. If(answerhourcorrect, false, If[answerminutecorrect, false, true]) → answerbothwrong
  64. Midpoint(A, D') → M_{AD'}
  65. Rotate(M_{AD'}, -15°, A) → M_{D}
  66. Ellipse(A, D', M_{D}) → d
  67. Midpoint(A, B') → M_{AB'}
  68. Rotate(M_{AB'}, -45°, A) → M_{B'}
  69. Ellipse(A, B', M_{B'}) → e
  70. Sequence(Rotate[D, (-6° * i), A], i, 1, 60) → Li2
  71. Circle(Element[Li2, If[A16 ≟ 0, 60, (A16 * 5)]], 0.7) → f

AI 绘图提示语参考

画一个五分钟计时器,包含一个中心圆和多个旋转角度标记,通过圆、旋转、切线和相交等操作构建,展示时间与角度的关系,最终形成计时器的几何形态。
以上提示语为根据原始绘图命令整理而来,仅供参考。