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寻找表达式：几何与代数结合的探索

寻找表达式：几何与代数结合的探索
几何画板及绘图内容加载中，请稍等……
2025-11-26 03:48
所属专题 Quadratzahlen und Quadratwurzeln
这个范例展示了如何通过几何图形和代数表达式建立联系。核心数学概念包括三角形、圆、多边形、角度和向量。作图要点涉及使用GeoGebra命令如Polygon、Circle、Angle和Vector来构造图形，并结合Length和PointIn等工具进行验证。适合初中生或高中生用于几何作图和代数应用练习。

GeoGebra 命令及参数

  1. SelectedIndex(dropdownStudent2) → Index2
  2. SelectedIndex(dropdownStudent) → studentAnswer
  3. Shuffle({2, 3, 4, 5, 6, 7, 9}) → RandomNormal, {4, 7, 3, 6, 2, 5, 9}
  4. Shuffle({1, 8, 10}) → RandomSchwierig, {10, 1, 8}
  5. Element(randomNumbersQuestion, questionCount) → actualRandomTask
  6. SelectedIndex(dropdownStudent) → Index1
  7. Textfield(input1) → InputBox1
  8. TextToUnicode(Text[InputBox1]) → l2
  9. Translate(BlackBoxE1, (4.35, 4.93)) → BlackBoxE1'
  10. Translate(BlackBoxE2, (4.35, 4.93)) → BlackBoxE2'
  11. Translate(BlackBoxE3, (4.35, 4.93)) → BlackBoxE3'
  12. Translate(BlackBoxE4, (4.35, 4.93)) → BlackBoxE4'
  13. Polygon(LimitBoxE1, LimitBoxE2, LimitBoxE3, LimitBoxE4) → v2, limitboxe1, limitboxe2, limitboxe3, limitboxe4
  14. Circle(Center, 1) → g
  15. IsInRegion(ValPos1, g) → auswahl1
  16. IsInRegion(ValPos2, g) → auswahl2
  17. IsInRegion(ValPos3, g) → auswahl3
  18. IsInRegion(ValPos4, g) → auswahl4
  19. IsInRegion(ValPos5, g) → auswahl5
  20. Length(randomNumbersQuestion) → numberOfQuestions
  21. Shuffle(1…5) → randomNumbersChild, {2, 1, 5, 3, 4}
  22. Shuffle(1…5) → randomNumbersPostIt, {3, 4, 1, 5, 2}
  23. Element(randomNumbersChild, Mod[questionCount, Length[randomNumbersChild]] + 1) → actualRandomChild
  24. Element(randomNumbersPostIt, Mod[questionCount, Length[randomNumbersPostIt]] + 1) → actualRandomPostIt
  25. Polygon(BlackBoxE1, BlackBoxE2, BlackBoxE3, BlackBoxE4) → v1, c, e, f, d
  26. PointIn(v1) → G
  27. Line(E, E + (0, 1)) → h
  28. Point(h) → J
  29. Angle(J, E, G) → α
  30. Rotate(E + (3.21, 4.45), α, E) → F
  31. Line(G, E) → i
  32. OrthogonalLine(G, i) → j
  33. Intersect(g, j) → LightCircP4, LightCircP1
  34. Rotate(E + (-0.44, 2.67), α, E) → LichtStart1
  35. Rotate(E + (-0.44, 2.67), α, E) → O
  36. Rotate(E + (0.21, 2.73), α, E) → LichtStart2
  37. Semicircle(LightCircP1, LightCircP4) → k
  38. Point(k) → LightCircP2
  39. Point(k) → LightCircP3
  40. Segment(LichtMid1, LightCircP2) → ray3
  41. Segment(LichtMid2, LightCircP3) → ray4
  42. Segment(BlackBoxE1, BlackBoxE2) → l
  43. Point(l) → T
  44. Segment(T, BlackBoxE3) → m
  45. Point(m) → U
  46. Segment(U, BlackBoxE4) → n
  47. Point(n) → V
  48. Segment(BlackBoxE1, V) → p
  49. SpeechBubbleRight(W_1, 3, 1) → Vieleck1
  50. SpeechBubbleRight(Z_1, 5.9, If[actualRandomTask ∈ (1…8), 1.3, 1.8]) → Vieleck2
  51. Point(g) → C_2
  52. Point(g) → D_2
  53. Point(g) → E_2
  54. Point(g) → F_2
  55. OrthogonalLine(G_2, Line[G_2, Center]) → r
  56. Point(r) → H_2
  57. Point(r) → I_2
  58. Point(r) → J_2
  59. Point(r) → K_2
  60. Segment(E_2, H_2) → ElRey3
  61. Segment(F_2, I_2) → ElRey4
  62. Segment(C_2, J_2) → ElRey1
  63. Segment(D_2, K_2) → ElRey2
  64. Point(g) → V_2
  65. Sequence(Rotate[V_2, (360° * i / 8), Center], i, 1, 8) → l3
  66. Vector(NewTopDog, M_2) → vv1
  67. Vector(NewTopDog, N_2) → vv2
  68. Vector(NewTopDog, Q_2) → vv3
  69. Vector(NewTopDog, O_2) → vv4
  70. Vector(NewTopDog, P_2) → vv5
  71. Vector(NewTopDog, R_2) → vv6
  72. Vector(NewTopDog, S_2) → vv7
  73. Vector(NewTopDog, T_2) → vv8
  74. Vector(NewTopDog, V_2) → vv9
  75. Vector(NewTopDog, l3(1)) → vv10
  76. Vector(NewTopDog, l3(2)) → vv11
  77. Vector(NewTopDog, l3(3)) → vv12
  78. Vector(NewTopDog, l3(4)) → vv13
  79. Vector(NewTopDog, l3(5)) → vv14
  80. Vector(NewTopDog, l3(6)) → vv15
  81. Vector(NewTopDog, l3(7)) → vv16
  82. Vector(NewTopDog, FlashL1) → u
  83. Vector(NewTopDog, FlashL2) → v
  84. Vector(NewTopDog, Center) → w
  85. Vector(Center, NewTopDog) → q
  86. Polygon(NewTopDog, NewTopDog + (-0.95, -1.03), NewTopDog + (-1.45, -1.17), NewTopDog + (-1.54, -1.54), NewTopDog + (-1.34, -1.76), NewTopDog + (-1.34, -1.76), NewTopDog + (-0.99, -2.02), NewTopDog + (-0.62, -1.85), NewTopDog + (-0.59, -1.52), NewTopDog + (0.31, -0.38)) → MagnumOpus, s, m_1, t, f_1, g_1, h_1, i_1, j_1, k_1, l_1
  87. Vector(NewTopDog, T_2) → u_1
  88. Length(Opt1List(actualRandomTask)) → lengthOpt1
  89. Length(Opt2List(actualRandomTask)) → lengthOpt2
  90. Length(Opt3List(actualRandomTask)) → lengthOpt3
  91. Length(Opt4List(actualRandomTask)) → lengthOpt4
  92. Length(Opt5List(actualRandomTask)) → lengthOpt5