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Finding Expressions: Geometric and Algebraic Exploration

Finding Expressions: Geometric and Algebraic Exploration
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2025-11-26 03:48
In collections Quadratzahlen und Quadratwurzeln
This example demonstrates how geometric shapes and algebraic expressions can be connected. Key mathematical concepts include triangles, circles, polygons, angles, and vectors. Construction involves using GeoGebra commands like Polygon, Circle, Angle, and Vector, along with Length and PointIn for verification. Suitable for middle school or high school students for geometric construction and algebra

GeoGebra Commands & Parameters

  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