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混合圆题袋：圆面积计算与作图练习

混合圆题袋：圆面积计算与作图练习
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2024-12-19 16:42
所属专题 Kreis Umfang und Flächeninhalt
这个范例演示了如何通过几何作图计算圆的面积，特别是半圆、四分之一圆和八分之一圆的面积。核心数学概念包括圆的面积公式、近似计算方法以及几何作图技巧。作图要点包括使用GeoGebra命令如Polygon、PointIn、IsInRegion等来构造圆和区域，并标注面积计算步骤。适合小学7-8年级学生用于几何学习练习和课堂活动。

GeoGebra 命令及参数

  1. Polygon(TüteBound1_{4}, TüteBound1_1, TüteBound1_2, TüteBound1_3) → TüteBound1, tütebound1_{4}, tütebound1_1, tütebound1_2, tütebound1_3
  2. PointIn(TüteBound1) → Zettel1Anchor_1
  3. Polygon(Zettel1Anchor_1, Zettel1Anchor_2, Zettel1Anchor_3, Zettel1Anchor_4) → Zettel1, zettel1anchor_1, zettel1anchor_2, zettel1anchor_3, zettel1anchor_4
  4. PointIn(TüteBound1) → Zettel2Anchor_1
  5. PointIn(TüteBound1) → Zettel3Anchor_1
  6. PointIn(TüteBound1) → Zettel4Anchor_1
  7. Polygon(Zettel2Anchor_1, Zettel2Anchor_2, Zettel2Anchor_3, Zettel2Anchor_4) → Zettel2, zettel2anchor_1, zettel2anchor_2, zettel2anchor_3, zettel2anchor_4
  8. Polygon(Zettel3Anchor_1, Zettel3Anchor_2, Zettel3Anchor_3, Zettel3Anchor_4) → Zettel3, zettel3anchor_1, zettel3anchor_2, zettel3anchor_3, zettel3anchor_4
  9. Polygon(Zettel4Anchor_1, Zettel4Anchor_2, Zettel4Anchor_3, Zettel4Anchor_4) → Zettel4, zettel4anchor_1, zettel4anchor_2, zettel4anchor_3, zettel4anchor_4
  10. Polygon(TüteBound2_1, TüteBound2_2, TüteBound2_3, TüteBound2_4) → TüteBound2, tütebound2_1, tütebound2_2, tütebound2_3, tütebound2_4
  11. PointIn(TüteBound2) → Zettel5Anchor_1
  12. PointIn(TüteBound2) → Zettel6Anchor_1
  13. PointIn(TüteBound2) → Zettel7Anchor_1
  14. PointIn(TüteBound2) → Zettel8Anchor_1
  15. Polygon(Zettel5Anchor_1, Zettel5Anchor_2, Zettel5Anchor_3, Zettel5Anchor_4) → Zettel5, zettel5anchor_1, zettel5anchor_2, zettel5anchor_3, zettel5anchor_4
  16. Polygon(Zettel6Anchor_1, Zettel6Anchor_2, Zettel6Anchor_3, Zettel6Anchor_4) → Zettel6, zettel6anchor_1, zettel6anchor_2, zettel6anchor_3, zettel6anchor_4
  17. Polygon(Zettel7Anchor_1, Zettel7Anchor_2, Zettel7Anchor_3, Zettel7Anchor_4) → Zettel7, zettel7anchor_1, zettel7anchor_2, zettel7anchor_3, zettel7anchor_4
  18. Polygon(Zettel8Anchor_1, Zettel8Anchor_2, Zettel8Anchor_3, Zettel8Anchor_4) → Zettel8, zettel8anchor_1, zettel8anchor_2, zettel8anchor_3, zettel8anchor_4
  19. Polygon(DecisionBound_1, DecisionBound_2, DecisionBound_3, DecisionBound_4) → DecisionArea, decisionbound_1, decisionbound_2, decisionbound_3, decisionbound_4
  20. IsInRegion(Zettel1Anchor_1, DecisionArea) → zettel1dec
  21. IsInRegion(Zettel2Anchor_1, DecisionArea) → zettel2dec
  22. IsInRegion(Zettel3Anchor_1, DecisionArea) → zettel3dec
  23. IsInRegion(Zettel4Anchor_1, DecisionArea) → zettel4dec
  24. IsInRegion(Zettel5Anchor_1, DecisionArea) → zettel5dec
  25. IsInRegion(Zettel6Anchor_1, DecisionArea) → zettel6dec
  26. IsInRegion(Zettel7Anchor_1, DecisionArea) → zettel7dec
  27. IsInRegion(Zettel8Anchor_1, DecisionArea) → zettel8dec
  28. Polygon(AngabeAnchor_1, AngabeAnchor_2, AngabeAnchor_3, AngabeAnchor_4) → Angabe, angabeanchor_1, angabeanchor_2, angabeanchor_3, angabeanchor_4
  29. Segment(UmrandungAnchor_1, UmrandungAnchor_2) → Umrandung_1
  30. Segment(UmrandungAnchor_2, UmrandungAnchor_{4}) → Umrandung_2
  31. Segment(UmrandungAnchor_{4}, UmrandungAnchor_3) → Umrandung_3
  32. Segment(UmrandungAnchor_3, UmrandungAnchor_1) → Umrandung_4
  33. Textfield(input1) → InputBox1
  34. Textfield(input2) → InputBox2
  35. Textfield(input3) → InputBox3
  36. If(aufgabeNum ≟ 1, Defined[input1], aufgabeNum ≟ 6, Defined[input6], aufgabeNum ≟ 7, Defined[input7], aufgabeNum ≟ 8, Defined[input8], false, aufgabeNum ≟ 2, Defined[input2], aufgabeNum ≟ 3, Defined[input3], aufgabeNum ≟ 4, Defined[input4], aufgabeNum ≟ 5, Defined[input5]) → fixed
  37. Segment(PosA1 + (0, (-dis)), PosA1 + (radius1, (-dis))) → seg11
  38. Segment(PosA1 + (radius1, (-dis)), PosA1 + ((2 * radius1), (-dis))) → seg12
  39. Segment(PosA1 + ((2 * radius1), (-dis)), PosA1 + ((3 * radius1), (-dis))) → seg13
  40. Segment(PosA1 + ((3 * radius1) + dis, 0), PosA1 + ((3 * radius1) + dis, (2 * radius1))) → seg14
  41. Textfield(input7) → InputBox7
  42. Segment(PosA7 + ((-2 * radius7), radius7 + dis), PosA7 + (0, radius7 + dis)) → seg71
  43. Segment(PosA7 + ((0 * radius7), radius7 + dis), PosA7 + ((2 * radius7), radius7 + dis)) → seg72
  44. Segment(PosA3 + ((-radius3), radius3 + dis), PosA3 + (0, radius3 + dis)) → seg31
  45. Segment(PosA3 + (0, radius3 + dis), PosA3 + (radius3, radius3 + dis)) → seg32
  46. Segment(PosA3 + (radius3 + dis, radius3), PosA3 + (radius3 + dis, 0)) → seg33
  47. Segment(PosA3 + (radius3 + dis, 0), PosA3 + (radius3 + dis, (-radius3))) → seg34
  48. Segment(PosA2 + (0, (-dis)), PosA2 + ((2 * radius2), (-dis))) → seg21
  49. Segment(PosA2 + ((2 * radius2) + dis, 0), PosA2 + ((2 * radius2) + dis, radius2 / 2)) → seg22
  50. Segment(PosA2 + ((2 * radius2) + dis, radius2 / 2 + radius2), PosA2 + ((2 * radius2) + dis, radius2 / 2)) → seg23
  51. Textfield(input5) → InputBox5
  52. Segment(PosA5 + ((0 * radius5), (-dis)), PosA5 + ((1 * radius5), (-dis))) → seg51
  53. Segment(PosA5 + ((1 * radius5), (-dis)), PosA5 + ((2 * radius5), (-dis))) → seg52
  54. Segment(PosA5 + ((2 * radius5), (-dis)), PosA5 + ((3 * radius5), (-dis))) → seg53
  55. Segment(PosA5 + ((3 * radius5) + dis, (0 * radius5)), PosA5 + ((3 * radius5) + dis, (1 * radius5))) → seg54
  56. Segment(PosA5 + ((3 * radius5) + dis, (1 * radius5)), PosA5 + ((3 * radius5) + dis, (2 * radius5))) → seg55
  57. Segment(PosA5 + ((3 * radius5) + dis, (2 * radius5)), PosA5 + ((3 * radius5) + dis, (3 * radius5))) → seg56
  58. Textfield(input4) → InputBox4
  59. Segment(PosA4 + (0, (-radius4) - dis), PosA4 + ((2 * radius4), (-radius4) - dis)) → seg41
  60. Segment(PosA4 + ((4 * radius4), (-radius4) - dis), PosA4 + ((2 * radius4), (-radius4) - dis)) → seg42
  61. Segment(PosA4 + ((4 * radius4) + dis, 0), PosA4 + ((4 * radius4) + dis, radius4)) → seg44
  62. Segment(PosA4 + ((4 * radius4) + dis, (-radius4)), PosA4 + ((4 * radius4) + dis, 0)) → seg43
  63. Textfield(input6) → InputBox6
  64. Segment(PosA6 + (0, (5 * radius6) + dis), PosA6 + ((0.25 * radius6), (5 * radius6) + dis)) → seg61
  65. Segment(PosA6 + ((0.25 * radius6), (5 * radius6) + dis), PosA6 + ((2.25 * radius6), (5 * radius6) + dis)) → seg62
  66. Segment(PosA6 + ((2.25 * radius6), (5 * radius6) + dis), PosA6 + ((2.75 * radius6), (5 * radius6) + dis)) → seg63
  67. Segment(PosA6 + ((2.75 * radius6), (5 * radius6) + dis), PosA6 + ((4.75 * radius6), (5 * radius6) + dis)) → seg64
  68. Segment(PosA6 + ((4.75 * radius6), (5 * radius6) + dis), PosA6 + ((5 * radius6), (5 * radius6) + dis)) → seg65
  69. Segment(PosA6 + ((5 * radius6) + dis, (5 * radius6)), PosA6 + ((5 * radius6) + dis, (5 * radius6) - (0.25 * radius6))) → seg66
  70. Segment(PosA6 + ((5 * radius6) + dis, (4.75 * radius6)), PosA6 + ((5 * radius6) + dis, (2.75 * radius6))) → seg67
  71. Segment(PosA6 + ((5 * radius6) + dis, (2.75 * radius6)), PosA6 + ((5 * radius6) + dis, (2.25 * radius6))) → seg68
  72. Segment(PosA6 + ((5 * radius6) + dis, (2.25 * radius6)), PosA6 + ((5 * radius6) + dis, (0.25 * radius6))) → seg69
  73. Segment(PosA6 + ((5 * radius6) + dis, (0.25 * radius6)), PosA6 + ((5 * radius6) + dis, (0 * radius6))) → seg610
  74. Segment(PosA8 + (0, (-dis)), PosA8 + ((5 / 9 * radius8), (-dis))) → seg81
  75. Segment(PosA8 + ((5 / 9 * radius8), (-dis)), PosA8 + (radius8 + (4 / 9 * radius8), (-dis))) → seg82
  76. Segment(PosA8 + (radius8 + (4 / 9 * radius8), (-dis)), PosA8 + ((2 * radius8), (-dis))) → seg83
  77. Segment(PosA8 + ((2 * radius8) + dis, 0), PosA8 + ((2 * radius8) + dis, radius8)) → seg84
  78. Textfield(input8) → InputBox8
  79. Text("\textsf{m²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit8
  80. Text("\textsf{cm²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit6
  81. Text("\textsf{m²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit5
  82. Text("\textsf{cm²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit1
  83. Text("\textsf{dm}", PosIB + (2.6, 0.15), false, true, 1, -1) → txtUnit7
  84. Text("\textsf{mm}", PosIB + (2.6, 0.1), false, true, 1, -1) → txtUnit2
  85. Text("\textsf{m²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit4
  86. Text("\textsf{dm²}", PosIB + (2.6, 0.125), false, true, 1, -1) → txtUnit3