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通过三角形寻找圆面积公式

通过三角形寻找圆面积公式
几何画板及绘图内容加载中，请稍等……
2017-09-09 06:41
测试改名0圆几何作图
①本范例通过动态演示三角形旋转构成圆形的过程，直观展示圆面积公式的推导；②涉及核心数学概念包括圆、三角形、旋转、勾股定理等；③作图要点提炼自构造摘要，使用了Min、Circle、Rotate、CircleArc、Segment等GeoGebra命令与对象；④适合高中数学教学，用于帮助学生理解圆面积公式的几何意义和推导过程。

GeoGebra 命令及参数

  1. Min(a - 1, -0.01) → a_1
  2. Circle(A, B) → c
  3. Rotate(B, ((2 * π) * x(B) / ((-x(A)) + x(B))), A) → B'
  4. CircleArc(A, B, B') → d
  5. Segment(B, C) → b
  6. CircleArc(A, B, B') → g
  7. Segment(B, C) → h
  8. Circle(A, B) → k
  9. Segment(A2, B2) → C2
  10. Rotate(A2, ((2 * π) * x(A2) / ((-x(A)) + x(A2))), A) → D2
  11. Rotate(A3, ((2 * π) * x(A3) / ((-x(A)) + x(A3))), A) → D3
  12. Rotate(A4, ((2 * π) * x(A4) / ((-x(A)) + x(A4))), A) → D4
  13. Rotate(A5, ((2 * π) * x(A5) / ((-x(A)) + x(A5))), A) → D5
  14. Rotate(A6, ((2 * π) * x(A6) / ((-x(A)) + x(A6))), A) → D6
  15. Rotate(A7, ((2 * π) * x(A7) / ((-x(A)) + x(A7))), A) → D7
  16. Rotate(A8, ((2 * π) * x(A8) / ((-x(A)) + x(A8))), A) → D8
  17. Rotate(A9, ((2 * π) * x(A9) / ((-x(A)) + x(A9))), A) → D9
  18. Rotate(A10, ((2 * π) * x(A10) / ((-x(A)) + x(A10))), A) → D10
  19. Rotate(A11, ((2 * π) * x(A11) / ((-x(A)) + x(A11))), A) → D11
  20. Rotate(A12, ((2 * π) * x(A12) / ((-x(A)) + x(A12))), A) → D12
  21. Rotate(A13, ((2 * π) * x(A13) / ((-x(A)) + x(A13))), A) → D13
  22. Rotate(A14, ((2 * π) * x(A14) / ((-x(A)) + x(A14))), A) → D14
  23. Rotate(A15, ((2 * π) * x(A15) / ((-x(A)) + x(A15))), A) → D15
  24. Rotate(A16, ((2 * π) * x(A16) / ((-x(A)) + x(A16))), A) → D16
  25. Rotate(A17, ((2 * π) * x(A17) / ((-x(A)) + x(A17))), A) → D17
  26. Rotate(A18, ((2 * π) * x(A18) / ((-x(A)) + x(A18))), A) → D18
  27. Rotate(A19, ((2 * π) * x(A19) / ((-x(A)) + x(A19))), A) → D19
  28. Rotate(A20, ((2 * π) * x(A20) / ((-x(A)) + x(A20))), A) → D20
  29. Rotate(A21, ((2 * π) * x(A21) / ((-x(A)) + x(A21))), A) → D21
  30. Rotate(A22, ((2 * π) * x(A22) / ((-x(A)) + x(A22))), A) → D22
  31. Rotate(A23, ((2 * π) * x(A23) / ((-x(A)) + x(A23))), A) → D23
  32. Rotate(A24, ((2 * π) * x(A24) / ((-x(A)) + x(A24))), A) → D24
  33. Rotate(A25, ((2 * π) * x(A25) / ((-x(A)) + x(A25))), A) → D25
  34. Rotate(A26, ((2 * π) * x(A26) / ((-x(A)) + x(A26))), A) → D26
  35. Rotate(A27, ((2 * π) * x(A27) / ((-x(A)) + x(A27))), A) → D27
  36. Rotate(A28, ((2 * π) * x(A28) / ((-x(A)) + x(A28))), A) → D28
  37. Rotate(A29, ((2 * π) * x(A29) / ((-x(A)) + x(A29))), A) → D29
  38. Rotate(A30, ((2 * π) * x(A30) / ((-x(A)) + x(A30))), A) → D30
  39. Rotate(A31, ((2 * π) * x(A31) / ((-x(A)) + x(A31))), A) → D31
  40. CircleArc(A, A2, D2) → E2
  41. CircleArc(A, A3, D3) → E3
  42. CircleArc(A, A4, D4) → E4
  43. CircleArc(A, A5, D5) → E5
  44. CircleArc(A, A6, D6) → E6
  45. CircleArc(A, A7, D7) → E7
  46. CircleArc(A, A8, D8) → E8
  47. CircleArc(A, A9, D9) → E9
  48. CircleArc(A, A10, D10) → E10
  49. CircleArc(A, A11, D11) → E11
  50. CircleArc(A, A12, D12) → E12
  51. CircleArc(A, A13, D13) → E13
  52. CircleArc(A, A14, D14) → E14
  53. CircleArc(A, A15, D15) → E15
  54. CircleArc(A, A16, D16) → E16
  55. CircleArc(A, A17, D17) → E17
  56. CircleArc(A, A18, D18) → E18
  57. CircleArc(A, A19, D19) → E19
  58. CircleArc(A, A20, D20) → E20
  59. CircleArc(A, A21, D21) → E21
  60. CircleArc(A, A22, D22) → E22
  61. CircleArc(A, A23, D23) → E23
  62. CircleArc(A, A24, D24) → E24
  63. CircleArc(A, A25, D25) → E25
  64. CircleArc(A, A26, D26) → E26
  65. CircleArc(A, A27, D27) → E27
  66. CircleArc(A, A28, D28) → E28
  67. CircleArc(A, A29, D29) → E29
  68. CircleArc(A, A30, D30) → E30
  69. CircleArc(A, A31, D31) → E31
  70. Segment(A3, B3) → C3
  71. Segment(A4, B4) → C4
  72. Segment(A5, B5) → C5
  73. Segment(A6, B6) → C6
  74. Segment(A7, B7) → C7
  75. Segment(A8, B8) → C8
  76. Segment(A9, B9) → C9
  77. Segment(A10, B10) → C10
  78. Segment(A11, B11) → C11
  79. Segment(A12, B12) → C12
  80. Segment(A13, B13) → C13
  81. Segment(A14, B14) → C14
  82. Segment(A15, B15) → C15
  83. Segment(A16, B16) → C16
  84. Segment(A17, B17) → C17
  85. Segment(A18, B18) → C18
  86. Segment(A19, B19) → C19
  87. Segment(A20, B20) → C20
  88. Segment(A21, B21) → C21
  89. Segment(A22, B22) → C22
  90. Segment(A23, B23) → C23
  91. Segment(A24, B24) → C24
  92. Segment(A25, B25) → C25
  93. Segment(A26, B26) → C26
  94. Segment(A27, B27) → C27
  95. Segment(A28, B28) → C28
  96. Segment(A29, B29) → C29
  97. Segment(A30, B30) → C30
  98. Segment(A31, B31) → C31
  99. Circle(A, A2) → F2
  100. Circle(A, A3) → F3
  101. Circle(A, A4) → F4
  102. Circle(A, A5) → F5
  103. Circle(A, A6) → F6
  104. Circle(A, A7) → F7
  105. Circle(A, A8) → F8
  106. Circle(A, A9) → F9
  107. Circle(A, A10) → F10
  108. Circle(A, A11) → F11
  109. Circle(A, A12) → F12
  110. Circle(A, A13) → F13
  111. Circle(A, A14) → F14
  112. Circle(A, A15) → F15
  113. Circle(A, A16) → F16
  114. Circle(A, A17) → F17
  115. Circle(A, A18) → F18
  116. Circle(A, A19) → F19
  117. Circle(A, A20) → F20
  118. Circle(A, A21) → F21
  119. Circle(A, A22) → F22
  120. Circle(A, A23) → F23
  121. Circle(A, A24) → F24
  122. Circle(A, A25) → F25
  123. Circle(A, A26) → F26
  124. Circle(A, A27) → F27
  125. Circle(A, A28) → F28
  126. Circle(A, A29) → F29
  127. Circle(A, A30) → F30
  128. Circle(A, A31) → F31