积极 AI Logo 积极 AI

圆视角下的椭圆面积

圆视角下的椭圆面积
几何画板及绘图内容加载中，请稍等……
2020-06-21 15:33
圆解析几何变换几何作图
①本范例演示了从圆形视角观察椭圆时面积的变化；②涉及核心数学概念包括椭圆、圆、面积计算、几何变换；③构造要点：使用Point, Segment, OrthogonalLine, Vector, Sequence, Conic, Sum, Element, Circumference, Midpoint等GeoGebra命令和对象；④适合高中及以上学生学习和理解几何变换与面积关系。

GeoGebra 命令及参数

  1. Point(yAxis) → C
  2. Segment(A, C) → g
  3. Segment(A + (g, 0), F) → j
  4. Point(j) → B
  5. Segment(A, B) → f
  6. OrthogonalLine(A, f) → h
  7. Vector(A, B) → u
  8. Vector(A, C) → v
  9. Sequence(A + (cos(k) * u) + (sin(k) * v), k, 0, (2 * π), (2 * π / n)) → l1
  10. Conic(Element[l1, 1], Element[l1, 2], Element[l1, 3], Element[l1, 4], Element[l1, 5]) → c
  11. Sequence(Arc[c, Element[l1, i], Element[l1, i + 1]], i, 1, Length[l1]) → l2
  12. Sum(l2) → a
  13. Sequence(Segment[A, Element[l1, i]], i, 1, Length[l1]) → l3
  14. Element(l2, A1) → B1
  15. Element(l2, A2) → B2
  16. Element(l2, A3) → B3
  17. Element(l2, A4) → B4
  18. Element(l2, A5) → B5
  19. Element(l2, A6) → B6
  20. Element(l2, A7) → B7
  21. Element(l2, A8) → B8
  22. Element(l2, A9) → B9
  23. Element(l2, A10) → B10
  24. Element(l2, A11) → B11
  25. Element(l2, A12) → B12
  26. Element(l2, A13) → B13
  27. Element(l2, A14) → B14
  28. Element(l2, A15) → B15
  29. Element(l2, A16) → B16
  30. Element(l2, A17) → B17
  31. Element(l2, A18) → B18
  32. Element(l2, A19) → B19
  33. Element(l2, A20) → B20
  34. Element(l2, A21) → B21
  35. Element(l2, A22) → B22
  36. Element(l2, A23) → B23
  37. Element(l2, A24) → B24
  38. Element(l2, A25) → B25
  39. Element(l2, A26) → B26
  40. Element(l2, A27) → B27
  41. Element(l2, A28) → B28
  42. Element(l2, A29) → B29
  43. Element(l2, A30) → B30
  44. Element(l2, A31) → B31
  45. Element(l2, A32) → B32
  46. Element(l2, A33) → B33
  47. Element(l2, A34) → B34
  48. Element(l2, A35) → B35
  49. Element(l2, A36) → B36
  50. Element(l2, A37) → B37
  51. Element(l2, A38) → B38
  52. Element(l2, A39) → B39
  53. Element(l2, A40) → B40
  54. Element(l2, A41) → B41
  55. Element(l2, A42) → B42
  56. Element(l2, A43) → B43
  57. Element(l2, A44) → B44
  58. Element(l2, A45) → B45
  59. Element(l2, A46) → B46
  60. Element(l2, A47) → B47
  61. Element(l2, A48) → B48
  62. Element(l2, A49) → B49
  63. Element(l2, A50) → B50
  64. Circumference(c) → b
  65. Sequence(Sector[c, Element[l1, i], Element[l1, i + 1]], i, 1, Length[l1]) → l5
  66. Sum(l5) → i
  67. Element(l5, A1) → C1
  68. Element(l5, A2) → C2
  69. Element(l5, A3) → C3
  70. Element(l5, A4) → C4
  71. Element(l5, A5) → C5
  72. Element(l5, A6) → C6
  73. Element(l5, A7) → C7
  74. Element(l5, A8) → C8
  75. Element(l5, A9) → C9
  76. Element(l5, A10) → C10
  77. Element(l5, A11) → C11
  78. Element(l5, A12) → C12
  79. Element(l5, A13) → C13
  80. Element(l5, A14) → C14
  81. Element(l5, A15) → C15
  82. Element(l5, A16) → C16
  83. Element(l5, A17) → C17
  84. Element(l5, A18) → C18
  85. Element(l5, A19) → C19
  86. Element(l5, A20) → C20
  87. Element(l5, A21) → C21
  88. Element(l5, A22) → C22
  89. Element(l5, A23) → C23
  90. Element(l5, A24) → C24
  91. Element(l5, A25) → C25
  92. Element(l5, A26) → C26
  93. Element(l5, A27) → C27
  94. Element(l5, A28) → C28
  95. Element(l5, A29) → C29
  96. Element(l5, A30) → C30
  97. Element(l5, A31) → C31
  98. Element(l5, A32) → C32
  99. Element(l5, A33) → C33
  100. Element(l5, A34) → C34
  101. Element(l5, A35) → C35
  102. Element(l5, A36) → C36
  103. Element(l5, A37) → C37
  104. Element(l5, A38) → C38
  105. Element(l5, A39) → C39
  106. Element(l5, A40) → C40
  107. Element(l5, A41) → C41
  108. Element(l5, A42) → C42
  109. Element(l5, A43) → C43
  110. Element(l5, A44) → C44
  111. Element(l5, A45) → C45
  112. Element(l5, A46) → C46
  113. Element(l5, A47) → C47
  114. Element(l5, A48) → C48
  115. Element(l5, A49) → C49
  116. Element(l5, A50) → C50
  117. Midpoint(f) → D
  118. Midpoint(g) → E