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Ellipse Area Seen by Circle

Ellipse Area Seen by Circle
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2020-06-21 15:33
CircleCoordinate GeometryTransformationGeometric Construction
This example demonstrates how the area of an ellipse changes when viewed from a circle. It involves core math concepts like ellipse, circle, area calculation, and geometric transformation. Construction uses commands/objects such as Point, Segment, OrthogonalLine, Vector, Sequence, Conic, Sum, Element, Circumference, Midpoint in GeoGebra. Suitable for high school and above students to understand geometric transformations and area relationships.

GeoGebra Commands & Parameters

  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