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Circle to Parallelogram

Circle to Parallelogram
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2014-11-26 01:26
CirclePolygonGeometric Construction
This example demonstrates how to transform a circle into a parallelogram using geometric constructions. Key mathematical concepts include properties of circles, definitions of parallelograms, and geometric transformations. Construction involves GeoGebra commands such as Circle, Segment, OrthogonalLine, Rotate, etc., to create objects like A, B, C, D. Suitable for middle or high school mathematics to understand geometric transformations and relationships.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(A, B) → a
  3. OrthogonalLine(B, a) → b
  4. OrthogonalLine(A, a) → d
  5. Intersect(c, d, 2) → C
  6. Intersect(c, d, 1) → D
  7. Rotate(D, -22.5°, A) → D'_1
  8. Rotate(D, 22.5°, A) → D'
  9. Rotate(C, 15°, A) → C'
  10. Rotate(C, -15°, A) → C'_1
  11. Segment(A, D'_1) → e
  12. Segment(A, D') → f
  13. CircleArc(A, D'_1, D') → g
  14. Mirror(g, b) → g'
  15. Mirror(A, b) → A'
  16. Mirror(D'_1, b) → E
  17. Segment(A', E) → e'
  18. Mirror(A, b) → A'_1
  19. Mirror(D', b) → D''
  20. Segment(A'_1, D'') → f'
  21. Mirror(D, b) → D'_2
  22. Vector(E, A') → u
  23. Translate(g', u) → g''
  24. Translate(A', u) → A''
  25. Translate(E, u) → E'
  26. Segment(A'', E') → e''
  27. Translate(A'_1, u) → F
  28. Translate(D'', u) → D'''
  29. Segment(F, D''') → f''
  30. Translate(D'_2, u) → G
  31. Rotate(g'', -180°, A') → g'''
  32. Rotate(A'', -180°, A') → A'''
  33. Rotate(E', -180°, A') → E''
  34. Segment(A''', E'') → e'''
  35. Rotate(F, -180°, A') → F'
  36. Rotate(D''', -180°, A') → H
  37. Segment(F', H) → f'''
  38. Rotate(A'_1, -180°, A') → I
  39. Rotate(G, -180°, A') → G'
  40. Line(H, b) → h
  41. Mirror(g', h) → g''_1
  42. Mirror(g''', h) → k
  43. Mirror(A', h) → A''_1
  44. Mirror(E, h) → E'_1
  45. Segment(A''_1, E'_1) → e''_1
  46. Mirror(A'_1, h) → J
  47. Mirror(D'', h) → D'''_1
  48. Segment(J, D'''_1) → f''_1
  49. Mirror(A''', h) → K
  50. Mirror(E'', h) → E'''
  51. Segment(K, E''') → i
  52. Mirror(F', h) → F''
  53. Mirror(H, h) → H'
  54. Segment(F'', H') → j
  55. Mirror(u, h) → u'
  56. Mirror(D'_2, h) → L
  57. Mirror(E', h) → E''_1
  58. Mirror(I, h) → I'
  59. Line(D'''_1, h) → l
  60. Mirror(g''_1, l) → p
  61. Mirror(k, l) → k'
  62. Mirror(A''_1, l) → M
  63. Mirror(E'_1, l) → N
  64. Segment(M, N) → m
  65. Mirror(J, l) → J'
  66. Mirror(D'''_1, l) → O
  67. Segment(J', O) → n
  68. Mirror(K, l) → K'
  69. Mirror(E''', l) → P
  70. Segment(K', P) → i'
  71. Mirror(F'', l) → F'''
  72. Mirror(H', l) → H''
  73. Segment(F''', H'') → j'
  74. Mirror(H, l) → H'_1
  75. Mirror(L, l) → L'
  76. Mirror(E''_1, l) → Q
  77. Mirror(I', l) → I''
  78. Vector(D''', A') → v
  79. Translate(g'', v) → g'''_1
  80. Translate(A'', v) → A'''_1
  81. Translate(E', v) → E''_2
  82. Segment(A'''_1, E''_2) → e'''_1
  83. Translate(F, v) → F'_1
  84. Translate(D''', v) → R
  85. Segment(F'_1, R) → f'''_1
  86. Translate(A'_1, v) → S
  87. Translate(E'', v) → E'''_1
  88. Translate(I, v) → I'_1
  89. CircleSector(A', D'', E) → q
  90. CircleSector(H, E, E'_1) → r
  91. CircleSector(A''_1, E'_1, D'''_1) → s
  92. CircleSector(M, D'''_1, N) → t
  93. CircleSector(N, H'', M) → c_1
  94. CircleSector(D'''_1, M, A''_1) → d_1
  95. CircleSector(E'_1, A''_1, H) → e_1
  96. CircleSector(E, H, A') → f_1
  97. Area(c) → o
  98. PointIn(c) → Pointc_1
  99. Circumference(c) → circumferencec
  100. PointIn(c) → Pointc_2
  101. Circumference(c) → w
  102. PointIn(c) → Pointc

AI Drawing Prompt Reference

Start by drawing a circle with points A and B. Then, create two segments and their perpendicular lines, and find the intersection points C and D with the circle. Rotate points D and C around point A to generate new points and segments. Use mirroring and rotating operations to gradually form the four vertices and sides of a parallelogram.
The prompt above was compiled from the original drawing commands and is for reference only.