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Area of Circle by Suchetha

Area of Circle by Suchetha
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2015-12-26 19:20
CircleCoordinate GeometryGeometric Construction
This example demonstrates how to understand the area of a circle through geometric construction. Key mathematical concepts include the properties of circles and the area formula. Using GeoGebra commands such as Circle, Point, Vector, Translate, etc., the process of calculating the area of a circle is dynamically illustrated. Suitable for middle school and above students learning geometry and area calculation.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Point(c) → B
  3. Vector(B, A) → u
  4. Translate(C, Vector[-u]) → C'_2
  5. Rotate(C'_2, (g / 100 * 15)°, C'_2) → C''_2
  6. Line(B, A) → b
  7. Rotate(B, 30*°, A) → B'
  8. Angle(B, A, B') → α
  9. Line(B', A) → d
  10. Circle(C, a) → e
  11. Vector(A, B') → v
  12. Vector(B, B') → w
  13. Translate(C, v) → C'_1
  14. Rotate(C'_2, 60*°, C) → C''_1
  15. Rotate(C'_1, 60*°, C) → D
  16. Line(C'_2, C) → f
  17. Mirror(C'_1, f) → E
  18. Mirror(C''_1, f) → C'''
  19. Mirror(D, f) → D'
  20. Polygon(E, C'_2, C) → poly1, c_1, e_1, c'
  21. Rotate(E, (g / 100 * 15)°, C'_2) → E'_1
  22. Rotate(C, (g / 100 * 15)°, C'_2) → C'_3
  23. Polygon(E'_1, C''_2, C'_3) → poly1', c'_1, e', c''
  24. Polygon(C''', E, C) → poly2, c_2, c''', e_2
  25. Rotate(C''', g / 100 * β, F) → G
  26. Rotate(E, g / 100 * β, F) → E'
  27. Rotate(C, g / 100 * β, F) → C'_4
  28. Polygon(G, E', C'_4) → poly2', c'_2, g_1, e'_1
  29. Polygon(C, D', C''') → poly3, c'''_1, c_3, d'
  30. Rotate(C, g / 100 * γ, H) → C'
  31. Rotate(D', g / 100 * γ, H) → D''
  32. Rotate(C''', g / 100 * γ, H) → I
  33. Polygon(C', D'', I) → poly3', i, c'_3, d''
  34. Mirror(C', f) → C''_3
  35. Mirror(D'', f) → D'''_1
  36. Mirror(I, f) → I'_1
  37. Polygon(C''_3, D'''_1, I'_1) → poly3''_1, i', c''_1, d'''
  38. Mirror(G, f) → G'_1
  39. Mirror(E', f) → E''_1
  40. Mirror(C'_4, f) → J
  41. Polygon(G'_1, E''_1, J) → poly2''_1, j, g', e''
  42. Mirror(E'_1, f) → K
  43. Mirror(C''_2, f) → L
  44. Mirror(C'_3, f) → M
  45. Polygon(K, L, M) → poly1''_1, m, k, l
  46. OrthogonalLine(C, f) → h
  47. Mirror(C', h) → C''
  48. Mirror(D'', h) → D'''
  49. Mirror(I, h) → I'
  50. Polygon(C'', D''', I') → poly3'', i'_1, c''_2, d'''_1
  51. Mirror(G, h) → G'
  52. Mirror(E', h) → E''
  53. Mirror(C'_4, h) → N
  54. Polygon(G', E'', N) → poly2'', n, g'_1, e''_1
  55. Mirror(E'_1, h) → O
  56. Mirror(C''_2, h) → P
  57. Mirror(C'_3, h) → Q
  58. Polygon(O, P, Q) → poly1'', q, o, p
  59. Mirror(K, h) → K'
  60. Mirror(L, h) → L'
  61. Mirror(M, h) → M'
  62. Polygon(K', L', M') → poly4, m', k', l'
  63. Mirror(G'_1, h) → R
  64. Mirror(E''_1, h) → S
  65. Mirror(J, h) → J'
  66. Polygon(R, S, J') → poly5, j', r, s
  67. Mirror(C''_3, h) → T
  68. Mirror(D'''_1, h) → U
  69. Mirror(I'_1, h) → V
  70. Polygon(T, U, V) → poly6, v_1, t, u_1
  71. Vector((0, 0), (-3.27, 2.09)) → offsetvector
  72. Point(c) → W
  73. Rotate(W, 30*°, A) → W'
  74. Angle(W, A, W') → δ
  75. Vector(W', W) → z
  76. Vector(W', A) → w_1
  77. Polygon(TestPoint, E_1, D_1, J_1, TestB, Z, F_1, A_1, G_1, B_1, H_1, C_1, I_1) → poly7, testpoint, i_1, d_1, j_1, testb, e_3, z_1, f_1, a_1, g_2, b_1, h_1, c_4
  78. Translate(TestPoint, Vector[(g - 100) / 100 * w_1]) → TestPoint'_1
  79. Translate(E_1, Vector[(g - 100) / 100 * w_1]) → K_1
  80. Translate(Z, Vector[(g - 100) / 100 * w_1]) → Z'_1
  81. Translate(F_1, Vector[(g - 100) / 100 * w_1]) → L_1
  82. Translate(A_1, Vector[(g - 100) / 100 * w_1]) → M_1
  83. Translate(G_1, Vector[(g - 100) / 100 * w_1]) → N_1
  84. Translate(B_1, Vector[(g - 100) / 100 * w_1]) → O_1
  85. Translate(H_1, Vector[(g - 100) / 100 * w_1]) → P_1
  86. Translate(C_1, Vector[(g - 100) / 100 * w_1]) → Q_1
  87. Translate(I_1, Vector[(g - 100) / 100 * w_1]) → R_1
  88. Translate(D_1, Vector[(g - 100) / 100 * w_1]) → S_1
  89. Translate(J_1, Vector[(g - 100) / 100 * w_1]) → T_1
  90. Translate(TestB, Vector[(g - 100) / 100 * w_1]) → TestB'_1
  91. Polygon(TestPoint'_1, K_1, S_1, T_1, TestB'_1, Z'_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1) → poly7'_1, testpoint', r_1, s_1, t_1, testb', k_1, z', l_1, m_1, n_1, o_1, p_1, q_1
  92. Mirror(TestPoint, h) → TestPoint'
  93. Mirror(E_1, h) → U_1
  94. Mirror(Z, h) → Z'
  95. Mirror(F_1, h) → V_1
  96. Mirror(A_1, h) → W_1
  97. Mirror(G_1, h) → Z_1
  98. Mirror(B_1, h) → A_2
  99. Mirror(H_1, h) → B_2
  100. Mirror(C_1, h) → C_2
  101. Mirror(I_1, h) → D_2
  102. Mirror(D_1, h) → E_2
  103. Mirror(J_1, h) → F_2
  104. Mirror(TestB, h) → TestB'
  105. Polygon(TestPoint', U_1, E_2, F_2, TestB', Z', V_1, W_1, Z_1, A_2, B_2, C_2, D_2) → poly7', testpoint'_1, d_2, e_4, f_2, testb'_1, u_2, z'_1, v_2, w_2, z_2, a_2, b_2, c_5
  106. Segment(G_2, H_2) → h_2
  107. Segment(I_2, J_2) → i_2