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Circle in a Square

Circle in a Square
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2016-01-13 04:28
CirclePolygonFunction
This example demonstrates the composite area of a circle within a square. Key mathematical concepts include circles, squares, and quadratic functions. It is constructed using GeoGebra commands such as Intersect, Circle, and Polygon. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 4) → c
  3. Intersect(c, xAxis, 2) → C
  4. Polygon(A, C, 4) → poly1, a, b, d, e, B, D
  5. Circle(A, f) → g
  6. Intersect(g, a, 1) → E
  7. Intersect(g, e, 1) → F
  8. Circle(E, A) → k
  9. Intersect(k, a, 2) → H
  10. Circle(F, A) → q
  11. Intersect(q, e, 2) → I
  12. Circle(I, F) → r
  13. Intersect(r, e, 2) → J
  14. Circle(H, E) → s
  15. Intersect(s, a, 2) → K
  16. Intersect(k, q, 2) → G
  17. Circle(G, E) → h
  18. Circle(J, I) → p
  19. Circle(K, H) → t
  20. Intersect(p, e, 2) → L
  21. Intersect(t, a, 2) → M
  22. Circle(L, J) → c_1
  23. Circle(M, K) → d_1
  24. Intersect(c_1, e, 2) → N
  25. Intersect(d_1, a, 2) → O
  26. Circle(N, L) → e_1
  27. Circle(O, M) → f_1
  28. OrthogonalLine(G, e) → i
  29. Intersect(t, i, 1) → P
  30. Intersect(t, i, 1) → Q
  31. Circle(P, K) → g_1
  32. OrthogonalLine(E, i) → j
  33. Intersect(p, j, 1) → R
  34. Circle(R, J) → h_1
  35. Intersect(e_1, j, 1) → S
  36. Circle(S, N) → k_1
  37. Intersect(f_1, i, 1) → T
  38. OrthogonalLine(I, e) → l
  39. OrthogonalLine(H, a) → m
  40. Intersect(h_1, m, 1) → U
  41. Intersect(g_1, l, 1) → V
  42. Circle(T, O) → p_1
  43. Intersect(p_1, l, 1) → W
  44. Intersect(k_1, m, 1) → Z
  45. Line(P, V) → a_1
  46. Line(T, W) → b_1
  47. Line(R, U) → i_1
  48. Line(S, Z) → j_1
  49. OrthogonalLine(L, e) → l_1
  50. OrthogonalLine(M, a) → m_1
  51. Intersect(a_1, j_1) → A_1
  52. Intersect(a_1, i_1) → B_1
  53. Intersect(b_1, i_1) → C_1
  54. Intersect(j_1, b_1) → D_1
  55. Circle(A_1, Z) → q_1
  56. Intersect(m_1, j_1) → E_1
  57. Intersect(i_1, m_1) → F_1
  58. Circle(D_1, E_1) → r_1
  59. Circle(C_1, W) → s_1
  60. Circle(B_1, U) → t_1
  61. Intersect(e_1, e, 2) → G_1
  62. Intersect(f_1, a, 2) → H_1
  63. Circle(G_1, N) → c_2
  64. Circle(H_1, O) → d_2
  65. Intersect(c_2, e, 2) → I_1
  66. Intersect(d_2, a, 2) → J_1
  67. Circle(I_1, G_1) → e_2
  68. Circle(J_1, H_1) → f_2
  69. Intersect(f_2, i, 1) → K_1
  70. Intersect(e_2, j, 1) → L_1
  71. Circle(L_1, I_1) → g_2
  72. Circle(K_1, J_1) → h_2
  73. Line(I_1, L_1) → n_1
  74. Line(J_1, K_1) → a_2
  75. Intersect(k_1, c_2, 2) → M_1
  76. Intersect(j, i) → N_1
  77. Intersect(p_1, d_2) → O_1, P_1, ,
  78. Line(G_1, M_1) → b_2
  79. Line(H_1, P_1) → i_2
  80. Intersect(m, n_1) → Q_1
  81. Intersect(a_1, n_1) → R_1
  82. Intersect(m_1, n_1) → S_1
  83. Intersect(b_1, n_1) → T_1
  84. Intersect(n_1, i_2) → U_1
  85. Intersect(n_1, a_2) → V_1
  86. Intersect(a_2, b_2) → W_1
  87. Intersect(b_1, b_2) → Z_1
  88. Intersect(q_1, b_2, 1) → A_2
  89. Intersect(j_1, a_2) → B_2
  90. Intersect(l_1, a_2) → C_2
  91. Intersect(i_1, a_2) → D_2
  92. Intersect(l, a_2) → E_2
  93. Circle(R_1, Q_1) → k_2
  94. Circle(T_1, S_1) → p_2
  95. Circle(V_1, U_1) → q_2
  96. Circle(B_2, W_1) → r_2
  97. Circle(D_2, C_2) → s_2
  98. Intersect(e_2, e, 2) → F_2
  99. Intersect(f_2, a, 2) → G_2
  100. Circle(F_2, I_1) → t_2
  101. Circle(G_2, J_1) → c_3
  102. Intersect(t_2, e, 2) → H_2
  103. Intersect(c_3, a, 2) → I_2
  104. OrthogonalLine(H_2, e) → j_2
  105. OrthogonalLine(F_2, e) → l_2
  106. OrthogonalLine(I_2, a) → m_2
  107. OrthogonalLine(G_2, a) → n_2
  108. Intersect(a_1, l_2) → J_2
  109. Intersect(b_1, l_2) → K_2
  110. Intersect(a_2, l_2) → L_2
  111. Intersect(n_1, n_2) → M_2
  112. Intersect(j_1, n_2) → N_2
  113. Intersect(i_1, n_2) → O_2
  114. Intersect(h_2, c_3, 2) → P_2
  115. Intersect(j, j_2) → Q_2
  116. Intersect(a_1, j_2) → R_2
  117. Intersect(b_1, j_2) → S_2
  118. Intersect(a_2, j_2) → T_2
  119. Intersect(j_2, m_2) → U_2
  120. Intersect(i, m_2) → V_2
  121. Intersect(i_1, m_2) → W_2
  122. Intersect(j_1, m_2) → Z_2
  123. Intersect(n_1, m_2) → A_3
  124. Circle(Q_2, H_2) → d_3
  125. Circle(R_2, J_2) → e_3
  126. Circle(S_2, K_2) → f_3
  127. Circle(T_2, L_2) → g_3
  128. Intersect(j_2, n_2) → B_3
  129. Circle(U_2, B_3) → h_3
  130. Circle(A_3, M_2) → k_3
  131. Circle(Z_2, N_2) → p_3
  132. Circle(W_2, O_2) → q_3
  133. Circle(V_2, P_2) → r_3
  134. Circle(Q_2, H_2) → s_3
  135. Circle(R_2, J_2) → t_3
  136. Circle(S_2, K_2) → c_4
  137. Circle(T_2, L_2) → d_4
  138. Circle(U_2, B_3) → e_4
  139. Circle(A_3, M_2) → f_4
  140. Circle(V_1, W_1) → g_4
  141. Circle(T_1, U_1) → h_4
  142. Circle(R_1, S_1) → k_4
  143. Circle(L_1, Q_1) → p_4
  144. Circle(S, M_1) → q_4
  145. Circle(A_1, A_2) → r_4
  146. Circle(D_1, Z_1) → s_4
  147. Circle(B_2, N_2) → t_4
  148. Circle(Z_2, N_2) → c_5
  149. Circle(W_2, O_2) → d_5
  150. Circle(V_2, P_2) → e_5
  151. Circle(K_1, E_2) → f_5
  152. Circle(D_2, C_2) → g_5
  153. Circle(C_1, F_1) → h_5
  154. Circle(T, P_1) → k_5
  155. Circle(P, V) → p_5
  156. Circle(B_1, F_1) → q_5
  157. Circle(R, U) → r_5
  158. Circle(G, E) → s_5

AI Drawing Prompt Reference

Draw a square with a circle inscribed inside, touching all four sides. Construct a quadrilateral inside the square using the intersections of the circle with the axes. Then, draw a larger circle centered at the square's center, and add several smaller circles centered at the intersections of this circle with the axes. Finally, connect some key points with lines to create a more intricate and decorative pattern.
The prompt above was compiled from the original drawing commands and is for reference only.