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Root Rectangles

Root Rectangles
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2019-04-21 16:19
PolygonVectorGeometric Construction
This example demonstrates the construction of root rectangles. A root rectangle is a special rectangle where the diagonal length is the square root of the side length. The core mathematical concepts involved include rectangles, vectors, and geometric construction. Using GeoGebra commands such as Point, Segment, and Polygon, the properties of root rectangles are visually illustrated. Suitable for middle school and above students to learn geometric construction and related concepts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → D
  4. Point(yAxis) → E
  5. Segment(O, P) → n
  6. Point(xAxis) → C
  7. Point(xAxis) → G
  8. Polygon(C, G, 4) → poly1, f, g, h, i, H, I
  9. Segment(C, H) → j
  10. Line(C, G) → k
  11. Circle(C, H) → c
  12. Intersect(c, k, 2) → J
  13. OrthogonalLine(J, k) → l
  14. Line(H, k) → m
  15. Intersect(l, m) → A_1
  16. Polygon(G, H, A_1, J) → q1, g_1, h_1, a_1, j_1
  17. Circle(C, A_1) → d
  18. Intersect(d, k, 2) → B_1
  19. Line(B_1, l) → p
  20. Intersect(m, p) → C_1
  21. Polygon(J, B_1, C_1, A_1) → q2, j_2, b_1, c_1, q
  22. Circle(C, C_1) → e
  23. Intersect(e, k, 2) → D_1
  24. Line(D_1, p) → r
  25. Intersect(m, r) → E_1
  26. Polygon(B_1, D_1, E_1, C_1) → q3, s, d_1, e_1, t
  27. Circle(C, E_1) → f_1
  28. Intersect(f_1, k, 2) → F_1
  29. Line(F_1, r) → a
  30. Intersect(m, a) → G_1
  31. Polygon(D_1, F_1, G_1, E_1) → q4, b, i_1, k_1, l_1
  32. Circle(C, G_1) → p_1
  33. Intersect(p_1, k, 2) → H_1
  34. Line(H_1, a) → m_1
  35. Intersect(m, m_1) → I_1
  36. Polygon(F_1, H_1, I_1, G_1) → q5, n_1, q_1, r_1, s_1
  37. Circle(C, I_1) → t_1
  38. Intersect(t_1, k, 2) → J_1
  39. Line(J_1, m_1) → f_2
  40. Intersect(m, f_2) → K_1
  41. Polygon(H_1, J_1, K_1, I_1) → q6, g_2, h_2, i_2, k_2
  42. Circle(C, K_1) → c_2
  43. Intersect(c_2, k, 2) → L_1
  44. Line(L_1, f_2) → l_2
  45. Intersect(m, l_2) → M_1
  46. Polygon(J_1, L_1, M_1, K_1) → q7, m_2, n_2, p_2, q_2
  47. Circle(C, M_1) → d_2
  48. Intersect(d_2, k, 2) → N_1
  49. Line(N_1, l_2) → r_2
  50. Intersect(m, r_2) → O_1
  51. Polygon(L_1, N_1, O_1, M_1) → q8, s_2, t_2, o_1, a_2
  52. CircleArc(C, J, H) → e_2
  53. CircleArc(C, B_1, A_1) → c_3
  54. CircleArc(C, D_1, C_1) → d_3
  55. CircleArc(C, F_1, E_1) → e_3
  56. CircleArc(C, J_1, I_1) → f_3
  57. CircleArc(C, H_1, G_1) → g_3
  58. CircleArc(C, L_1, K_1) → h_3
  59. CircleArc(C, N_1, M_1) → k_3
  60. Segment(G, I) → b_2
  61. Circle(C, G) → p_3
  62. Circle(G, C) → q_3
  63. Intersect(q_3, b_2, 1) → P_1
  64. Intersect(p_3, j, 1) → Q_1
  65. Line(P_1, Q_1) → i_3
  66. Intersect(i_3, i) → R_1
  67. Intersect(i_3, g) → S_1
  68. Distance(P_1, Q_1) → distanceP1Q1
  69. Intersect(p_3, i_3, 1) → T_1
  70. Segment(C, S_1) → j_3
  71. Segment(G, R_1) → l_3
  72. Intersect(p_3, j_3, 1) → U_1
  73. Intersect(q_3, l_3, 1) → V_1
  74. Line(V_1, U_1) → m_3
  75. Intersect(m_3, i) → W_1
  76. Intersect(m_3, g) → Z_1
  77. Distance(V_1, U_1) → distanceV1U1
  78. Segment(C, Z_1) → n_3
  79. Segment(G, W_1) → r_3
  80. Intersect(q_3, r_3, 1) → A_2
  81. Intersect(p_3, n_3, 1) → B_2
  82. Line(A_2, B_2) → s_3
  83. Intersect(s_3, i) → C_2
  84. Intersect(s_3, g) → D_2
  85. Distance(A_2, B_2) → distanceA2B2
  86. Segment(P_1, T_1) → t_3
  87. Segment(V_1, U_1) → a_3
  88. Segment(A_2, B_2) → b_3
  89. Segment(R_1, S_1) → f_4
  90. Segment(W_1, Z_1) → g_4
  91. Segment(C_2, D_2) → h_4
  92. Segment(C, D_2) → i_4
  93. Segment(G, C_2) → j_4
  94. Intersect(q_3, j_4, 1) → E_2
  95. Intersect(p_3, i_4, 1) → F_2
  96. Distance(E_2, F_2) → distanceE2F2
  97. Intersect(p_3, i_4, 1) → G_2
  98. Segment(C, Z_1) → k_4
  99. Polygon(C, G, 4) → poly2, l_4, m_4, n_4, p_4, H_2, I_2
  100. Line(E_2, G_2) → q_4
  101. Intersect(q_4, p_4) → J_2
  102. Intersect(q_4, g_1) → K_2
  103. Segment(C, K_2) → r_4
  104. Segment(G, J_2) → s_4
  105. Segment(E_2, G_2) → t_4
  106. Segment(J_2, K_2) → a_4
  107. Intersect(p_3, r_4, 1) → L_2
  108. Intersect(q_3, s_4, 1) → M_2
  109. Segment(M_2, L_2) → b_4
  110. Line(M_2, L_2) → c_4
  111. Intersect(c_4, p_4) → N_2
  112. Intersect(c_4, g_1) → O_2
  113. Segment(C, O_2) → d_4
  114. Segment(G, N_2) → e_4
  115. Segment(N_2, O_2) → f_5
  116. Intersect(q_3, e_4, 1) → P_2
  117. Intersect(p_3, d_4, 1) → Q_2
  118. Segment(P_2, Q_2) → g_5
  119. Line(P_2, Q_2) → h_5
  120. Intersect(h_5, p_4) → R_2
  121. Intersect(h_5, g_1) → S_2
  122. Segment(C, S_2) → i_5
  123. Segment(G, R_2) → j_5
  124. Intersect(q_3, j_5, 1) → T_2
  125. Intersect(p_3, i_5, 1) → U_2
  126. Segment(T_2, U_2) → k_5
  127. Segment(R_2, S_2) → l_5
  128. Line(T_2, U_2) → m_5
  129. Intersect(m_5, p_4) → V_2
  130. Intersect(m_5, g_1) → W_2
  131. Segment(C, W_2) → n_5
  132. Segment(G, V_2) → p_5
  133. Segment(V_2, W_2) → q_5
  134. Intersect(q_3, p_5, 1) → Z_2
  135. Intersect(p_3, n_5, 1) → A_3
  136. Segment(Z_2, A_3) → r_5
  137. Line(Z_2, A_3) → s_5
  138. Intersect(s_5, p_4) → B_3
  139. Intersect(s_5, g_1) → C_3
  140. Segment(B_3, C_3) → t_5
  141. Segment(C, C_3) → a_5
  142. Segment(G, B_3) → b_5
  143. Intersect(q_3, b_5, 1) → D_3
  144. Intersect(p_3, a_5, 1) → E_3
  145. Segment(D_3, E_3) → c_5
  146. Line(D_3, E_3) → d_5
  147. Intersect(d_5, p_4) → F_3
  148. Intersect(d_5, g_1) → G_3
  149. Segment(C, G_3) → e_5
  150. Segment(G, F_3) → f_6
  151. Intersect(q_3, f_6, 1) → H_3
  152. Intersect(p_3, e_5, 1) → I_3
  153. Segment(H_3, I_3) → g_6
  154. Line(H_3, I_3) → h_6
  155. Intersect(h_6, p_4) → J_3
  156. Intersect(h_6, g_1) → K_3

AI Drawing Prompt Reference

Draw a root rectangle by first creating points A, B, D, and C on the x-axis, and point E on the y-axis. Then, draw a circle with center C and radius H, intersecting line CH to get point J. Draw a perpendicular line to CH through J, intersecting the previous line to get point A1. Next, draw a circle with center A1 and radius C, intersecting line CH to get point B1, and continue this process to form a grid of root rectangles.
The prompt above was compiled from the original drawing commands and is for reference only.