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Step-by-step Construction of the Sri-Yantra

Step-by-step Construction of the Sri-Yantra
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2020-09-15 18:53
CirclePolygonAngleTransformationGeometric Construction
This example demonstrates how to construct the key symmetrical structure of the Sri-Yantra pattern on a plane using a precise sequence of geometric construction steps. The main mathematical ideas include: constructing points and lines (lines, rays, segments), creating and using circles and semicircles for curved constraints, determining new vertices via intersections, using midpoint to establish controlled symmetry, building perpendicular (orthogonal) relations, and generating invariances through mirror symmetry, line bisectors, and angular bisectors. The construction workflow is implemented with GeoGebra commands such as Intersect, Point, Semicircle, Line, OrthogonalLine, Ray, Segment, Midpoint, Circle, Parabola, Mirror, LineBisector, AngularBisector, and Polygon. It is well suited for geometry-construction instruction, math clubs, and competition-style learning, especially for students who want to connect elementary Euclidean constructions with algorithmic dynamic geometry modeling.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Semicircle(B, A) → c_6
  4. Semicircle(A, B) → d_3
  5. Line(B, A) → f
  6. OrthogonalLine(C, f) → g
  7. OrthogonalLine(E, f) → h
  8. Intersect(c_6, g, 1) → G
  9. Intersect(c_6, h, 1) → H
  10. Line(B, H) → i
  11. Line(A, G) → j
  12. Intersect(d_3, g, 1) → I
  13. Line(A, I) → k
  14. Intersect(d_3, h, 1) → J
  15. Line(B, J) → l
  16. Intersect(g, i) → K
  17. OrthogonalLine(D, f) → q
  18. Intersect(h, j) → Q
  19. Intersect(f, yAxis) → Q_1
  20. Ray(F, K) → m
  21. Intersect(h, m) → L
  22. Ray(C, L) → n
  23. Intersect(j, n) → M
  24. OrthogonalLine(M, f) → p
  25. Intersect(f, p) → N
  26. Intersect(q, n) → O
  27. Ray(N, O) → r
  28. Segment(D, K) → s
  29. Intersect(q, m) → P
  30. Segment(P, C) → t
  31. Intersect(s, t) → R
  32. Ray(B, R) → a_7
  33. Intersect(g, a_7) → S
  34. Intersect(g, r) → T
  35. Line(D, a_7) → f_1
  36. Line(Q, r) → g_1
  37. Intersect(f_1, g) → U
  38. Intersect(g_1, g) → V
  39. Midpoint(D, C) → W
  40. OrthogonalLine(Q, g) → b_7
  41. Intersect(g, b_7) → Z
  42. Midpoint(Z, Q) → A_1
  43. OrthogonalLine(A_1, b_7) → e
  44. OrthogonalLine(W, f) → h_1
  45. OrthogonalLine(U, g) → i_1
  46. OrthogonalLine(V, g) → j_1
  47. Midpoint(U, T) → B_1
  48. Midpoint(S, V) → C_1
  49. OrthogonalLine(B_1, g) → k_1
  50. OrthogonalLine(C_1, g) → l_1
  51. Intersect(k_1, h_1) → F_1
  52. Intersect(l_1, e) → G_1
  53. Segment(G_1, V) → m_1
  54. Segment(U, F_1) → n_1
  55. Midpoint(U, F_1) → H_1
  56. Midpoint(G_1, V) → I_1
  57. OrthogonalLine(I_1, m_1) → p_1
  58. OrthogonalLine(H_1, n_1) → q_1
  59. Intersect(k_1, q_1) → J_1
  60. Intersect(p_1, l_1) → K_1
  61. Intersect(p_1, j_1) → L_1
  62. Intersect(i_1, q_1) → M_1
  63. Intersect(e, j_1) → E_1
  64. Circle(V, L_1) → c_1
  65. Intersect(c_1, j_1) → D_1, N_1
  66. Intersect(g, f_1) → O_1
  67. Circle(U, M_1) → d_1
  68. Intersect(d_1, i_1) → P_1, R_1
  69. OrthogonalLine(R_1, i_1) → r_1
  70. OrthogonalLine(N_1, j_1) → s_1
  71. Parabola(K_1, s_1) → e_1
  72. Parabola(J_1, r_1) → t_1
  73. Intersect(t_1, e_1) → S_1, T_1, ,
  74. OrthogonalLine(S_1, g) → a_1
  75. Intersect(a_1, g) → U_1
  76. OrthogonalLine(T_1, h_1) → b_1
  77. Intersect(k_1, r_1) → V_1
  78. Intersect(k_1, s_1) → W_1
  79. Line(V_1, K_1) → f_2
  80. Line(W_1, f_2) → g_2
  81. Intersect(l_1, g_2) → Z_1
  82. Circle(K_1, Z_1) → c_2
  83. Intersect(c_2, l_1) → A_2, B_2
  84. Segment(J_1, Z_1) → h_2
  85. Line(J_1, B_2) → i_2
  86. Intersect(l_1, r_1) → C_2
  87. Circle(J_1, Z_1, C_2) → d_2
  88. Intersect(d_2, i_2) → D_2, E_2
  89. Intersect(c_2, d_2) → F_2, G_2, ,
  90. Line(Z_1, G_2) → j_2
  91. Intersect(j_2, i_2) → H_2
  92. Semicircle(K_1, H_2) → e_2
  93. Semicircle(H_2, K_1) → k_2
  94. Intersect(c_2, k_2) → I_2, M_3, ,
  95. Circle(J_1, E_2, I_2) → p_2
  96. Ray(D, U_1) → l_2
  97. Intersect(i, l_2) → J_2
  98. OrthogonalLine(J_2, f) → m_2
  99. Intersect(m_2, f) → K_2
  100. Segment(K_2, P) → n_2
  101. Intersect(l_2, a_7) → L_2
  102. OrthogonalLine(L_2, f) → q_2
  103. Intersect(j_2, r) → M_2
  104. Intersect(r, q_2) → N_2
  105. Ray(Q, N_2) → r_2
  106. Intersect(l_2, r_2) → O_2
  107. Intersect(r_2, f) → P_2
  108. OrthogonalLine(P_2, f) → s_2
  109. Intersect(i, s_2) → Q_2
  110. Intersect(s_2, l_2) → R_2
  111. OrthogonalLine(F, f) → t_2
  112. Line(P_2, Q) → a_2
  113. Intersect(p, a_2) → S_2
  114. Intersect(t_2, n) → T_2
  115. Intersect(j, t_2) → U_2
  116. Intersect(i, j) → V_2
  117. Intersect(m, m_2) → W_2
  118. Intersect(n, l_2) → Z_2
  119. OrthogonalLine(Z_2, f) → b_2
  120. Intersect(n_2, b_2) → A_3
  121. Mirror(T_2, f) → B_3
  122. Mirror(S_2, f) → C_3
  123. Mirror(W_2, f) → D_3
  124. Mirror(R_2, f) → E_3
  125. Mirror(A_3, f) → F_3
  126. Mirror(L_2, f) → G_3
  127. Mirror(N_2, f) → H_3
  128. Mirror(P, f) → P'
  129. Midpoint(D, Z_2) → I_3
  130. LineBisector(D, Z_2) → l_7
  131. Intersect(l_7, f) → J_3
  132. AngularBisector(b_2, l_2) → g_3, h_3
  133. Intersect(g_3, f) → K_3
  134. Segment(A_3, E) → i_3
  135. Segment(E, H) → j_3
  136. Segment(H, B) → k_3
  137. Semicircle(B, A) → c_3
  138. Segment(A, G) → l_3
  139. Segment(G, C) → m_3
  140. Segment(C, T_2) → n_3
  141. Segment(T_2, F) → p_3
  142. Segment(F, W_2) → q_3
  143. Segment(W_2, K_2) → r_3
  144. Segment(K_2, P) → s_3
  145. Segment(P, D) → t_3
  146. Segment(D, R_2) → a_3
  147. Segment(R_2, P_2) → b_3
  148. Segment(P_2, S_2) → f_4
  149. Segment(S_2, N) → g_4
  150. Segment(N, N_2) → h_4
  151. Segment(N_2, H_3) → i_4
  152. Segment(H_3, N) → j_4
  153. Segment(N, C_3) → k_4
  154. Segment(C_3, P_2) → l_4
  155. Segment(P_2, E_3) → m_4
  156. Segment(E_3, D) → n_4
  157. Segment(D, P') → p_4
  158. Segment(P', K_2) → q_4
  159. Segment(K_2, D_3) → r_4
  160. Segment(D_3, F) → s_4
  161. Segment(F, B_3) → t_4
  162. Segment(B_3, C) → a_4
  163. Segment(C, I) → b_4
  164. Segment(I, A) → c_4
  165. Semicircle(A, B) → d_4
  166. Segment(B, J) → e_4
  167. Segment(J, E) → f_5
  168. Segment(E, F_3) → g_5
  169. Segment(F_3, A_3) → h_5
  170. Polygon(F_3, E, A_3) → t2, i_5, j_5, e_5
  171. Polygon(K_2, P', P) → t3, p_5, k_5, p'
  172. Polygon(H_3, N_2, N) → t4, n_5, l_5, m_5
  173. Polygon(C, B_3, T_2) → t5, q_5, c_5, r_5
  174. Polygon(E_3, D, R_2) → t6, s_5, t_5, d_5
  175. Polygon(P_2, C_3, S_2) → t7, a_5, b_5, f_6
  176. Polygon(D_3, F, W_2) → t8, w_2, g_6, f_7
  177. Polygon(B, J, H) → t9, h_6, b_6, j_6
  178. Polygon(I, G, A) → t10, a_6, i_6, g_7
  179. Intersect(g_3, f) → L_3

AI Drawing Prompt Reference

Draw a symmetric geometric figure with two circular arcs and a straight line. The arcs' endpoints are the intersection points of the line. The line intersects the arcs, and perpendicular lines to the line intersect the arcs to create new points. Connect these points with line segments, and use perpendicular lines to intersect the line. Finally, form a closed figure using these segments and perpendicular lines. The figure should maintain symmetry and have clear lines.
The prompt above was compiled from the original drawing commands and is for reference only.