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Shree Yanthra Geometric Construction

Shree Yanthra Geometric Construction
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2019-12-15 17:30
CirclePolygonTrigonometryTransformationGeometric Construction
This example demonstrates the geometric construction of Shree Yanthra, integrating polygons, circumcircles, and trigonometric functions. Key math concepts include polygon construction, circumcircle, cosine theorem, rotation, and reflection. GeoGebra commands used are points, circles, orthogonal lines, intersections, rotations, angles, rays, reflections, segments, and polygons. Suitable for high school and above learners to explore geometric constructions and transformation principles.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, Radius) → c
  3. OrthogonalLine(A, xAxis) → f
  4. Intersect(c, xAxis) → B, C
  5. Intersect(c, f) → D, E
  6. Rotate(A, DnAngle / 2, E) → A'
  7. Angle(A, E, A') → α
  8. Ray(E, A') → g
  9. Mirror(E, f) → E'
  10. Mirror(A', f) → A''
  11. Ray(E', A'') → g'
  12. Rotate(A, UpAngle / 2, D) → A'_1
  13. Angle(A, D, A'_1) → β
  14. Ray(D, A'_1) → h
  15. Mirror(D, f) → D'
  16. Mirror(A'_1, f) → F
  17. Ray(D', F) → h'
  18. Intersect(c, h) → G, H
  19. Intersect(c, h') → I, J
  20. Intersect(c, g') → K, L
  21. Intersect(c, g) → M, N
  22. Segment(L, N) → i
  23. Segment(N, E) → j
  24. Segment(E, L) → k
  25. Segment(D, J) → l
  26. Segment(J, H) → m
  27. Segment(H, D) → n
  28. Intersect(m, f) → O
  29. Circle(B, A) → d
  30. Circle(C, A) → e
  31. Intersect(c, d) → P, Q, ,
  32. Intersect(e, c) → R, S, ,
  33. Rotate(D, Dn2Angle / 2, O) → D'_1
  34. Angle(D, O, D'_1) → γ
  35. Ray(O, D'_1) → p
  36. Mirror(O, f) → O'
  37. Mirror(D'_1, f) → T
  38. Ray(O', T) → p'
  39. Intersect(m, g') → U
  40. Intersect(m, g) → V
  41. Intersect(h', l) → W
  42. Intersect(p, h') → Z
  43. Intersect(p', i) → A_1
  44. Intersect(p, i) → B_1
  45. Line(V, B_1) → q
  46. Line(U, A_1) → r
  47. Intersect(q, r) → C_1
  48. OrthogonalLine(C_1, f) → s
  49. Intersect(s, p') → D_1
  50. Intersect(p, s) → E_1
  51. Segment(D_1, E_1) → t
  52. Segment(E_1, O) → a
  53. Segment(O, D_1) → b
  54. Rotate(C, SlashAngle, A) → C'
  55. Angle(C, A, C') → δ
  56. Ray(A, C') → f_1
  57. Intersect(p, a) → F_1
  58. Intersect(f_1, p) → G_1
  59. Circle(A, G_1) → c_1
  60. Intersect(c_1, f) → H_1, I_1
  61. Ray(H_1, G_1) → g_1
  62. Mirror(H_1, f) → J_1
  63. Mirror(G_1, f) → K_1
  64. Ray(J_1, K_1) → h_1
  65. Intersect(i, h) → L_1
  66. Intersect(h', l) → M_1
  67. Intersect(h', l) → N_1
  68. Intersect(h', l) → O_1
  69. Intersect(i, h') → P_1
  70. Intersect(m, h_1) → Q_1
  71. Intersect(m, g_1) → R_1
  72. Intersect(g', k) → S_1
  73. Intersect(h_1, g') → T_1
  74. Intersect(g_1, g) → U_1
  75. Line(T_1, U_1) → i_1
  76. Intersect(r, i_1) → V_1
  77. Intersect(q, i_1) → W_1
  78. Segment(C_1, W_1) → j_1
  79. Segment(W_1, V_1) → k_1
  80. Segment(V_1, C_1) → l_1
  81. Line(L_1, Q_1) → m_1
  82. Line(R_1, P_1) → n_1
  83. Intersect(m_1, n_1) → Z_1
  84. Intersect(m_1, r) → A_2
  85. Intersect(n_1, q) → B_2
  86. Intersect(h, n) → C_2
  87. Intersect(p', b) → D_2
  88. Intersect(h, n) → E_2
  89. Intersect(h, n) → F_2
  90. Intersect(h, n) → G_2
  91. Intersect(h, n) → H_2
  92. Intersect(p', b) → I_2
  93. Intersect(p', b) → J_2
  94. Intersect(h, n) → K_2
  95. Intersect(h, n) → L_2
  96. Intersect(p', h) → M_2
  97. Line(M_2, Z) → p_1
  98. Intersect(m_1, p_1) → N_2
  99. Intersect(n_1, p_1) → O_2
  100. Line(Z_1, xAxis) → q_1
  101. Intersect(h_1, q_1) → P_2
  102. Intersect(g_1, q_1) → Q_2
  103. Segment(H_1, Q_2) → r_1
  104. Segment(Q_2, P_2) → s_1
  105. Segment(P_2, H_1) → t_1
  106. Segment(Z_1, N_2) → a_1
  107. Segment(N_2, O_2) → b_1
  108. Segment(O_2, Z_1) → d_1
  109. Intersect(g', k) → R_2
  110. Intersect(h, n) → S_2
  111. Intersect(h, g') → T_2
  112. Intersect(h', g) → U_2
  113. Intersect(g', k) → V_2
  114. Intersect(q_1, s_1) → W_2
  115. Intersect(q_1, g') → Z_2
  116. Intersect(q_1, g) → A_3
  117. Intersect(n_1, i_1) → B_3
  118. Intersect(m_1, i_1) → C_3
  119. Intersect(s, h) → D_3
  120. Intersect(s, h') → E_3
  121. Intersect(q, p_1) → F_3
  122. Intersect(r, p_1) → G_3
  123. Intersect(i_1, f) → H_3
  124. Intersect(f, i) → I_3
  125. Line(H_1, xAxis) → f_5
  126. Intersect(f_5, r) → J_3
  127. Intersect(q, f_5) → K_3
  128. Segment(J_3, K_3) → g_5
  129. Segment(K_3, H_3) → h_5
  130. Segment(H_3, J_3) → i_5
  131. Intersect(f_5, p) → L_3
  132. Intersect(f_5, p') → M_3
  133. Intersect(p_1, f) → N_3
  134. Ray(N_3, M_3) → j_5
  135. Ray(N_3, L_3) → k_5
  136. Intersect(m_1, j_5) → O_3
  137. Intersect(k_5, n_1) → P_3
  138. Segment(N_3, P_3) → l_5
  139. Segment(P_3, O_3) → m_5
  140. Segment(O_3, N_3) → n_5
  141. Intersect(i_5, m) → Q_3
  142. Intersect(d, h_5) → R_3,
  143. Intersect(m, h_5) → S_3
  144. Intersect(i_5, h_1) → T_3
  145. Intersect(g_1, r_1) → U_3
  146. Intersect(h_5, g_1) → V_3
  147. Intersect(p, a) → W_3
  148. Intersect(m_5, p) → Z_3
  149. Intersect(p', b) → A_4
  150. Intersect(m_5, p') → B_4
  151. Intersect(i_5, n_5) → C_4
  152. Intersect(h_5, l_5) → D_4
  153. Intersect(i, n_5) → E_4
  154. Intersect(l_5, i) → F_4
  155. Line(K_1, G_1) → e_1
  156. Intersect(i_5, e_1) → G_4
  157. Intersect(e_1, h_5) → H_4
  158. Segment(G_4, I_3) → f_2
  159. Segment(I_3, H_4) → g_2
  160. Segment(H_4, G_4) → h_2
  161. Polygon(H, D, J) → t1, j_2, h_3, d_2
  162. Polygon(V_1, C_1, W_1) → t2, w_1, v_1, i_2
  163. Polygon(P_2, H_1, Q_2) → t3, q_2, p_2, k_2
  164. Polygon(O_3, N_3, P_3) → t4, p_3, o_3, n_3
  165. Polygon(G_4, I_3, H_4) → t5, h_4, g_4, i_3
  166. Polygon(O_3, N_3, P_3) → t6, l_2, m_2, n_2
  167. Polygon(E, L, N) → t7, n_4, e_2, l_3
  168. Polygon(Z_1, N_2, O_2) → t8, o_2, z_1, r_2
  169. Polygon(O, D_1, E_1) → t9, s_2, o, t_2
  170. Polygon(H_3, J_3, K_3) → t10, k_3, a_2, j_3
  171. Polygon(K_1, H_1, G_1) → t11, b_2, c_2, f_3