MathPlotAI Logo MathPlotAI

Squares and Greek Crosses

Squares and Greek Crosses
Loading the math board and drawing, please wait…
2019-03-21 00:42
PolygonTransformationGeometric Construction
In collections Cutting up squares
This example demonstrates the geometric relationship and construction methods between squares and Greek crosses. Core math concepts include polygons, rotation, concurrent lines, congruence, and incircle. Construction highlights involve commands/objects like Polygon, Point, Vector, Translate, Intersect, Segment, Rotate, and Midpoint in GeoGebra. Suitable for high school mathematics teaching on geometric transformations and polygon properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, K, L, C, D, E, F, G, H, I, J) → poly1, a, j, k, l, b, c, d, e, f, g, h, i
  2. Point(c) → N
  3. Vector(M, N) → u
  4. Translate(A, u) → A'
  5. Translate(B, u) → B'
  6. Translate(C, u) → C'
  7. Translate(D, u) → D'
  8. Translate(E, u) → E'
  9. Translate(F, u) → F'
  10. Translate(G, u) → G'
  11. Translate(H, u) → H'
  12. Translate(I, u) → I'
  13. Translate(J, u) → J'
  14. Translate(K, u) → K'
  15. Translate(L, u) → L'
  16. Polygon(A', B', K', L', C', D', E', F', G', H', I', J') → poly1', a', j', k', l', b', c', d', e', f', g', h', i'
  17. Intersect(d, c) → O
  18. Vector(O, P) → v
  19. Translate(A, v) → A'_1
  20. Translate(B, v) → B'_1
  21. Translate(C, v) → C'_1
  22. Translate(D, v) → D'_1
  23. Translate(E, v) → E'_1
  24. Translate(F, v) → F'_1
  25. Translate(G, v) → G'_1
  26. Translate(H, v) → H'_1
  27. Translate(I, v) → I'_1
  28. Translate(J, v) → J'_1
  29. Translate(K, v) → K'_1
  30. Translate(L, v) → L'_1
  31. Polygon(A'_1, B'_1, K'_1, L'_1, C'_1, D'_1, E'_1, F'_1, G'_1, H'_1, I'_1, J'_1) → poly1'_1, a'_1, j'_1, k'_1, l'_1, b'_1, c'_1, d'_1, e'_1, f'_1, g'_1, h'_1, i'_1
  32. Intersect(l, a) → Q
  33. Intersect(f, e) → R
  34. Vector(Q, R) → w
  35. Translate(A, w) → A'_2
  36. Translate(B, w) → B'_2
  37. Translate(C, w) → C'_2
  38. Translate(D, w) → D'_2
  39. Translate(E, w) → E'_2
  40. Translate(F, w) → F'_2
  41. Translate(G, w) → G'_2
  42. Translate(H, w) → H'_2
  43. Translate(I, w) → I'_2
  44. Translate(J, w) → J'_2
  45. Translate(K, w) → K'_2
  46. Translate(L, w) → L'_2
  47. Polygon(A'_2, B'_2, K'_2, L'_2, C'_2, D'_2, E'_2, F'_2, G'_2, H'_2, I'_2, J'_2) → poly1'_2, a'_2, j'_2, k'_2, l'_2, b'_2, c'_2, d'_2, e'_2, f'_2, g'_2, h'_2, i'_2
  48. Intersect(g, f) → S
  49. Vector(S, T) → z
  50. Translate(A, z) → A'_3
  51. Translate(B, z) → B'_3
  52. Translate(C, z) → C'_3
  53. Translate(D, z) → D'_3
  54. Translate(E, z) → E'_3
  55. Translate(F, z) → F'_3
  56. Translate(G, z) → G'_3
  57. Translate(H, z) → H'_3
  58. Translate(I, z) → I'_3
  59. Translate(J, z) → J'_3
  60. Translate(K, z) → K'_3
  61. Translate(L, z) → L'_3
  62. Polygon(A'_3, B'_3, K'_3, L'_3, C'_3, D'_3, E'_3, F'_3, G'_3, H'_3, I'_3, J'_3) → poly1'_3, a'_3, j'_3, k'_3, l'_3, b'_3, c'_3, d'_3, e'_3, f'_3, g'_3, h'_3, i'_3
  63. Translate(A', w) → A''
  64. Translate(B', w) → B''
  65. Translate(C', w) → C''
  66. Translate(D', w) → D''
  67. Translate(E', w) → E''
  68. Translate(F', w) → F''
  69. Translate(G', w) → G''
  70. Translate(H', w) → H''
  71. Translate(I', w) → I''
  72. Translate(J', w) → J''
  73. Translate(K', w) → K''
  74. Translate(L', w) → L''
  75. Polygon(A'', B'', K'', L'', C'', D'', E'', F'', G'', H'', I'', J'') → poly1'', a'', j'', k'', l'', b'', c'', d'', e'', f'', g'', h'', i''
  76. Segment(U, V) → m
  77. Segment(V, W) → n
  78. Segment(W, Z) → p
  79. Segment(Z, U) → q
  80. Intersect(k', j') → B_1
  81. Intersect(b'_1, a'_1) → C_1
  82. Intersect(e'_1, d'_1) → D_1
  83. Intersect(h', g') → E_1
  84. Polygon(B_1, Q, T, C_1, U) → poly2, b_1, q_1, t, c_1, u_1
  85. Polygon(B_1, V, E_1, O, N) → poly3, b_2, v_1, e_1, o, n_1
  86. Polygon(R, E_1, W, D_1, S) → poly4, r, e_2, w_1, d_1, s
  87. Polygon(C_1, M, P, D_1, Z) → poly5, c_2, m_1, p_1, d_2, z_1
  88. Rotate(B_1, (-α), C_1) → F_1
  89. Rotate(Q, (-α), C_1) → Q'
  90. Rotate(T, (-α), C_1) → T'
  91. Rotate(C_1, (-α), C_1) → G_1
  92. Rotate(U, (-α), C_1) → U'
  93. Polygon(F_1, Q', T', G_1, U') → poly2', f_1, q', t', g_1, u'
  94. Rotate(C_1, (-α), D_1) → H_1
  95. Rotate(M, (-α), D_1) → M'
  96. Rotate(P, (-α), D_1) → P'
  97. Rotate(D_1, (-α), D_1) → I_1
  98. Rotate(Z, (-α), D_1) → Z'
  99. Polygon(H_1, M', P', I_1, Z') → poly5', h_1, m', p', i_1, z'
  100. Rotate(R, (-α), E_1) → R'
  101. Rotate(E_1, (-α), E_1) → J_1
  102. Rotate(W, (-α), E_1) → W'
  103. Rotate(D_1, (-α), E_1) → K_1
  104. Rotate(S, (-α), E_1) → S'
  105. Polygon(R', J_1, W', K_1, S') → poly4', r', j_1, w', k_1, s'
  106. Rotate(B_1, (-α), B_1) → L_1
  107. Rotate(V, (-α), B_1) → V'
  108. Rotate(E_1, (-α), B_1) → M_1
  109. Rotate(O, (-α), B_1) → O'
  110. Rotate(N, (-α), B_1) → N'
  111. Polygon(L_1, V', M_1, O', N') → poly3', l_1, v', m_2, o', n'
  112. Translate(A'', w) → A'''
  113. Translate(B'', w) → B'''
  114. Translate(C'', w) → C'''
  115. Translate(D'', w) → D'''
  116. Translate(E'', w) → E'''
  117. Translate(F'', w) → F'''
  118. Translate(G'', w) → G'''
  119. Translate(H'', w) → H'''
  120. Translate(I'', w) → I'''
  121. Translate(J'', w) → J'''
  122. Translate(K'', w) → K'''
  123. Translate(L'', w) → L'''
  124. Polygon(A''', B''', K''', L''', C''', D''', E''', F''', G''', H''', I''', J''') → poly1''', a''', j''', k''', l''', b''', c''', d''', e''', f''', g''', h''', i'''
  125. Translate(A'', u) → A'''_1
  126. Translate(B'', u) → B'''_1
  127. Translate(C'', u) → C'''_1
  128. Translate(D'', u) → D'''_1
  129. Translate(E'', u) → E'''_1
  130. Translate(F'', u) → F'''_1
  131. Translate(G'', u) → G'''_1
  132. Translate(H'', u) → H'''_1
  133. Translate(I'', u) → I'''_1
  134. Translate(J'', u) → J'''_1
  135. Translate(K'', u) → K'''_1
  136. Translate(L'', u) → L'''_1
  137. Polygon(A'''_1, B'''_1, K'''_1, L'''_1, C'''_1, D'''_1, E'''_1, F'''_1, G'''_1, H'''_1, I'''_1, J'''_1) → poly1'''_1, a'''_1, j'''_1, k'''_1, l'''_1, b'''_1, c'''_1, d'''_1, e'''_1, f'''_1, g'''_1, h'''_1, i'''_1
  138. Translate(A''', u) → N_1
  139. Translate(B''', u) → O_1
  140. Translate(C''', u) → P_1
  141. Translate(D''', u) → Q_1
  142. Translate(E''', u) → R_1
  143. Translate(F''', u) → S_1
  144. Translate(G''', u) → T_1
  145. Translate(H''', u) → U_1
  146. Translate(I''', u) → V_1
  147. Translate(J''', u) → W_1
  148. Translate(K''', u) → Z_1
  149. Translate(L''', u) → A_2
  150. Polygon(N_1, O_1, Z_1, A_2, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1) → poly6, n_2, w_2, z_2, a_2, o_1, p_2, q_2, r_1, s_1, t_1, u_2, v_2
  151. Segment(B_2, E_2) → a_1
  152. Segment(E_2, D_2) → f_2
  153. Segment(D_2, C_2) → g_2
  154. Segment(C_2, B_2) → h_2
  155. Point(c'') → F_2
  156. Point(f'') → G_2
  157. Point(c''') → H_2
  158. Point(f'''_1) → I_2
  159. Intersect(g'''_1, f'''_1) → J_2
  160. Intersect(e'', d'') → K_2
  161. Intersect(d'', c'') → L_2
  162. Polygon(F_2, C_2, I_2, J_2, K_2, L_2) → poly7, f_3, c_3, i_2, j_2, k_2, l_2
  163. Intersect(c''', b''') → M_2
  164. Polygon(I_2, D_2, H_2, M_2, K_2, J_2) → poly8, i_3, d_3, h_3, m_3, k_3, j_3
  165. Intersect(f'', e'') → N_2
  166. Polygon(H_2, E_2, G_2, N_2, K_2, M_2) → poly9, h_4, e_3, g_3, n_3, k_4, m_4
  167. Polygon(G_2, B_2, F_2, L_2, K_2, N_2) → poly10, g_4, b_3, f_4, l_3, k_5, n_4
  168. Midpoint(C_2, K_2) → O_2
  169. Midpoint(B_2, K_2) → P_2
  170. Midpoint(K_2, E_2) → Q_2
  171. Midpoint(D_2, K_2) → R_2
  172. Rotate(F_2, β, O_2) → S_2
  173. Rotate(C_2, β, O_2) → T_2
  174. Rotate(I_2, β, O_2) → U_2
  175. Rotate(J_2, β, O_2) → V_2
  176. Rotate(K_2, β, O_2) → W_2
  177. Rotate(L_2, β, O_2) → Z_2
  178. Polygon(S_2, T_2, U_2, V_2, W_2, Z_2) → poly7', s_2, t_2, u_3, v_3, w_3, z_3
  179. Rotate(I_2, β, R_2) → A_3
  180. Rotate(D_2, β, R_2) → B_3
  181. Rotate(H_2, β, R_2) → C_3
  182. Rotate(M_2, β, R_2) → D_3
  183. Rotate(K_2, β, R_2) → E_3
  184. Rotate(J_2, β, R_2) → F_3
  185. Polygon(A_3, B_3, C_3, D_3, E_3, F_3) → poly8', a_3, b_4, c_4, d_4, e_4, f_5
  186. Rotate(H_2, β, Q_2) → G_3
  187. Rotate(E_2, β, Q_2) → H_3
  188. Rotate(G_2, β, Q_2) → I_3
  189. Rotate(N_2, β, Q_2) → J_3
  190. Rotate(K_2, β, Q_2) → K_3
  191. Rotate(M_2, β, Q_2) → L_3
  192. Polygon(G_3, H_3, I_3, J_3, K_3, L_3) → poly9', g_5, h_5, i_4, j_4, k_6, l_4
  193. Rotate(G_2, β, P_2) → M_3
  194. Rotate(B_2, β, P_2) → N_3
  195. Rotate(F_2, β, P_2) → O_3
  196. Rotate(L_2, β, P_2) → P_3
  197. Rotate(K_2, β, P_2) → Q_3
  198. Rotate(N_2, β, P_2) → R_3
  199. Polygon(M_3, N_3, O_3, P_3, Q_3, R_3) → poly10', m_5, n_5, o_3, p_3, q_3, r_3