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魔方解法指南

魔方解法指南
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2015-12-10 02:00
多边形角几何作图
这个范例演示了解魔方的方法。它涉及逻辑思维、角度和颜色变换等核心数学概念。通过使用GeoGebra命令如Segment、Point、CircleArc等，可以构造出魔方的各个面和颜色变换。适合用于初中及以上学生进行几何作图和逻辑思维训练。

GeoGebra 命令及参数

  1. Segment((x(Z) + 0.5, y(Z) - 0.25), (x(Z) + 2, y(Z) - 0.25)) → j_3
  2. Point(j_3) → M
  3. Segment((x(Z) + 0.5, y(Z) + 0.25), (x(Z) + 2, y(Z) + 0.25)) → n_2
  4. Point(n_2) → L
  5. Segment(M, L) → m_4
  6. CircleArc((x(Z) + 1.75, y(Z)), M, L) → e_4
  7. Vector((0, 0, 0), (0, 0, 1)) → kbek
  8. Sequence(Sequence[Cube[(-2.5 + i, -2.5 + j, -1.5), (i - 1.5, -2.5 + j, -1.5), kbek], i, 1, 3, 1], j, 1, 3, 1) → down
  9. Sequence(Sequence[Cube[(-2.5 + i, -2.5 + j, -0.5), (i - 1.5, -2.5 + j, -0.5), kbek], i, 1, 3, 1], j, 1, 3, 1) → middlehorizontal
  10. Sequence(Sequence[Cube[(-2.5 + i, -2.5 + j, 0.5), (i - 1.5, -2.5 + j, 0.5), kbek], i, 1, 3, 1], j, 1, 3, 1) → up
  11. Vector((0, 0, 0), (1, 0, 0)) → ibek
  12. Vector((0, 0, 0), (0, 1, 0)) → jbek
  13. Sequence(Sequence[Cube[(-2.5 + i, -1.5, -2.5 + j), (i - 1.5, -1.5, -2.5 + j), kbek], j, 1, 3, 1], i, 1, 3, 1) → front
  14. Sequence(Sequence[Cube[(-2.5 + i, -0.5, -2.5 + j), (i - 1.5, -0.5, -2.5 + j), kbek], j, 1, 3, 1], i, 1, 3, 1) → middleverticalside
  15. Sequence(Sequence[Cube[(-2.5 + i, 0.5, -2.5 + j), (i - 1.5, 0.5, -2.5 + j), kbek], j, 1, 3, 1], i, 1, 3, 1) → back
  16. Line((0, 0, 0), (0, 1, 0)) → yaxis
  17. Polygon(A, A_1, A_2, A_3) → poligonoa1, a, a_1, a_2, a_3
  18. Polygon(B, B_1, B_2, B_3) → poligonoa2, b, b_1, b_2, b_3
  19. Polygon(C, C_1, C_2, C_3) → poligonoa3, c, c_1, c_2, c_3
  20. Polygon(D, D_1, D_2, D_3) → poligonoa4, d, d_1, d_2, d_3
  21. Polygon(E, E_1, E_2, E_3) → poligonoa5, e, e_1, e_2, e_3
  22. Polygon(F, F_1, F_2, F_3) → poligonoa6, f, f_1, f_2, f_3
  23. Polygon(G, G_1, G_2, G_3) → poligonoa7, g, g_1, g_2, g_3
  24. Polygon(H, H_1, H_2, H_3) → poligonoa8, h, h_1, h_2, h_3
  25. Polygon(I, I_1, I_2, I_3) → poligonoa9, i, i_1, i_2, i_3
  26. Line((0, 0, 0), (0, 0, 1)) → zaxis
  27. Line((0, 0, 0), (1, 0, 0)) → xaxis
  28. Sequence(Sequence[Cube[(1.5, -2.5 + i, -2.5 + j), (1.5, i - 1.5, -2.5 + j), kbek], j, 1, 3, 1], i, 1, 3, 1) → right
  29. Sequence(Sequence[Cube[(0.5, -2.5 + i, -2.5 + j), (0.5, i - 1.5, -2.5 + j), kbek], j, 1, 3, 1], i, 1, 3, 1) → middleverticalfront
  30. Sequence(Sequence[Cube[(-0.5, -2.5 + i, -2.5 + j), (-0.5, i - 1.5, -2.5 + j), kbek], j, 1, 3, 1], i, 1, 3, 1) → left
  31. Polygon(A2, A2_1, A2_2, A2_3) → poligonoa10, a2, a2_1, a2_2, a2_3
  32. Polygon(B2, B2_1, B2_2, B2_3) → poligonoa11, b2, b2_1, b2_2, b2_3
  33. Polygon(C2, C2_1, C2_2, C2_3) → poligonoa12, c2, c2_1, c2_2, c2_3
  34. Polygon(D2, D2_1, D2_2, D2_3) → poligonoa13, d2, d2_1, d2_2, d2_3
  35. Polygon(E2, E2_1, E2_2, E2_3) → poligonoa14, e2, e2_1, e2_2, e2_3
  36. Polygon(F2, F2_1, F2_2, F2_3) → poligonoa15, f2, f2_1, f2_2, f2_3
  37. Polygon(G2, G2_1, G2_2, G2_3) → poligonoa16, g2, g2_1, g2_2, g2_3
  38. Polygon(H2, H2_1, H2_2, H2_3) → poligonoa17, h2, h2_1, h2_2, h2_3
  39. Polygon(I2, I2_1, I2_2, I2_3) → poligonoa18, i2, i2_1, i2_2, i2_3
  40. Polygon(A3, A3_1, A3_2, A3_3) → poligonoa19, a3, a3_1, a3_2, a3_3
  41. Polygon(B3, B3_1, B3_2, B3_3) → poligonoa20, b3, b3_1, b3_2, b3_3
  42. Polygon(C3, C3_1, C3_2, C3_3) → poligonoa21, c3, c3_1, c3_2, c3_3
  43. Polygon(D3, D3_1, D3_2, D3_3) → poligonoa22, d3, d3_1, d3_2, d3_3
  44. Polygon(E3, E3_1, E3_2, E3_3) → poligonoa23, e3, e3_1, e3_2, e3_3
  45. Polygon(F3, F3_1, F3_2, F3_3) → poligonoa24, f3, f3_1, f3_2, f3_3
  46. Polygon(G3, G3_1, G3_2, G3_3) → poligonoa25, g3, g3_1, g3_2, g3_3
  47. Polygon(H3, H3_1, H3_2, H3_3) → poligonoa26, h3, h3_1, h3_2, h3_3
  48. Polygon(I3, I3_1, I3_2, I3_3) → poligonoa27, i3, i3_1, i3_2, i3_3
  49. Polygon(A4, A4_1, A4_2, A4_3) → poligonoa28, a4, a4_1, a4_2, a4_3
  50. Polygon(B4, B4_1, B4_2, B4_3) → poligonoa29, b4, b4_1, b4_2, b4_3
  51. Polygon(C4, C4_1, C4_2, C4_3) → poligonoa30, c4, c4_1, c4_2, c4_3
  52. Polygon(D4, D4_1, D4_2, D4_3) → poligonoa31, d4, d4_1, d4_2, d4_3
  53. Polygon(E4, E4_1, E4_2, E4_3) → poligonoa32, e4, e4_1, e4_2, e4_3
  54. Polygon(F4, F4_1, F4_2, F4_3) → poligonoa33, f4, f4_1, f4_2, f4_3
  55. Polygon(G4, G4_1, G4_2, G4_3) → poligonoa34, g4, g4_1, g4_2, g4_3
  56. Polygon(H4, H4_1, H4_2, H4_3) → poligonoa35, h4, h4_1, h4_2, h4_3
  57. Polygon(I4, I4_1, I4_2, I4_3) → poligonoa36, i4, i4_1, i4_2, i4_3
  58. Polygon(D, D2, D3, D4) → black1, j, k, l, m
  59. Polygon(G, G2, G3, G4) → black2, n, p, q, r
  60. Polygon(A5, A5_1, A5_2, A5_3) → poligonoa37, a5, a5_1, a5_2, a5_3
  61. Polygon(B5, B5_1, B5_2, B5_3) → poligonoa38, b5, b5_1, b5_2, b5_3
  62. Polygon(C5, C5_1, C5_2, C5_3) → poligonoa39, c5, c5_1, c5_2, c5_3
  63. Polygon(D5, D5_1, D5_2, D5_3) → poligonoa40, d5, d5_1, d5_2, d5_3
  64. Polygon(E5, E5_1, E5_2, E5_3) → poligonoa41, e5, e5_1, e5_2, e5_3
  65. Polygon(F5, F5_1, F5_2, F5_3) → poligonoa42, f5, f5_1, f5_2, f5_3
  66. Polygon(G5, G5_1, G5_2, G5_3) → poligonoa43, g5, g5_1, g5_2, g5_3
  67. Polygon(H5, H5_1, H5_2, H5_3) → poligonoa44, h5, h5_1, h5_2, h5_3
  68. Polygon(I5, I5_1, I5_2, I5_3) → poligonoa45, i5, i5_1, i5_2, i5_3
  69. Polygon(A6, A6_1, A6_2, A6_3) → poligonoa52, a6, a6_1, a6_2, a6_3
  70. Polygon(B6, B6_1, B6_2, B6_3) → poligonoa53, b6, b6_1, b6_2, b6_3
  71. Polygon(C6, C6_1, C6_2, C6_3) → poligonoa54, c6, c6_1, c6_2, c6_3
  72. Polygon(D6, D6_1, D6_2, D6_3) → poligonoa49, d6, d6_1, d6_2, d6_3
  73. Polygon(E6, E6_1, E6_2, E6_3) → poligonoa50, e6, e6_1, e6_2, e6_3
  74. Polygon(F6, F6_1, F6_2, F6_3) → poligonoa51, f6, f6_1, f6_2, f6_3
  75. Polygon(G6, G6_1, G6_2, G6_3) → poligonoa46, g6, g6_1, g6_2, g6_3
  76. Polygon(I6, I6_1, I6_2, I6_3) → poligonoa48, i6, i6_1, i6_2, i6_3
  77. Polygon(H6, H6_1, H6_2, H6_3) → poligonoa47, h6, h6_1, h6_2, h6_3
  78. Polygon(B, C3, I3_3, B5) → black3, s, j_1, k_1, l_1
  79. Polygon(C, B3, H3_3, C5) → black4, c_4, b3_4, h3_4, c5_4
  80. Polygon(D5, F5_1, B2, C4) → black5, d5_4, f5_4, b2_4, c4_4
  81. Polygon(G5, I5_1, C2, B4) → black6, m_1, n_1, p_1, q_1
  82. If(t ≟ 1, 0, kopiay2) → y2
  83. If(t ≟ 1, 0, kopiay1) → y1
  84. If(t ≟ 1, 0, kopiaz3) → z3
  85. If(t ≟ 1, 0, kopiax2) → x2
  86. If(t ≟ 1, 0, kopiax1) → x1
  87. If(t ≟ 1, 0, kopiaz2) → z2
  88. If(t ≟ 1, 0, kopiax3) → x3
  89. If(t ≟ 1, 0, kopiay3) → y3
  90. If(t ≟ 1, 0, kopiaz1) → z1
  91. CircleArc(O, J, K) → r_1
  92. Translate(r_1, Vector[(0, 0, 4)]) → s_1
  93. Translate(r_1, Vector[(0, 0, -4)]) → t_1
  94. Vector((0, 1, 4), (-0.5, 1, 4)) → u
  95. Vector((0, 1, -4), (-0.5, 1, -4)) → v
  96. Rotate(s_1, ((-π)) / 2, yaxis) → k_2
  97. Translate(k_2, Vector[(8, 0, 0)]) → p_2
  98. Vector((-4, -1, 0), (-4, -1, -0.5)) → w
  99. Vector((4, -1, 0), (4, -1, -0.5)) → u_1
  100. Rotate(s_1, π / 2, xaxis) → q_2
  101. Rotate(q_2, π, yaxis) → r_2
  102. Translate(r_2, Vector[(0, 8, 0)]) → s_2
  103. Vector((0, -4, 1), (0.5, -4, 1)) → v_1
  104. Vector((0, 4, 1), (0.5, 4, 1)) → w_1
  105. Rotate(k_2, π, xaxis) → t_2
  106. Rotate(p_2, π, xaxis) → k_3
  107. Rotate(s_1, π, zaxis) → p_3
  108. Rotate(t_1, π, zaxis) → q_3
  109. Rotate(r_2, π, yaxis) → r_3
  110. Rotate(s_2, π, yaxis) → s_3
  111. Vector((0, 1, 4), (0.5, 1, 4)) → u_2
  112. Vector((4, -1, 0), (4, -1, 0.5)) → v_2
  113. Vector((0, 1, -4), (0.5, 1, -4)) → w_2
  114. Vector((0, -4, 1), (-0.5, -4, 1)) → j_2
  115. Vector((-4, -1, 0), (-4, -1, 0.5)) → l_2
  116. Vector((0, 4, 1), (-0.5, 4, 1)) → m_2
  117. Polygon((0, 0), (1, 0), 4) → poligonoa56
  118. Polygon((4, 0), (5, 0), 4) → poligonoa57
  119. Polygon((2, 0), (3, 0), 4) → poligonoa55
  120. Polygon((0, -2), (1, -2), 4) → poligonoa58
  121. Polygon((4, -2), (5, -2), 4) → poligonoa60
  122. Polygon((2, -2), (3, -2), 4) → poligonoa59
  123. CountIf(urdinak ≟ "blue", urdinak, koloreakzenbatzeko) → howmanybluecolored
  124. CountIf(zuriak ≟ "white", zuriak, koloreakzenbatzeko) → howmanywhitecolored
  125. CountIf(berdeak ≟ "Dark Green", berdeak, koloreakzenbatzeko) → howmanygreencolored
  126. CountIf(gorriak ≟ "red", gorriak, koloreakzenbatzeko) → howmanyredcolored
  127. CountIf(horiak ≟ "yellow", horiak, koloreakzenbatzeko) → howmanyyellowcolored
  128. CountIf(laranjak ≟ "orange", laranjak, koloreakzenbatzeko) → howmanyorangecolored
  129. Text(howmanygreencolored) → testua9
  130. Text(howmanyyellowcolored) → testua10
  131. Text(howmanybluecolored) → testua11
  132. Text(howmanywhitecolored) → testua12
  133. Text(howmanyorangecolored) → testua13
  134. Text(howmanyredcolored) → testua14
  135. Polygon((0, 0), (1, 0), 4) → poligonoa62
  136. Polygon((2, 0), (3, 0), 4) → poligonoa63
  137. Polygon((4, 0), (5, 0), 4) → poligonoa64
  138. Polygon((0, -2), (1, -2), 4) → poligonoa65
  139. Polygon((2, -2), (3, -2), 4) → poligonoa66
  140. Polygon((4, -2), (5, -2), 4) → poligonoa67
  141. Circle(Z, 0.025) → d_4
  142. Point(n_2) → N
  143. Point(j_3) → P
  144. Tangent(N, d_4) → l_3, m_3
  145. Intersect(d_4, l_3) → Q
  146. Tangent(P, d_4) → n_3, a_4
  147. Intersect(d_4, a_4) → R
  148. Segment(Q, N) → b_4
  149. Segment(R, P) → f_4
  150. Translate(j_3, (0, 0.5 / 3)) → h_4
  151. Translate(j_3, (0, 1 / 3)) → i_4
  152. Point(i_4) → S
  153. Point(h_4) → T
  154. CircleArc(Z2, S, T) → k_4
  155. Translate(k_4, (0, 0.5 / 3)) → p_4
  156. Translate(k_4, (0, -0.5 / 3)) → q_4
  157. Circle(Z, 0.2) → r_4
  158. Intersect(r_4, b_4) → U,
  159. Intersect(r_4, f_4) → V,
  160. CircleArc((x(Z) - 0.05, y(Z)), V, U) → s_4
  161. CircleArc(Z, Q, R) → t_4
  162. Point(h_4) → W
  163. Point(i_4) → J_1
  164. Segment(M, W) → g_4
  165. Point(edges1) → K_1
  166. Locus(L_1, K_1) → locus1
  167. Segment(W, J_1) → j_4
  168. Segment(J_1, L) → l_4
  169. Point(edges2) → M_1
  170. Locus(N_1, M_1) → locus2
  171. Point(edges4) → O_1
  172. Locus(P_1, O_1) → locus4
  173. Point(edges3) → Q_1
  174. Locus(R_1, Q_1) → locus3
  175. Segment(R, V) → n_4
  176. Segment(Q, U) → a_5
  177. Point(edges5) → S_1
  178. Locus(T_1, S_1) → locus5
  179. Segment(P, V) → t_3
  180. Segment(U, N) → b_5
  181. Point(edges6) → U_1
  182. Locus(V_1, U_1) → locus6
  183. Random(1, 18) → position
  184. If(solve ≟ true, "R", "X") → testua2
  185. If(solve ≟ true, "L", "X") → testua3
  186. If(solve ≟ true, "U", "Z") → testua4
  187. If(solve ≟ true, "D", "Z") → testua5
  188. If(solve ≟ true, "F", "Y") → testua7
  189. If(solve ≟ true, "B", "Y") → testua6