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剥开一个立方体

剥开一个立方体
几何画板及绘图内容加载中，请稍等……
2018-04-06 05:55
向量立体几何几何作图
这个范例演示了如何通过逐步剥开立方体的面来展示其面积和体积的变化。核心数学概念包括立体几何中的面、体积和向量。通过使用GeoGebra命令如Polygon、Join、Text等，可以动态展示立方体的各个面及其变化。适合初中及以上学生学习立体几何。

GeoGebra 命令及参数

  1. Zip(y(AAA), AAA, removedFaces) → yValues
  2. Zip(x(AAA), AAA, removedFaces) → xValues
  3. Polygon((lengthStarter, widthStarter, heightStarter), (lengthEnder, widthStarter, heightStarter), (lengthEnder, widthEnder, heightStarter), (lengthStarter, widthEnder, heightStarter)) → bottom, f, g, h, i
  4. Polygon((lengthStarter, widthStarter, heightEnder), (lengthEnder, widthStarter, heightEnder), (lengthEnder, widthEnder, heightEnder), (lengthStarter, widthEnder, heightEnder)) → top, j, k, l, m
  5. Polygon((lengthStarter, widthStarter, heightStarter), (lengthEnder, widthStarter, heightStarter), (lengthEnder, widthStarter, heightEnder), (lengthStarter, widthStarter, heightEnder)) → front, n, p, q, r
  6. Polygon((lengthStarter, widthEnder, heightStarter), (lengthEnder, widthEnder, heightStarter), (lengthEnder, widthEnder, heightEnder), (lengthStarter, widthEnder, heightEnder)) → back, s, t, a, b
  7. Polygon((lengthStarter, widthStarter, heightStarter), (lengthStarter, widthEnder, heightStarter), (lengthStarter, widthEnder, heightEnder), (lengthStarter, widthStarter, heightEnder)) → left, c, d, e, f_1
  8. Polygon((lengthEnder, widthStarter, heightStarter), (lengthEnder, widthEnder, heightStarter), (lengthEnder, widthEnder, heightEnder), (lengthEnder, widthStarter, heightEnder)) → right, g_1, h_1, i_1, j_1
  9. Join({Sequence[Segment[(lengthStarter, widthStarter, i), (lengthStarter, widthEnder, i)], i, heightStarter, heightEnder], Sequence[Segment[(lengthStarter, i, heightStarter), (lengthStarter, i, heightEnder)], i, widthStarter, widthEnder]}) → leftLines
  10. Join({Sequence[Segment[(lengthStarter, widthStarter, i), (lengthEnder, widthStarter, i)], i, heightStarter, heightEnder], Sequence[Segment[(i, widthStarter, heightStarter), (i, widthStarter, heightEnder)], i, lengthStarter, lengthEnder]}) → frontLines
  11. Join({Sequence[Segment[(lengthStarter, i, heightEnder), (lengthEnder, i, heightEnder)], i, widthStarter, widthEnder], Sequence[Segment[(i, widthStarter, heightEnder), (i, widthEnder, heightEnder)], i, lengthStarter, lengthEnder]}) → topLines
  12. Text(length, Midpoint[f] + (0, -2, 0)) → text1
  13. Text(height, Midpoint[f_1] + (-2, -2, 0)) → text2
  14. Text(width, Midpoint[g] + (2, 0, 0)) → text3
  15. Join({Sequence[Segment[(lengthStarter, widthEnder, i), (lengthEnder, widthEnder, i)], i, heightStarter, heightEnder], Sequence[Segment[(i, widthEnder, heightStarter), (i, widthEnder, heightEnder)], i, lengthStarter, lengthEnder]}) → backLines
  16. Join({Sequence[Segment[(lengthStarter, i, heightStarter), (lengthEnder, i, heightStarter)], i, widthStarter, widthEnder], Sequence[Segment[(i, widthStarter, heightStarter), (i, widthEnder, heightStarter)], i, lengthStarter, lengthEnder]}) → bottomLines
  17. Join({Sequence[Segment[(lengthEnder, widthStarter, i), (lengthEnder, widthEnder, i)], i, heightStarter, heightEnder], Sequence[Segment[(lengthEnder, i, heightStarter), (lengthEnder, i, heightEnder)], i, widthStarter, widthEnder]}) → rightLines
  18. Point(xAxis) → P_4
  19. Flatten(Sequence[Sequence[Point[{(11 * i), (11 * j)}], i, 0, 5], j, 0, 4]) → quadStarters
  20. Polygon(quadStarters(1), quadStarters(1) + (x1, 0), quadStarters(1) + (x1, y1), quadStarters(1) + (0, y1)) → poly1, k_1, l_1, m_1, n_1
  21. Polygon(quadStarters(2), quadStarters(2) + (x2, 0), quadStarters(2) + (x2, y2), quadStarters(2) + (0, y2)) → poly2, p_1, q_1, r_1, s_1
  22. Polygon(quadStarters(3), quadStarters(3) + (x3, 0), quadStarters(3) + (x3, y3), quadStarters(3) + (0, y3)) → poly3, t_1, a_1, b_1, c_1
  23. Polygon(quadStarters(4), quadStarters(4) + (x4, 0), quadStarters(4) + (x4, y4), quadStarters(4) + (0, y4)) → poly4, d_1, e_1, f_2, g_2
  24. Polygon(quadStarters(5), quadStarters(5) + (x5, 0), quadStarters(5) + (x5, y5), quadStarters(5) + (0, y5)) → poly5, h_2, i_2, j_2, k_2
  25. Polygon(quadStarters(6), quadStarters(6) + (x6, 0), quadStarters(6) + (x6, y6), quadStarters(6) + (0, y6)) → poly6, l_2, m_2, n_2, p_2
  26. Polygon(quadStarters(7), quadStarters(7) + (x7, 0), quadStarters(7) + (x7, y7), quadStarters(7) + (0, y7)) → poly7, q_2, r_2, s_2, t_2
  27. Polygon(quadStarters(8), quadStarters(8) + (x8, 0), quadStarters(8) + (x8, y8), quadStarters(8) + (0, y8)) → poly8, a_2, b_2, c_2, d_2
  28. Polygon(quadStarters(9), quadStarters(9) + (x9, 0), quadStarters(9) + (x9, y9), quadStarters(9) + (0, y9)) → poly9, e_2, f_3, g_3, h_3
  29. Polygon(quadStarters(10), quadStarters(10) + (x10, 0), quadStarters(10) + (x10, y10), quadStarters(10) + (0, y10)) → poly10, i_3, j_3, k_3, l_3
  30. Polygon(quadStarters(11), quadStarters(11) + (x11, 0), quadStarters(11) + (x11, y11), quadStarters(11) + (0, y11)) → poly11, m_3, n_3, p_3, q_3
  31. Polygon(quadStarters(12), quadStarters(12) + (x12, 0), quadStarters(12) + (x12, y12), quadStarters(12) + (0, y12)) → poly12, r_3, s_3, t_3, a_3
  32. Polygon(quadStarters(13), quadStarters(13) + (x13, 0), quadStarters(13) + (x13, y13), quadStarters(13) + (0, y13)) → poly13, b_3, c_3, d_3, e_3
  33. Polygon(quadStarters(14), quadStarters(14) + (x14, 0), quadStarters(14) + (x14, y14), quadStarters(14) + (0, y14)) → poly14, f_4, g_4, h_4, i_4
  34. Polygon(quadStarters(15), quadStarters(15) + (x15, 0), quadStarters(15) + (x15, y15), quadStarters(15) + (0, y15)) → poly15, j_4, k_4, l_4, m_4
  35. Polygon(quadStarters(16), quadStarters(16) + (x16, 0), quadStarters(16) + (x16, y16), quadStarters(16) + (0, y16)) → poly16, n_4, p_4, q_4, r_4
  36. Polygon(quadStarters(17), quadStarters(17) + (x17, 0), quadStarters(17) + (x17, y17), quadStarters(17) + (0, y17)) → poly17, s_4, t_4, a_4, b_4
  37. Polygon(quadStarters(18), quadStarters(18) + (x18, 0), quadStarters(18) + (x18, y18), quadStarters(18) + (0, y18)) → poly18, c_4, d_4, e_4, f_5
  38. Polygon(quadStarters(19), quadStarters(19) + (x19, 0), quadStarters(19) + (x19, y19), quadStarters(19) + (0, y19)) → poly19, g_5, h_5, i_5, j_5
  39. Polygon(quadStarters(20), quadStarters(20) + (x20, 0), quadStarters(20) + (x20, y20), quadStarters(20) + (0, y20)) → poly20, k_5, l_5, m_5, n_5
  40. Polygon(quadStarters(21), quadStarters(21) + (x21, 0), quadStarters(21) + (x21, y21), quadStarters(21) + (0, y21)) → poly21, p_5, q_5, r_5, s_5
  41. Polygon(quadStarters(22), quadStarters(22) + (x22, 0), quadStarters(22) + (x22, y22), quadStarters(22) + (0, y22)) → poly22, t_5, a_5, b_5, c_5
  42. Polygon(quadStarters(23), quadStarters(23) + (x23, 0), quadStarters(23) + (x23, y23), quadStarters(23) + (0, y23)) → poly23, d_5, e_5, f_6, g_6
  43. Polygon(quadStarters(24), quadStarters(24) + (x24, 0), quadStarters(24) + (x24, y24), quadStarters(24) + (0, y24)) → poly24, h_6, i_6, j_6, k_6
  44. Polygon(quadStarters(25), quadStarters(25) + (x25, 0), quadStarters(25) + (x25, y25), quadStarters(25) + (0, y25)) → poly25, l_6, m_6, n_6, p_6
  45. Polygon(quadStarters(26), quadStarters(26) + (x26, 0), quadStarters(26) + (x26, y26), quadStarters(26) + (0, y26)) → poly26, q_6, r_6, s_6, t_6
  46. Polygon(quadStarters(27), quadStarters(27) + (x27, 0), quadStarters(27) + (x27, y27), quadStarters(27) + (0, y27)) → poly27, a_6, b_6, c_6, d_6
  47. Polygon(quadStarters(28), quadStarters(28) + (x28, 0), quadStarters(28) + (x28, y28), quadStarters(28) + (0, y28)) → poly28, e_6, f_7, g_7, h_7
  48. Polygon(quadStarters(29), quadStarters(29) + (x29, 0), quadStarters(29) + (x29, y29), quadStarters(29) + (0, y29)) → poly29, i_7, j_7, k_7, l_7
  49. Polygon(quadStarters(30), quadStarters(30) + (x30, 0), quadStarters(30) + (x30, y30), quadStarters(30) + (0, y30)) → poly30, m_7, n_7, p_7, q_7
  50. Sequence(Sequence[Segment[quadStarters(i) + (j, 0), quadStarters(i) + (j, yValues(i))], j, 0, xValues(i)], i, 1, faceCount) → L_5
  51. Sequence(Sequence[Segment[quadStarters(i) + (0, j), quadStarters(i) + (xValues(i), j)], j, 0, yValues(i)], i, 1, faceCount) → L_6