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立方体切割演示 by 久保塾　今治

立方体切割演示 by 久保塾　今治
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2019-03-22 16:32
立体几何变换几何作图
①本范例演示立方体通过变换和几何作图进行切割的过程；②涉及相似变换、向量、平面、二次函数等核心数学概念；③构造中运用了Point, Intersect, Mirror, OrthogonalLine, OrthogonalPlane, Circle, Rotate, Cube, Segment, Plane, IntersectPath等GeoGebra命令和对象；④适合高中及以上学生学习和理解立体几何与变换。

GeoGebra 命令及参数

  1. Point(yAxis) → G
  2. Intersect(zAxis, yAxis) → H
  3. Point(Circle[G, Distance[H, G], Segment[H, G]]) → I
  4. Mirror(I, G) → I'
  5. OrthogonalLine(H, xOyPlane) → n
  6. Point(n) → F
  7. OrthogonalPlane(F, n) → b
  8. PointIn(b) → A
  9. Circle(n, A) → c
  10. Rotate(A, 90°, F) → A'
  11. Point(Circle[A', Distance[A, A'], Segment[A, A']]) → B
  12. Cube(A, A', B) → a, C, faceBCKJ, faceDEJK, edgeAC, edgeAA', edgeA'B, edgeBC, edgeAD, edgeCK, edgeDK, edgeDE, D, edgeA'E, edgeEJ, edgeBJ, edgeJK, E, J, K, faceAA'BC, faceACKD, faceAA'ED, faceA'BJE
  13. Point(a) → L
  14. Point(a) → M
  15. Intersect(n, faceDEJK) → N
  16. Rotate(D, α, zAxis) → D'
  17. Segment(N, D') → g
  18. Intersect(g, edgeDE) → O
  19. Intersect(edgeEJ, g) → P
  20. Intersect(g, edgeJK) → Q
  21. Intersect(edgeDK, g) → R
  22. Plane(O, M, L) → h
  23. Plane(P, L, M) → i
  24. Plane(Q, L, M) → j
  25. Plane(R, M, L) → k
  26. IntersectPath(h, a) → poly1, S, r, s, t, T, U, V, W, Z, m, p, q
  27. IntersectPath(i, a) → poly2, A_1, i_1, j_1, d_1, B_1, C_1, D_1, E_1, R_1, f_1, g_1, h_1
  28. Plane(Q, M, L) → o
  29. IntersectPath(o, a) → poly3, F_1, n_1, p_1, c_1, G_1, H_1, I_1, J_1, Q_1, k_1, l_1, m_1
  30. Plane(R, M, L) → u
  31. IntersectPath(u, a) → poly4, K_1, t_1, a_1, b_1, L_1, M_1, N_1, O_1, P_1, q_1, r_1, s_1