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Cube Cutting Demonstration by 久保塾　今治

Cube Cutting Demonstration by 久保塾　今治
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2019-03-22 16:32
Solid GeometryTransformationGeometric Construction
This example demonstrates the process of cutting a cube through transformations and geometric constructions. It involves core mathematical concepts such as similarity transformation, vectors, planes, and quadratic functions. GeoGebra commands and objects like Point, Intersect, Mirror, OrthogonalLine, OrthogonalPlane, Circle, Rotate, Cube, Segment, Plane, IntersectPath are used in the construction. Suitable for high school and above students to learn and understand solid geometry and transformations.

GeoGebra Commands & Parameters

  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