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Divide a Cube into Two Parts by Diego Lieban

Divide a Cube into Two Parts by Diego Lieban
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2019-04-04 01:54
VectorSolid GeometryGeometric Construction
In collections Dissecting a cube into equal parts Developing games and puzzles with 3D printing for STEAM
This example demonstrates how to divide a cube into two equal parts. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Intersect, Point, Cube, Midpoint, Plane, Sphere, Segment, Polygon, Vector, and Transform, the process of dividing the cube is visually demonstrated. Suitable for middle school and above students to learn solid geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Midpoint(edgeBF) → I
  6. Plane(I, xOyPlane) → b
  7. Midpoint(edgeCG) → J
  8. Midpoint(edgeDH) → K
  9. Midpoint(edgeAE) → L
  10. Point(edgeDH) → M
  11. Sphere(C, Distance[H, M]) → c
  12. Intersect(edgeCG, c) → N, T
  13. Segment(N, M) → f
  14. Sphere(E, Distance[H, M]) → d
  15. Intersect(edgeAE, d) → P, O
  16. Plane(P, M, N) → e
  17. Intersect(edgeBF, e) → Q
  18. Polygon(E, P, Q, F) → q1, e_1, p, q, f_1
  19. Polygon(F, G, N, Q) → q2, f_2, g, n, q_1
  20. Polygon(G, N, M, H) → q3, g_1, n_1, m, h
  21. Polygon(H, E, P, M) → q4, h_1, e_2, p_1, m_1
  22. Polygon(N, Q, P, M) → q5, n_2, q_2, p_2, m_2
  23. Sphere(A, i) → j
  24. Intersect(zAxis, j) → R, S
  25. Vector(A, S) → u
  26. Translate(q3, u) → q3'
  27. Translate(faceEFGH, u) → faceEFGH'
  28. Translate(q1, u) → q1'
  29. Translate(q2, u) → q2'
  30. Translate(q4, u) → q4'
  31. Translate(q5, u) → q5'
  32. Polygon(N, C, D, M) → q6, n_3, c_1, d_1, m_3
  33. Polygon(M, P, A, D) → q7, m_4, p_3, a_1, d_2
  34. Polygon(P, Q, B, A) → q8, p_4, q_3, b_1, a_2
  35. Polygon(Q, N, C, B) → q9, q_4, n_4, c_2, b_2
  36. Polygon(A, D, C, B) → q10, a_3, d_3, c_3, b_3
  37. Polygon(M, P, Q, N) → q11, m_5, p_5, q_5, n_5

AI Drawing Prompt Reference

Draw a cube and demonstrate how to divide it into two equal parts. First, mark the intersection points of the coordinate axes and key points of the cube, then construct the cube using these points. Next, find the midpoints of the cube's edges and use these midpoints and spheres to determine the division lines. Finally, translate the divided parts along a direction to show the two halves of the cube.
The prompt above was compiled from the original drawing commands and is for reference only.