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Cube Division Demonstration by Diego Lieban (4)

Cube Division Demonstration by Diego Lieban (4)
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2018-12-09 03:29
Solid GeometryCalculusDerivativeLimitGeometric Construction
This example demonstrates how to divide a cube into specific geometric shapes through rotation and intersection operations. It involves core mathematical concepts such as solid geometry, derivatives, limits, equilateral triangles, and set theory. Key GeoGebra commands used include Intersect, Point, Cube, Pyramid, Rotate, and Line for construction. Suitable for high school and above students to understand spatial geometry and calculus concepts.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → 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_1, edgeAB_1, edgeBC_1, edgeCD_1, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF_1, edgeFG, edgeCG_1, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Pyramid(A, C, D, G) → d, faceACD, edgeDG, faceACG, faceCDG, faceADG, edgeAC, edgeCD, edgeAD, edgeAG, edgeCG
  6. Pyramid(B, C, A, G) → b, faceABC, edgeAG_1, faceBCG, faceACG_1, faceABG, edgeBC, edgeAC_1, edgeAB, edgeBG, edgeCG_2
  7. Rotate(b, (-(90°)), edgeGH) → b_1
  8. Rotate(b_1, 90°, edgeCG) → b_2
  9. Rotate(b, If[0 < c ≤ 1, (-(((c * 90))°))], edgeGH) → b_{01}
  10. Rotate(b_1, If[1 < c ≤ 2, (((c - 1) * 90))°], edgeCG_2) → b_{12}
  11. Rotate(b_2, If[2 < c ≤ 3, (((c - 2) * 90))°], edgeFG) → b_{23}
  12. Rotate(b_2, 90°, edgeFG) → b_3
  13. Rotate(b_3, (-(90°)), edgeGH) → b_4
  14. Rotate(b_3, If[3 < c ≤ 4, (((-(c - 3)) * 90))°], edgeGH) → b_{34}
  15. Rotate(d, (-(90°)), edgeGH) → d_1
  16. Rotate(d_1, 90°, edgeCG) → d_2
  17. Rotate(d_2, 90°, edgeFG) → d_3
  18. Rotate(d_3, (-(90°)), edgeGH) → d_4
  19. Rotate(d, If[4 < c ≤ 5, (-(((c * 90))°))], edgeGH) → d_{01}
  20. Rotate(d_1, If[5 < c ≤ 6, (((c - 1) * 90))°], edgeCG_2) → d_{12}
  21. Rotate(d_2, If[6 < c ≤ 7, (((c - 2) * 90))°], edgeFG) → d_{23}
  22. Rotate(d_3, If[7 < c ≤ 8, (((-(c - 7)) * 90))°], edgeGH) → d_{34}
  23. Line(G, H) → r_1
  24. Line(C, G) → r_2
  25. Line(F, G) → r_3
  26. Line(G, H) → r_4