Activity 2: The Incredible Shrinking Cube

Activity 2: The Incredible Shrinking Cube
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2017-01-09 23:59
① This example dynamically demonstrates a cube shrinking and subdividing into smaller cubes, visualizing the recursive changes in area and volume. ② Core math concepts include cubes, geometric sequences, logarithmic functions, scaling of area and volume, and recursive division. ③ Construction highlights: using GeoGebra's Segment command to build edges and vertices (A to H and primed counterparts), with multiple segment objects (f, g, h, i, j, k, l, m, n, p, q, r, etc.) forming a 3D framework, and sliders or animations to control the scaling factor and observe the shrinking sequence. ④ Suitable for upper secondary or pre-university students, useful for exploring the connection between geometric scaling, sequences, and logarithmic functions, and as an interactive resource for math modeling or dynamic geometry lessons.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(A, D) → g
  3. Segment(A, H) → h
  4. Segment(B, E) → i
  5. Segment(E, F) → j
  6. Segment(E, H) → k
  7. Segment(F, G) → l
  8. Segment(D, G) → m
  9. Segment(H, G) → n
  10. Segment(B, C) → p
  11. Segment(C, F) → q
  12. Segment(C, D) → r
  13. Segment(A', D') → s
  14. Segment(A', H') → t
  15. Segment(A', B') → a
  16. Segment(B', E') → b
  17. Segment(E', F') → c
  18. Segment(E', H') → d
  19. Segment(D', G') → e
  20. Segment(F', G') → f_1
  21. Segment(H', G') → g_1
  22. Segment(B', C') → h_1
  23. Segment(C', F') → i_1
  24. Segment(C', D') → j_1
  25. Segment(A'', B'') → k_1
  26. Segment(A'', D'') → l_1
  27. Segment(A'', H'') → m_1
  28. Segment(B'', E'') → n_1
  29. Segment(E'', F'') → p_1
  30. Segment(E'', H'') → q_1
  31. Segment(D'', G'') → r_1
  32. Segment(F'', G'') → s_1
  33. Segment(G'', H'') → t_1
  34. Segment(B'', C'') → a_1
  35. Segment(C'', F'') → b_1
  36. Segment(C'', D'') → c_1