MathPlotAI Logo MathPlotAI

The Incredible Shrinking Cube

The Incredible Shrinking Cube
Loading the math board and drawing, please wait…
2017-07-22 01:05
Solid GeometryTransformationGeometric Construction
This activity demonstrates a cube shrinking continuously. Key mathematical concepts include the transformation of a cube in solid geometry. Using GeoGebra commands such as Segment, Intersect, and Dilate, the dynamic changes in the cube's faces and edges can be observed. Suitable for middle school and above students to learn about cube transformations and dynamic geometry.

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(D, G) → l
  8. Segment(F, G) → m
  9. Segment(H, G) → n
  10. Segment(B, C) → p
  11. Segment(C, F) → q
  12. Segment(C, D) → r
  13. Intersect(xAxis, yAxis) → I
  14. Dilate(A, 0.5, I) → A'
  15. Dilate(B, 0.5, I) → B'
  16. Dilate(E, 0.5, I) → E'
  17. Dilate(F, 0.5, I) → F'
  18. Dilate(H, 0.5, I) → H'
  19. Dilate(D, 0.5, I) → D'
  20. Dilate(G, 0.5, I) → G'
  21. Dilate(C, 0.5, I) → C'
  22. Segment(A', B') → s
  23. Segment(A', D') → t
  24. Segment(A', H') → a
  25. Segment(B', E') → b
  26. Segment(E', A) → c
  27. Segment(E', H') → d
  28. Segment(D', G') → e
  29. Segment(A, G') → f_1
  30. Segment(G', H') → g_1
  31. Segment(B', C') → h_1
  32. Segment(C', A) → i_1
  33. Segment(C', D') → j_1
  34. Dilate(A', 0.5, I) → A''
  35. Dilate(B', 0.5, I) → B''
  36. Dilate(C', 0.5, I) → C''
  37. Dilate(D', 0.5, I) → D''
  38. Dilate(E', 0.5, I) → E''
  39. Dilate(G', 0.5, I) → G''
  40. Dilate(H', 0.5, I) → H''
  41. Segment(A'', B'') → k_1
  42. Segment(A'', D'') → l_1
  43. Segment(A'', H'') → m_1
  44. Segment(B'', E'') → n_1
  45. Segment(E'', A') → p_1
  46. Segment(E'', H'') → q_1
  47. Segment(D'', G'') → r_1
  48. Segment(A', G'') → s_1
  49. Segment(H'', G'') → t_1
  50. Segment(B'', C'') → a_1
  51. Segment(C'', A') → b_1
  52. Segment(C'', D'') → c_1