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Cube and GCD/LCM Geometric Construction

Cube and GCD/LCM Geometric Construction
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2017-03-29 07:29
FunctionTrigonometryCoordinate GeometrySolid GeometryGeometric Construction
In collections Tessellations
This example dynamically demonstrates the geometric relationship between a cube and GCD/LCM, revealing the倍数与约数关系 in natural numbers. Core math concepts include cube construction, GCD, LCM, combinatorics, tangent function, and natural numbers. Construction highlights involve GeoGebra commands like Segment, OrthogonalLine, Point, Intersect, Vector, Translate to build points, lines, and geometric transformations. Suitable for high school mathematics teaching, integrating number theory with geometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. OrthogonalLine(B, f) → h
  4. Point(g) → C
  5. OrthogonalLine(C, g) → i
  6. Intersect(h, i) → D
  7. Segment(A, B) → j
  8. Segment(A, C) → k
  9. Segment(C, D) → l
  10. Segment(B, D) → m
  11. Segment(A, E) → n
  12. Segment(F, E) → p
  13. Segment(F, G) → q
  14. Segment(H, G) → r
  15. Segment(H, B) → s
  16. Vector(A, C) → u
  17. Translate(A, u) → A'
  18. Translate(E, u) → E'
  19. Segment(A', E') → n'
  20. Translate(F, u) → F'
  21. Translate(E, u) → E'_1
  22. Segment(F', E'_1) → p'
  23. Translate(F, u) → F'_1
  24. Translate(G, u) → G'
  25. Segment(F'_1, G') → q'
  26. Translate(H, u) → H'
  27. Translate(G, u) → G'_1
  28. Segment(H', G'_1) → r'
  29. Translate(H, u) → H'_1
  30. Translate(B, u) → B'
  31. Segment(H'_1, B') → s'
  32. Segment(A, I) → t
  33. Segment(I, J) → a
  34. Segment(J, K) → b
  35. Segment(K, L) → c
  36. Segment(L, M) → d
  37. Segment(N, O) → e
  38. Segment(P, C) → f_1
  39. Segment(M, N) → g_1
  40. Segment(O, P) → h_1