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Ratio of Perimeter, Area & Volume

Ratio of Perimeter, Area & Volume
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2017-12-18 18:44
Complex NumberGeometric Construction
This example demonstrates the ratio between perimeter, area, and volume. Key mathematical concepts include geometry, perimeter, area, and volume, as well as complex numbers. Using GeoGebra commands such as Intersect, Point, and Vector, it dynamically illustrates these concepts. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → C
  3. Point(xAxis) → B
  4. Point(xAxis) → E
  5. Point(xAxis) → F
  6. Vector(A, A) → v_0
  7. Sequence(E + Element[vectors, Element[combo_2, k]] + Element[vectors, Element[combo_2, k + 1]], k, 1, Length[combo_2], 2) → points_2
  8. Sequence(F + Element[vectors, Element[combo_3, k]] + Element[vectors, Element[combo_3, k + 1]], k, 1, Length[combo_3], 2) → points_3
  9. Point(points_2) → H
  10. Segment(E, H) → d_1
  11. Point(points_2) → I
  12. Segment(H, I) → e
  13. Point(points_2) → J
  14. Segment(I, J) → f
  15. Segment(J, E) → g
  16. Point(points_3) → K
  17. Segment(F, K) → h_1
  18. Point(points_3) → L
  19. Segment(K, L) → i
  20. Point(points_3) → M
  21. Segment(L, M) → j
  22. Segment(M, F) → k_1
  23. Point(points_3) → N
  24. Point(points_3) → O
  25. Segment(N, O) → l
  26. Point(points_3) → P
  27. Segment(O, P) → m
  28. Segment(P, G) → n
  29. Segment(G, N) → p
  30. Segment(M, N) → q
  31. Segment(L, G) → r
  32. Segment(F, O) → s
  33. Segment(K, P) → t
  34. Sequence(A + Element[vectors, k], k, 2, 4, 1) → points_1
  35. Point(points_1) → Q
  36. Segment(A, Q) → a
  37. Point(points_1) → R
  38. Segment(A, R) → b
  39. Point(points_1) → S
  40. Segment(A, S) → c
  41. Segment(A, B) → a_0
  42. Segment(A, C) → b_0
  43. Segment(A, D) → c_0
  44. Segment(E, E + (1, 0)) → d_0
  45. Segment(E + (1, 0), E + (1, 0) + (0, 1)) → e_0
  46. Segment(E + (1, 0) + (0, 1), E + (0, 1)) → f_0
  47. Segment(E, E + (0, 1)) → g_0
  48. Segment(F, F + (1, 0)) → h_0
  49. Segment(F + (1, 0), F + (1, 0) + (0, 1)) → i_0
  50. Segment(F + (1, 0) + (0, 1), F + (0, 1)) → j_0
  51. Segment(F, F + (0, 1)) → k_0
  52. Segment(F + (cos(π / 3), sin(π / 3)), F + (cos(π / 3), sin(π / 3)) + (0, 1)) → l_0
  53. Segment(F + (cos(π / 3), sin(π / 3)), F + (cos(π / 3), sin(π / 3)) + (1, 0)) → m_0
  54. Segment(F + (cos(π / 3), sin(π / 3)) + (1, 0), F + (cos(π / 3), sin(π / 3)) + (1, 0) + (0, 1)) → n_0
  55. Segment(F + (cos(π / 3), sin(π / 3)) + (1, 0) + (0, 1), F + (cos(π / 3), sin(π / 3)) + (0, 1)) → p_0
  56. Segment(F + (0, 1), F + (cos(π / 3), sin(π / 3)) + (0, 1)) → q_0
  57. Segment(F + (1, 0) + (0, 1), F + (1, 0) + (0, 1) + (cos(π / 3), sin(π / 3))) → r_0
  58. Segment(F, F + (cos(π / 3), sin(π / 3))) → s_0
  59. Segment(F + (1, 0), F + (1, 0) + (cos(π / 3), sin(π / 3))) → t_0