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Isometric View and Planar Graph

Isometric View and Planar Graph
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2017-11-21 14:46
Coordinate GeometrySolid Geometry
This example demonstrates isometric views and planar graphs. Using various GeoGebra commands such as Circle, Intersect, Rotate, Polygon, etc., it constructs isometric views and planar graphs. This involves knowledge of solid geometry and coordinate geometry. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(OO, 1, xOyPlane) → c
  2. Intersect(yAxis, c, 2) → A
  3. Rotate(A, 45°) → B
  4. Polygon(A, B, 8, xOyPlane) → veelhoek1, zijde, D, E, F, G, H, g, h, i, j, k, l, m, C
  5. Polygon(B, A, 4, xOyPlane) → veelhoek2, f, n, p, q, I, J
  6. Polygon(D, C, 4, xOyPlane) → veelhoek3, r, s, t, a, K, L
  7. Circle(r, K) → d
  8. Circle(f, J) → e
  9. Intersect(d, e) → M, N, ,
  10. Angle(J, B, N) → α
  11. Rotate(veelhoek2, -135°, zijde) → schuin
  12. Line(OO, OOO) → as
  13. LineBisector(A, B, xOyPlane) → b
  14. Circle(OO, zijde / 2, xOyPlane) → c_1
  15. Intersect(b, c_1) → O, P
  16. OrthogonalLine(O, b, xOyPlane) → f_1
  17. Intersect(zijde, f) → Q
  18. Intersect(b, zijde) → R
  19. Vector(R, P) → u
  20. Translate(veelhoek2, u) → veelhoek2'
  21. Translate(veelhoek2', Vector[(0, 0, z(N))]) → boven
  22. Translate(veelhoek2', Vector[(0, 0, (-z(N)) - zijde)]) → veelhoek2''
  23. Rotate(veelhoek2, 90°, zijde) → recht
  24. Sequence(Rotate[schuin, ((n * 90))°, as], n, 0, 3) → lijst_1
  25. Sequence(Rotate[recht, ((nn * 45))°, as], nn, 0, 7) → lijst_2
  26. Mirror(lijst_1, o) → lijst_3
  27. Mirror(lijst_2, o) → lijst_4
  28. Mirror(N, Midden) → N'
  29. Polygon(B, C, N) → driehoek1, n_1, b_1, c_2
  30. Sequence(Rotate[driehoek1, ((nn * 90))°, as], nn, 0, 3) → lijst_5
  31. Mirror(lijst_5, o) → lijst_6
  32. Polygon(LO, RO, 4) → veelhoek4, g_1, h_1, i_1, j_1, S, T
  33. Polygon(U, V, 8) → veelhoek5, k_1, Z, A_1, B_1, C_1, D_1, l_1, m_1, p_1, q_1, r_1, s_1, t_1, W
  34. Polygon(E_1, F_1, 8) → veelhoek6, a_1, H_1, I_1, J_1, K_1, L_1, d_1, e_1, f_2, g_2, h_2, i_2, j_2, G_1
  35. Polygon(M_1, N_1, 4) → veelhoek7, k_2, l_2, m_2, n_2, O_1, P_1
  36. Segment(T, B_1) → p_2
  37. Segment(T, C_1) → q_2
  38. Segment(A_1, S) → r_2
  39. Segment(Z, S) → s_2
  40. Segment(W, RO) → t_2
  41. Segment(V, RO) → a_2
  42. Segment(U, LO) → b_2
  43. Segment(D_1, LO) → d_2
  44. Segment(C_1, K_1) → e_2
  45. Segment(D_1, L_1) → f_3
  46. Segment(U, E_1) → g_3
  47. Segment(F_1, V) → h_3
  48. Segment(G_1, W) → i_3
  49. Segment(H_1, Z) → j_3
  50. Segment(I_1, A_1) → k_3
  51. Segment(J_1, B_1) → l_3
  52. Segment(P_1, K_1) → m_3
  53. Segment(P_1, J_1) → n_3
  54. Segment(O_1, I_1) → p_3
  55. Segment(O_1, H_1) → q_3
  56. Segment(N_1, G_1) → r_3
  57. Segment(N_1, F_1) → s_3
  58. Segment(M_1, E_1) → t_3
  59. Segment(L_1, M_1) → a_3

AI Drawing Prompt Reference

Draw an isometric view and a planar graph. Start by drawing a unit circle, then find the intersection point A on the y-axis, rotate A to get B, draw an octagon and a quadrilateral, and then use rotation and mirroring to generate a series of shapes, including triangles and polygons, and finally form a complex isometric view and planar graph.
The prompt above was compiled from the original drawing commands and is for reference only.