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Figure Eight Knot

Figure Eight Knot
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2018-06-30 02:07
FunctionSolid GeometryGeometric Construction
This example demonstrates the geometric shape of a figure eight knot. It involves geometric constructions of curves and 3D shapes. Using commands like Cylinder and Sphere, complex 3D figures can be constructed. Suitable for high school or university geometry and topology courses.

GeoGebra Commands & Parameters

  1. Cylinder(A, B, 0.5) → a, a_2, a_3, a_4
  2. Cylinder(C, B, 0.5) → e, e_2, e_3, e_4
  3. Cylinder(C, D, 0.5) → i, i_2, i_3, i_4
  4. Cylinder(D, E, 0.5) → l, l_2, l_3, l_4
  5. Cylinder(F, E, 0.5) → b, c, d, f
  6. Cylinder(F, G, 0.5) → g, h, k, j
  7. Cylinder(H, G, 0.5) → m, p, q, n
  8. Cylinder(H, I, 0.5) → o, r, s, t
  9. Cylinder(I, J, 0.5) → u, c_1, d_1, v
  10. Cylinder(J, K, 0.5) → w, e_1, f_1, a_1
  11. Cylinder(K, L, 0.5) → b_1, g_1, h_1, i_1
  12. Cylinder(M, L, 0.5) → j_1, k_1, p_1, l_1
  13. Cylinder(M, N, 0.5) → m_1, q_1, r_1, n_1
  14. Sphere(B, 0.5) → o_1
  15. Sphere(C, 0.5) → s_1
  16. Sphere(D, 0.5) → t_1
  17. Sphere(E, 0.5) → u_1
  18. Sphere(F, 0.5) → v_1
  19. Sphere(G, 0.5) → w_1
  20. Sphere(H, 0.5) → b_2
  21. Sphere(I, 0.5) → c_2
  22. Sphere(J, 0.5) → d_2
  23. Sphere(K, 0.5) → f_2
  24. Sphere(L, 0.5) → g_2
  25. Sphere(M, 0.5) → h_2