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Circle Tessellation

Circle Tessellation
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2019-11-08 07:26
CirclePolygonTransformation
This example demonstrates how to create a continuous, seamless pattern by tessellating circles. It involves core mathematical concepts such as circles, polygons, trigonometric functions, and geometric transformations. The construction uses commands like Polygon, Midpoint, Circle, and Rotate in GeoGebra. Suitable for high school mathematics education to understand geometric tiling and transformation principles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, f, F, g, h, i, j, k, C, D, E
  2. Midpoint((5.428986557915232, 2.602923418550408), (6.97797311583046, 0.04584683710081583)) → H
  3. Midpoint(B, A) → L
  4. Midpoint(C, D) → G
  5. Circle(C, G) → c
  6. Circle(E, H) → d
  7. Circle(A, L) → e
  8. Circle(B, L) → p
  9. Circle(D, G) → q
  10. Circle(F, H) → r
  11. Polygon(E, D, 6) → poly2, l, M, m, n, s, t, a, I, J, K
  12. Polygon(I, D, 6) → poly3, b, Q, f_1, g_1, h_1, i_1, j_1, N, O, P
  13. Polygon(C, B, 6) → poly4, k_1, U, l_1, m_1, n_1, p_1, q_1, R, S, T
  14. Polygon(B, A, 6) → poly5, r_1, A_1, s_1, t_1, a_1, b_1, c_1, V, W, Z
  15. Polygon(F, E, 6) → poly6, d_1, E_1, e_1, f_2, g_2, h_2, i_2, B_1, C_1, D_1
  16. Polygon(A, F, 6) → poly7, j_2, I_1, k_2, l_2, m_2, n_2, p_2, F_1, G_1, H_1
  17. Rotate(d, 120°, F) → d'
  18. Rotate(q, 120°, E) → q'
  19. Rotate(c, 120°, D) → c'
  20. Rotate(p, 120°, C) → p'
  21. Rotate(e, 120°, B) → e'
  22. Rotate(r, 120°, A) → r'
  23. Rotate(q', 120°, K) → q''
  24. Rotate(e', 120°, Z) → e''
  25. Rotate(p', 120°, T) → p''
  26. Rotate(d', 120°, D_1) → d''
  27. Rotate(p, 120°, R) → p'_1
  28. Rotate(e, 120°, V) → e'_1
  29. Rotate(r', 120°, H_1) → r''
  30. Rotate(r, 120°, E_1) → r'_1
  31. Rotate(d, 120°, M) → d'_1
  32. Rotate(q, 120°, I) → q'_1
  33. Rotate(c', 120°, Q) → c''
  34. Rotate(c, 120°, O) → c'_1