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Geometric Tiling Cost Calculation

Geometric Tiling Cost Calculation
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2019-04-29 00:39
TrigonometryCoordinate GeometryIntegralGeometric ConstructionSlider Animation
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This example demonstrates how to use GeoGebra to model geometric tiling and calculate material costs. It involves core math concepts like coordinate geometry, integral calculus, and symmetry analysis. Construction highlights include using commands such as Intersect, Point, Segment, Circle, Polygon, and Line. Suitable for high school mathematics teaching or STEM project practice, integrating mathematical modeling with real-world applications.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(Circle[A, sqrt(400)]) → B
  3. Segment(A, B) → f
  4. Circle(A, B) → c
  5. Intersect(c, yAxis) → C, D
  6. Polygon(D, B, A) → Triángulo_1, a, d, b
  7. Circle(D, sqrt(800)) → e
  8. Intersect(e, yAxis) → E, F
  9. Circle(F, 20) → g
  10. Circle(D, 20) → h
  11. Intersect(h, g) → G, H, ,
  12. Polygon(D, G, F) → Triángulo_2, f_1, d_1, g_1
  13. Circle(F, 20) → k
  14. Intersect(k, yAxis) → I, J
  15. Point(Circle[J, 20]) → K
  16. Segment(J, K) → i
  17. Polygon(F, J, K) → Triángulo_3, k_1, f_2, j
  18. Point(Circle[B, sqrt(800)]) → L
  19. Segment(B, L) → l
  20. Point(Circle[L, 20]) → M
  21. Segment(L, M) → m
  22. Line(M, yAxis) → n
  23. Point(n) → N
  24. Polygon(L, M, N) → Triángulo_4, n_1, l_1, m_1
  25. Line(F, xAxis) → p
  26. Intersect(p, n) → O
  27. Line(G, xAxis) → q
  28. Circle(N, 20) → r
  29. Intersect(r, q) → P, Q
  30. Polygon(N, Q, O) → Triángulo_5, o, n_2, q_1
  31. Circle(O, 20) → s
  32. Intersect(s, n) → R, S
  33. Circle(S, 20) → t
  34. Line(J, K) → h_1
  35. Intersect(t, h_1) → T, U
  36. Polygon(T, S, O) → Triángulo_6, o_1, t_1, s_1
  37. Polygon(K, T, O, N, L, B, D, F) → Octógono, k_2, t_2, o_2, n_3, l_2, b_1, d_2, f_3
  38. Circle(B, 20) → c_1
  39. Circle(L, 20) → e_1
  40. Intersect(e_1, c_1) → V, W, ,
  41. Polygon(B, L, V) → Triángulo_7, v, b_2, l_3
  42. Circle(K, 20) → p_1
  43. Circle(T, 20) → r_1
  44. Intersect(p_1, r_1) → Z, A_1, ,
  45. Polygon(K, Z, T) → Triángulo_8, t_3, k_3, z_1
  46. Polygon(A, M, 4) → Cuadrado, i_1, j_1, a_1, g_2, D_1, E_1