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Dome with Cantilever Construction

Dome with Cantilever Construction
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2017-02-08 21:50
TrigonometrySolid GeometryParametric EquationGeometric Construction
In collections muqarnas - English version
This example demonstrates the geometric construction of a dome with cantilever elements. It involves core mathematical concepts such as polygon construction, solid geometry generation, and symmetry analysis. Key GeoGebra commands and objects used in the construction include Segment, Point, Polygon, Prism, Surface, Line, Circle, Cylinder, Intersect, Rotate, and Mirror. It is suitable for high school and above students for learning spatial geometry and developing visualization skills.

GeoGebra Commands & Parameters

  1. Segment(A, AA) → f
  2. Point(f) → I
  3. Segment(A, I) → g
  4. Polygon(A, B, C, D) → veelhoek1, a_1, b_1, c, d
  5. Prism(veelhoek1, -1.5) → e, E, Ribbe1, Ribbe2, Ribbe3, Ribbe4, Ribbe5, Ribbe6, Ribbe7, Ribbe8, F, G, H, zijvlak1, zijvlak2, zijvlak3, zijvlak4, zijvlak5
  6. Surface(cos(α), sin(α), sin(α), α, 0°, 180°, α, 0°, 180°) → b
  7. Surface(cos(α), sin(α), cos(β), α, 0°, 360°, β, 0, 90°) → a
  8. Surface((sqrt(1 - h^(2)) * cos(θ)), (sqrt(1 - h^(2)) * sin(θ)), h, θ, 0, 6.28319, h, 0, 1) → h
  9. Line(O, OO) → as
  10. Circle(O, 1, as) → k
  11. Cylinder(k, 1.5) → i_3, i_2, i_3
  12. Intersect(yAxis, zijvlak4) → J
  13. Rotate(J, 22.5°, as) → J'
  14. Line(O, J') → m
  15. Intersect(m, zijvlak5) → K
  16. Segment(A, D) → n
  17. Intersect(m, n) → L
  18. Mirror(L, J) → L'
  19. Polygon(L, L', 8, xOyPlane) → veelhoek2, p, N, P, Q, R, S, q, r, s, t, f_1, g_1, h_1, M
  20. Segment(C, D) → i_1
  21. Rotate(L, -90°, i_1) → L'_1
  22. Polygon(L'_1, L, S) → veelhoek3, s_1, l'_1, l_1
  23. Rotate(veelhoek3, 90°, as) → veelhoek3'
  24. Rotate(veelhoek3, -90°, as) → veelhoek3'_1
  25. Rotate(veelhoek3, 180°, as) → veelhoek3'_2
  26. Rotate(L'_1, 90°, as) → T
  27. Rotate(L'_1, -90°, as) → U
  28. Rotate(L'_1, 180°, as) → V
  29. Polygon(H, E, U, L', L, L'_1) → veelhoek4, h_2, e_1, u, l', l_2, l'_2
  30. Polygon(E, F, V, N, M, U) → veelhoek5, e_2, f_2, v, n_1, m_1, u_1
  31. Polygon(F, G, T, Q, P, V) → veelhoek6, f_3, g_2, t_1, q_1, p_1, v_1
  32. Polygon(G, H, L'_1, S, R, T) → veelhoek7, g_3, h_3, o_2, s_2, r_1, t_2