MathPlotAI Logo MathPlotAI

World-Famous Domes

World-Famous Domes
Loading the math board and drawing, please wait…
2018-12-03 16:31
TrigonometrySolid GeometryGeometric Construction
This example showcases famous domes from around the world. It involves key mathematical concepts such as triangles, circles, and solid geometry. Using GeoGebra commands like Vector, OrthogonalLine, and Translate, the geometric shape of the domes can be constructed. Suitable for high school students and math enthusiasts.

GeoGebra Commands & Parameters

  1. Vector(O, Y) → v
  2. Vector(O, X) → w
  3. Vector(O, Z) → u
  4. OrthogonalLine(Vues, yAxis) → a_1
  5. OrthogonalLine(Vues, xAxis) → b
  6. Translate(O, Vector[(g * u)]) → A_1
  7. Segment(O, A_1) → d
  8. Mirror(A_1, O) → E_1
  9. Segment(E_1, O) → i
  10. Sequence(CurveCartesian[x(O) + ((R * cos(j°)) * sin(i)), y(O) + ((R * sin(j°)) * sin(i)), z(O) + ((R + a) * cos(i)), j, 0, 360], i, tt, t, π / ((10 * n))) → liste1
  11. Element(liste1, 1) → aa
  12. CurveCartesian(x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - 0.2, i, 0, 360) → o
  13. Vector(B, C) → z
  14. Translate(aa, z) → aa'
  15. Translate(aa, Vector[(2 * z)]) → aa'_1
  16. Segment(J, K) → r
  17. Sequence(I + (((r - 0.05) * cos(i)) * u) + (((r - 0.05) * sin(i)) * v), i, 0, 6.28319, π / n) → liste6
  18. Sequence((x(C) + ((r - 0.05) * cos(i)), y(C) + ((r - 0.05) * sin(i)), z(C)), i, 0, 6.28319, π / n) → liste5
  19. Sequence(Segment[Element[liste5, i], Element[liste6, i]], i, 1, Length[liste6]) → liste7
  20. Sequence((x(I) + ((r - 0.19) * cos(i)), y(I) + ((r - 0.19) * sin(i)), z(I)), i, 0, 6.28319, π / n) → liste8
  21. Sequence((x(D) + ((r - 0.19) * cos(i)), y(D) + ((r - 0.19) * sin(i)), z(D)), i, 0, 6.28319, π / n) → liste9
  22. Sequence(Segment[Element[liste8, i], Element[liste9, i]], i, 1, Length[liste8]) → liste10
  23. Sequence((x(D) + ((r - 0.35) * cos(i)), y(D) + ((r - 0.35) * sin(i)), z(D) + 0.1), i, 0, 6.28319, π / n) → liste12
  24. Sequence(Segment[Element[liste12, i], E], i, 1, Length[liste12]) → liste11
  25. Sequence(Translate[aa, Vector[(i * z)]], i, 0, 0.75, 0.2) → liste13
  26. Circle(G, E, xOyPlane) → c_1
  27. Sequence((x(C) + ((r - 0.05) * cos(i + bb)), y(C) + ((r - 0.05) * sin(i + bb)), z(C)), i, 0, 6.28319, π / n) → liste5b
  28. Sequence((x(I) + ((r - 0.05) * cos(i + bb)), y(I) + ((r - 0.05) * sin(i + bb)), z(I)), i, 0, 6.28319, π / n) → liste6b
  29. Sequence(Segment[Element[liste5b, i], Element[liste6b, i]], i, 1, Length[liste6]) → liste7b
  30. CurveCartesian(x(C) + ((r + 0.15) * cos(i)), y(C) + ((r + 0.15) * sin(i)), z(C) - 0.2, i, 0, 6.28319) → b_1
  31. Sequence(Translate[b_1, Vector[(i * z)]], i, 0, 1.75, 0.2) → liste14
  32. Sequence(Segment[Element[liste12, i], Element[liste12, i + 1]], i, 1, Length[liste12] + 1) → liste15
  33. Sequence((x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - 0.75), i, 0, 360, 180 / n) → liste16
  34. Sequence((x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - 0.2), i, 0, 360, 180 / n) → liste17
  35. Sequence(Segment[Element[liste16, i], Element[liste17, i]], i, 1, Length[liste17]) → liste18
  36. CurveCartesian(x(O) + (R * sin(i°)), y(O) - (R * cos(i°)), z(O) - 0.75, i, 0, 360) → f_1
  37. Vector(F, O) → u_1
  38. Sequence(Translate[f_1, Vector[(u_1 * i)]], i, 0, 1, 0.075) → liste19
  39. Segment(M, N) → j_1
  40. Sequence((x(O) + ((R + 0.2) * sin(i°)), y(O) - ((R + 0.2) * cos(i°)), z(O) - 1), i, 0, 360, 90 / n) → liste21
  41. Sequence((x(O) + ((R + 0.2) * sin(i°)), y(O) - ((R + 0.2) * cos(i°)), z(O) - 0.75), i, 0, 360, 90 / n) → liste20
  42. Sequence((x(O) + ((R + 0.3) * sin(i° + kk°)), y(O) - ((R + 0.3) * cos(i° + kk°)), z(O) - 1), i, 0, 360, 90 / n) → liste23
  43. Sequence(Polygon[Element[liste21, i], Element[liste21, i + 1], Element[liste20, 1 + i], Element[liste20, i]], i, 1, Length[liste20]) → liste22
  44. Sequence((x(O) + ((R + 0.3) * sin(i° + kk°)), y(O) - ((R + 0.3) * cos(i° + kk°)), z(O) - 0.75), i, 0, 360, 90 / n) → liste24
  45. Sequence(Polygon[Element[liste23, i], Element[liste23, i + 1], Element[liste24, 1 + i], Element[liste24, i]], i, 1, Length[liste24], 2) → liste25
  46. Sequence(CurveCartesian[x(O) + ((R * cos(j°)) * sin(i)), y(O) + ((R * sin(j°)) * sin(i)), z(O) + ((R + a) * cos(i)), i, tt, t], j, 0, 360, 180 / n) → liste2
  47. Sequence(CurveCartesian[x(O) + (((R + 0.1) * cos(j°)) * sin(i)), y(O) + (((R + 0.1) * sin(j°)) * sin(i)), z(O) + ((R + 0.1 + a) * cos(i)), i, tt, t], j, 0, 360, 180 / n) → liste3
  48. Sequence(CurveCartesian[x(O) + (((R + 0.05) * cos(j°)) * sin(i)), y(O) + (((R + 0.05) * sin(j°)) * sin(i)), z(O) + ((R + a + 0.05) * cos(i)), i, tt, t], j, 0, 360, 180 / ((3 * n))) → liste4
  49. CurveCartesian(x(I) + ((r - 0.05) * cos(i)), y(I) + ((r - 0.05) * sin(i)), z(I) - 0.07, i, 0, 6.28319) → d_1
  50. CurveCartesian(x(O) + ((R + 0.2) * sin(i°)), y(O) - ((R + 0.2) * cos(i°)), z(O) - 0.75, i, 0, 360) → g_1
  51. CurveCartesian(x(O) + ((R + 0.2) * sin(i°)), y(O) - ((R + 0.2) * cos(i°)), z(O) - 1, i, 0, 360) → h_1
  52. CurveCartesian(x(O) + (R * sin(i°)), y(O) - (R * cos(i°)), z(O) - (R * sin(i°)), i, 0, 360) → e
  53. CurveCartesian(x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - 0.75, i, 0, 360) → e_1
  54. CurveCartesian(x(O) + (R * sin(i°)^(3)), y(O) - (R * cos(i°)^(3)), z(O) - (R * sin(i°)^(3)), i, 0, 360) → f
  55. CurveCartesian(x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - (((R + 0.1) * 0) * sin(i°)), i, 0, 360) → j
  56. CurveCartesian(x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - 0.1, i, 0, 360) → l
  57. CurveCartesian(x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) + 0, i, 0, 360) → p
  58. CurveCartesian(x(I) + ((r - 0.05) * cos(i)), y(I) + ((r - 0.05) * sin(i)), z(I), i, 0, 6.28319) → s
  59. CurveCartesian(x(O) + (R * sin(i°)), y(O) - (R * cos(i°)), z(O) - ((R * 0) * sin(i°)), i, 0, 360) → h
  60. Segment(L, G + (0, 0, 0.125)) → i_1
  61. Surface(x(O) + ((R * cos(j°)) * sin(i)), y(O) + ((R * sin(j°)) * sin(i)), z(O) + ((R + a) * cos(i)), j, 0, 360, i, tt, t) → l_1

AI Drawing Prompt Reference

Draw the geometric shape of world-famous domes, showcasing key concepts like triangles, circles, and solid geometry. Start by constructing three basic vectors and creating orthogonal lines. Then, use translation and reflection to form the basic structure. Employ parametric equations to draw circular curves and generate multiple concentric circles and surfaces through sequence operations. Finally, combine all elements to form a complex dome structure, demonstrating the construction process of solid geometry.
The prompt above was compiled from the original drawing commands and is for reference only.