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World Famous Domes

World Famous Domes
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2018-12-06 04:29
Coordinate GeometrySolid GeometryGeometric Construction
This example showcases famous domes from around the world. It involves core concepts of circles and solid geometry. Using GeoGebra commands such as Sequence, CurveCartesian, and Point, dynamic construction and display of dome geometries are demonstrated. Suitable for high school students and architects.

GeoGebra Commands & Parameters

  1. Sequence((x(O) + (R * cos(i)), y(O) + (R * sin(i)), z(O)), i, 0, 6.283185307179586, 0.7853981633974483) → liste1
  2. Sequence(Segment[Element[liste1, i], Element[liste1, i + 1]], i, 1, Length[liste1]) → liste2
  3. CurveCartesian(x(O) + (R * cos(i)), y(O), z(O) + ((R + d) * sin(i)), i, 0, 1.3708) → e
  4. Sequence(Rotate[e, i, O], i, 0, 6.28319, 0.7854) → liste4
  5. Sequence((x(C) + (r * cos(i)), y(C) + (r * sin(i)), z(C) + 0.1), i, 0, 6.28319, 0.7854) → liste3
  6. Sequence(Segment[Element[liste3, i], Element[liste3, i + 1]], i, 1, Length[liste3]) → liste5
  7. Sequence((x(C) + ((r - 0.35) * cos(i)), y(C) + ((r - 0.35) * sin(i)), z(C)), i, 0, 6.28319, 1.5708) → liste7
  8. Sequence((x(C) + ((r - 0.35) * cos(i)), y(C) + ((r - 0.35) * sin(i)), z(C) + 1.3), i, 0, 6.28319, 1.5708) → liste8
  9. Sequence(Polygon[Element[liste7, i], Element[liste8, i], Element[liste8, i + 1], Element[liste7, i + 1]], i, 1, Length[liste7]) → liste10
  10. Sequence((x(C) + ((r - 0.35) * cos(i)), y(C) + ((r - 0.35) * sin(i)), z(C) + 0.7), i, 0, 6.28319, 0.7854) → liste11
  11. Sequence((x(C) + ((r - 0.25) * cos(i)), y(C) + ((r - 0.25) * sin(i)), z(C) + 1.3), i, 0, 6.28319, 1.5708) → liste13
  12. Sequence(Segment[Element[liste13, i], Element[liste13, i + 1]], i, 1, Length[liste13]) → liste14
  13. Sequence(Translate[liste14, Vector[(i * Vector[C + (0, 0, 1.2), C + (0, 0, 1.25)])]], i, 0, 1, 0.1) → liste15
  14. Sequence((x(C) + ((r - 0.38) * cos(i)), y(C) + ((r - 0.38) * sin(i)), z(C) + 1.3), i, 0, 6.28319, 0.3927) → liste16
  15. Sequence(Polygon[Element[liste16, i], Element[liste16, i + 1], D], i, 1, Length[liste16]) → liste17
  16. Segment(F, E) → b
  17. Segment(G, H) → c
  18. Point(liste4) → I
  19. Surface(x(O) + ((R * cos(i)) * cos(j)), y(O) + (R * sin(j)), z(O) + ((R + d) * sin(i)), i, 0, 1.3708, j, 0, 6.28319) → a
  20. Sequence((x(C) + ((r - 0.2) * cos(i)), y(C) + ((r - 0.2) * sin(i)), z(C) + 0.5), i, 0, 6.28319, 0.7854) → liste6b
  21. Sequence((x(O) + ((R + 0.2) * cos(i)), y(O) + ((R + 0.2) * sin(i)), z(O)), i, 0, 6.28319, 0.7854) → liste1b
  22. Sequence(Segment[Element[liste1b, i], Element[liste1b, i + 1]], i, 1, Length[liste1b]) → liste19
  23. Sequence(Segment[Element[liste11, i], Element[liste6b, i]], i, 1, Length[liste6b]) → liste12
  24. Sequence((x(C) + ((r - 0.2) * cos(i)), y(C) + ((r - 0.2) * sin(i)), z(C) + 0.1), i, 0, 6.28319, 0.7854) → liste3b
  25. Sequence(Segment[Element[liste3b, i], Element[liste6b, i]], i, 1, Length[liste3b]) → liste9
  26. Surface(x(O) + ((R * cos(i)) * cos(j)), y(O) + ((R * cos(i)) * sin(j)), z(O) + ((R + d) * sin(i)), i, 0, 1.37, j, 0, 6.28319) → f
  27. Sequence(Polygon[Element[liste3, i], Element[liste3, i + 1], C + (0, 0, 0.3)], i, 1, Length[liste3]) → liste18
  28. Sequence(Segment[Element[liste13, i], Element[liste13, i] + (0, 0, 0.5)], i, 1, Length[liste13]) → liste6
  29. Sequence(Translate[liste19, Vector[(i * Vector[O, O - (0, 0, 1)])]], i, 0, 1, 0.025) → liste20
  30. Sequence((x(O) + (R * cos(i)), y(O), z(O) + ((R + d) * sin(i))), i, 0, 1.3708, 0.07853981633974483) → liste22
  31. Join(Sequence[Rotate[liste22, i, O], i, 0, 6.28319, 0.07854]) → liste23
  32. Sequence(Segment[Element[liste23, i], Element[liste23, i + g]], i, 1, Length[liste23]) → liste24
  33. Sequence(Rotate[e, i, O], i, 0, 6.28319, 0.031415926535897934) → liste21
  34. Sequence((x(O) + (R * cos(i)), y(O), z(O) + ((R + d) * sin(i))), i, 0.175, 1.3, 0.4066666666666667) → liste25
  35. Join(Sequence[Rotate[liste25, i, O], i, 0, 6.28319, 0.19634954084936207]) → liste26