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From Circular Arc to Dome

From Circular Arc to Dome
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2017-02-08 20:55
CirclePolygonSolid Geometry
In collections muqarnas - English version
This example demonstrates how to construct a dome from a circular arc. It involves key concepts in circle, polygon, and solid geometry. Using GeoGebra commands such as CircumcircleArc, Rotate, and Polygon, one can visually understand how a circular arc expands into a complete dome structure. Suitable for high school or university-level solid geometry studies.

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. Line((0, 0, 0), (0, 0, 2)) → as
  9. Circle(O, 1, as) → k
  10. Cylinder(k, 1.5) → i_3, i_2, i_3
  11. Surface((sqrt(1 - h^(2)) * cos(θ)), (sqrt(1 - h^(2)) * sin(θ)), h, θ, 0, hoek, h, 0, 1) → h
  12. Surface((sqrt(1 - h^(2)) * cos(θ)), (sqrt(1 - h^(2)) * sin(θ)), h, θ, 180°, 180° + hoek, h, 0, 1) → m
  13. CircumcircleArc(ST, T, SE) → p
  14. Rotate(p, hoek, as) → p'
  15. Segment(ST, SE) → n

AI Drawing Prompt Reference

Draw a dome structure starting from a circular arc. First, create a circular arc, then rotate it around an axis to form a semicircle. Next, use four points to create a quadrilateral and extend it into a quadrilateral prism. Finally, replace the top of the prism with a dome shape to complete the structure.
The prompt above was compiled from the original drawing commands and is for reference only.