How to Support a Spherical Dome?

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2017-02-08 21:39

This example demonstrates how to construct the supporting structure of a spherical dome using geometric construction tools. Key mathematical concepts include solid geometry and coordinate geometry. Using GeoGebra commands such as Segment, Point, Polygon, Prism, etc., the various faces and supporting structures of the dome can be built. Suitable for high school or university students and teachers.

GeoGebra Commands & Parameters

Segment(A, AA) → f
Point(f) → I
Segment(A, I) → g
Polygon(A, B, C, D) → veelhoek1, a_1, b_1, c, d
Prism(veelhoek1, -1.5) → e, E, Ribbe1, Ribbe2, Ribbe3, Ribbe4, Ribbe5, Ribbe6, Ribbe7, Ribbe8, F, G, H, zijvlak1, zijvlak2, zijvlak3, zijvlak4, zijvlak5
Surface(cos(α), sin(α), sin(α), α, 0°, 180°, α, 0°, 180°) → b
Surface(cos(α), sin(α), cos(β), α, 0°, 360°, β, 0, 90°) → a
Surface((sqrt(1 - h^(2)) * cos(θ)), (sqrt(1 - h^(2)) * sin(θ)), h, θ, 0, 6.28319, h, 0, 1) → h
Line(O, OO) → as
Circle(O, 1, as) → k
Cylinder(k, 1.5) → i_3, i_2, i_3