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Spiral Ramp 1

Spiral Ramp 1
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2018-01-13 17:16
FunctionCoordinate GeometrySolid GeometryParametric Equation
In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
This example demonstrates the 3D geometric construction and visualization of a spiral ramp. Key math concepts include coordinate geometry, function graphing, 3D surfaces, parametric equations, and geometric transformations. Construction highlights from GeoGebra commands: Ray, Surface, CurveCartesian, with objects like b (width), h (height), r (radius), H (height parameter), Text1-3 (annotations), Stange (pole), a (parameter), Boden (base), Glas_1-2 (glass), and γ_1-4 (angle parameters). Suitable for high school students and above learning spatial geometry, parametric equations, 3D modeling, and physics applications like motion trajectories.

GeoGebra Commands & Parameters

  1. Ray((0, 0, 0), (0, 0, 1)) → Stange
  2. Surface(((((a * r) * (t + 1)) + (s * b)) * cos(t)), ((((a * r) * (t + 1)) + (s * b)) * sin(t)), (h / ((2 * π)) * t), t, 0, (2 * π), s, 0, 1) → Boden
  3. Surface((((a * r) * (t + 1)) * cos(t)), (((a * r) * (t + 1)) * sin(t)), (h / ((2 * π)) * t) + (s * H), t, 0, (2 * π), s, 0, 1) → Glas_1
  4. Surface(((((a * r) * (t + 1)) + b) * cos(t)), ((((a * r) * (t + 1)) + b) * sin(t)), (h / ((2 * π)) * t) + (s * H), t, 0, (2 * π), s, 0, 1) → Glas_2
  5. CurveCartesian((((a * r) * (t + 1)) * cos(t)), (((a * r) * (t + 1)) * sin(t)), (h / ((2 * π)) * t), t, 0, (2 * π)) → γ_1
  6. CurveCartesian(((((a * r) * (t + 1)) + b) * cos(t)), ((((a * r) * (t + 1)) + b) * sin(t)), (h / ((2 * π)) * t), t, 0, (2 * π)) → γ_2
  7. CurveCartesian((((a * r) * (t + 1)) * cos(t)), (((a * r) * (t + 1)) * sin(t)), H + (h / ((2 * π)) * t), t, 0, (2 * π)) → γ_3
  8. CurveCartesian(((((a * r) * (t + 1)) + b) * cos(t)), ((((a * r) * (t + 1)) + b) * sin(t)), 1 + (h / ((2 * π)) * t), t, 0, (2 * π)) → γ_4