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Crossed Rhombus 3D Surface Geometry Demo

Crossed Rhombus 3D Surface Geometry Demo
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2018-03-01 13:27
Solid GeometryIntegralTransformationGeometric Construction
This example demonstrates a curious 3D geometric figure utilizing GeoGebra's surface capabilities, focusing on crossed rhombus structures. Key mathematical concepts involve solid geometry, piecewise functions, definite integrals, and singular points. Construction relies on commands like Plane, Cylinder, Cube, Surface, Rotate, and IntersectPath, defining points, polygons, and curves to generate complex surfaces. Suitable for high school or college students exploring 3D spatial visualization, geometric transformations, and calculus applications, aiding understanding of surface-geometry interactions.

GeoGebra Commands & Parameters

  1. Plane(A, B, O) → c_1
  2. Plane(O, D, B) → d_1
  3. Cylinder(P_1, P_2, r) → a_5, a_2, a_3, a_4
  4. Cylinder(Q_1, Q_2, r) → b_1, b_2, b_3, b_4
  5. OrthogonalPlane(R_2, zAxis) → e
  6. Cube(N, M, e) → f, C, cara4, cara5, cara6, aresta1, aresta2, aresta3, aresta4, aresta5, aresta6, aresta7, E, aresta8, aresta9, aresta10, aresta11, aresta12, F, G, H, I, cara1, cara2, cara3
  7. IntersectPath(c_1, a_5) → g
  8. Corner(g) → J, K, L, P
  9. IntersectPath(d_1, a_5) → h
  10. Corner(h) → Q, R, S, T
  11. Polygon(A, S, L, D) → q1, a, d, c, b
  12. Circle(O, r, u) → k
  13. Circle(O, r, v) → p
  14. Center(g) → U
  15. Center(h) → V
  16. CurveCartesian((a / 2 * cos(t)), (a / 2 * cos(t)), (a / 2 * sin(t)), t, 0, (2 * π)) → i
  17. CurveCartesian((a / 2 * cos(t)), (((-a)) / 2 * cos(t)), (a / 2 * sin(t)), t, 0, (2 * π)) → l
  18. Surface((s * i(t)) + ((1 - s) * l(t)), s, 0, 1, t, ((-π)) / 2, π / 2) → m
  19. Rotate(m, π / 2, zAxis) → m'
  20. Rotate(m', π / 2, zAxis) → m''
  21. Rotate(m'', π / 2, zAxis) → m'''
  22. Rotate(m, α, zAxis) → mrot