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Printable Spiral Cylinder

Printable Spiral Cylinder
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2019-07-01 17:00
TrigonometryCoordinate GeometrySolid GeometryComplex NumberGeometric Construction
This example demonstrates how to construct a spiral cylinder using GeoGebra, involving core mathematical concepts such as cylinder, median line, complex numbers, mode, and right triangles. Key construction steps include using commands like Intersect, Point, Circle, Cylinder, Surface, CurveCartesian, and Translate. Suitable for high school students studying solid geometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xOyPlane) → A
  2. Point(zAxis) → B
  3. Circle(A, 3, zAxis) → c
  4. Cylinder(c, z(B)) → a, d, b
  5. Surface((u * cos(t)), (u * sin(t)), (z(B) * t / π), t, 0, π, u, -3, 3) → e
  6. CurveCartesian((3 * cos(t)), (3 * sin(t)), (z(B) * t / π), t, 0, π) → f
  7. CurveCartesian((3 * cos(t - π)), (3 * sin(t - π)), (z(B) * t / π), t, 0, π) → g
  8. Surface(f, π, zAxis) → h
  9. Surface(g, π, zAxis) → i
  10. CurveCartesian(t, 0, z(B), t, 0, 3) → k
  11. Surface(k, π, zAxis) → l
  12. CurveCartesian(t, 0, 0, t, -3, 0) → j
  13. Surface(j, π, zAxis) → m
  14. Translate(Rotate[l, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → o
  15. Translate(Rotate[i, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → p
  16. Translate(Rotate[m, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → q
  17. Translate(Rotate[e, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → r
  18. Translate(Rotate[f, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → s
  19. Translate(Rotate[g, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → t
  20. Surface(CurveCartesian[t, 0, z(B), t, -3, 0], π, zAxis) → u
  21. Surface(CurveCartesian[t, 0, 0, t, 0, 3], π, zAxis) → v