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Cylinder Partition

Cylinder Partition
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2020-03-03 07:48
Solid GeometryGeometric Construction
This example demonstrates the dynamic partitioning and geometric properties of a cylinder through interactive manipulation. It involves core mathematical concepts such as solid geometry, fractions, ratios, addition, LCM, and GCD. Construction highlights include commands like Intersect, Circle, Cylinder, PointIn, Line, Point, Segment, Spline, CurveCartesian, Surface, Vector, and Translate, as derived from the construction summary. Suitable for high school and above for teaching demonstrations and geometric exploration.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 2) → c
  3. Cylinder(c, 5) → a, d, b
  4. PointIn(b) → C
  5. Line(C, zAxis) → k
  6. Point(k) → H
  7. Segment(C, H) → p
  8. Point(p, n) → I
  9. PointIn(b) → B
  10. PointIn(b) → D
  11. PointIn(b) → E
  12. PointIn(b) → F
  13. PointIn(b) → G
  14. Spline(l1, 3) → e
  15. CurveCartesian((2 * cos(arg(e(t)))), (2 * sin(arg(e(t)))), z(e(t)), t, 0, 1) → f
  16. CurveCartesian((2 * cos(arg(f(t)))), (2 * sin(arg(f(t)))), z(f(t)), t, 0, 1) → g
  17. CurveCartesian((2 * cos(arg(f(t)))), (2 * sin(arg(f(t)))), 0, t, 0, 1) → h
  18. Surface(((1 - k) * h(t)) + (k * f(t)), k, 0, 1, t, 0, 1) → i
  19. Surface((k * g(1 - t)) + ((1 - k) * g(t)), k, 0, 1, t, 0, 1) → j
  20. Vector(C, I) → u
  21. Translate(d, u) → d'
  22. Translate(j, u) → j'
  23. Translate(g, u) → g'
  24. CurveCartesian((2 * cos(arg(f(t)))), (2 * sin(arg(f(t)))), 5, t, 0, 1) → l
  25. Surface(((1 - k) * l(t)) + (k * g(t)), k, 0, 1, t, 0, 1) → m
  26. Translate(m, u) → m'