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Holiday Fun (2): Cylinder-Rectangle Dynamic Construction

Holiday Fun (2): Cylinder-Rectangle Dynamic Construction
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2017-12-26 09:16
Solid GeometryTransformationParametric EquationGeometric ConstructionSlider Animation
① This GeoGebra example demonstrates a festive-themed 3D geometric construction based on a cylinder, incorporating rectangular sections, translations, and mirror transformations. ② Core mathematical concepts include solid geometry of cylinders, intersection paths between planes and surfaces, mirror symmetry, translation, and subtraction operations applied to geometric objects, blending 3D visualization with transformation geometry. ③ Construction highlights: the Surface command creates the cylindrical surface, Plane defines cutting sections, IntersectPath computes intersection curves, and Mirror with Line enables symmetric auxiliary elements; objects such as h, r, R, and numerous points/lines/planes are parameterized for dynamic adjustment. ④ Suitable for upper secondary or early university students as an exploratory exercise in solid geometry and dynamic mathematics, and ideal for holiday-themed math activities to enhance engagement.

GeoGebra Commands & Parameters

  1. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, 0, π / 6) → g
  2. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, π / 6, π / 3) → b
  3. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, π / 3, π / 2) → c
  4. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, π / 2, (2 * π / 3)) → d
  5. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, (2 * π / 3), (5 * π / 6)) → e
  6. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, (5 * π / 6), π) → f
  7. IntersectPath(y = 0, i) → k
  8. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, 0, h / 6) → j
  9. Plane((0, 0, 0), (3, 0, 0), (10, 0, 5)) → l
  10. Mirror(j, l) → j'
  11. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, h / 6, h / 3) → m
  12. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, h / 3, h / 2) → n
  13. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, h / 2, (2 * h / 3)) → o
  14. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, (2 * h / 3), (5 * h / 6)) → p
  15. Surface((-R) + (r * cos(u)), v, (r * sin(u)), u, 0, u_1, v, (5 * h / 6), h) → q
  16. Mirror(m, l) → m'
  17. Mirror(n, l) → n'
  18. Mirror(o, l) → o'
  19. Mirror(p, l) → p'
  20. Mirror(q, l) → q'
  21. Line((0, 0, 0), (0, 0, 1)) → s
  22. Line((0, 0, 0), (1, 0, 0)) → t
  23. Line((0, 0, 0), (0, 1, 0)) → a
  24. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, π, (7 * π / 6)) → v
  25. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, (7 * π / 6), (4 * π / 3)) → w
  26. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, (4 * π / 3), (3 * π / 2)) → a_1
  27. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, (3 * π / 2), (5 * π / 3)) → b_1
  28. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, (5 * π / 3), (11 * π / 6)) → c_1
  29. Surface(((R + (r * cos(u))) * cos(v)), ((R + (r * cos(u))) * sin(v)), (r * sin(u)), u, 0, u_1, v, (11 * π / 6), (2 * π)) → d_1