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Holiday Fun (2) - Cylinder and Inequalities

Holiday Fun (2) - Cylinder and Inequalities
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2018-01-17 02:16
Solid GeometryCalculusProbability & StatisticsTransformationInequality
This example demonstrates the intersection of a cylinder surface with a path, integrating inequalities and random experiments to showcase similarity transformations in solid geometry. Core concepts include cylinder volume calculation, inequality representation, random experiment simulation, and properties of similarity transformations. Construction highlights involve using Surface, IntersectPath, Plane, Mirror, and Line commands. Suitable for high school solid geometry, calculus, and probability & statistics teaching to visualize complex geometric relationships and dynamic changes.

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