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Animation Demonstrating Geometric Mean and Cylinder Intersection

Animation Demonstrating Geometric Mean and Cylinder Intersection
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2017-03-04 21:54
Solid GeometryGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2
This example dynamically illustrates the concept of geometric mean within the intersection of a cylinder and a cone through animation. Key mathematical concepts include geometric mean, means, cylinder, percentages, intersection, conic sections, and solid geometry. The construction leverages GeoGebra commands and objects such as Ray, Point, Midpoint, Circle, Semicircle, OrthogonalLine, Intersect, Segment, Line, Angle, Rotate, CircleArc, Dilate, CircleSector, Vector, and Translate. It is suitable for high school students and mathematics enthusiasts exploring the dynamic relationship between solid geometry, conic sections, and the application of geometric mean.

GeoGebra Commands & Parameters

  1. Ray(A, (1, 0)) → f
  2. Point(f) → B
  3. Ray(B, C) → g
  4. Point(g) → D
  5. Midpoint(A, D) → E
  6. Circle(E, D) → c
  7. Semicircle(A, D) → d
  8. OrthogonalLine(B, f) → h
  9. Intersect(d, h, 1) → F
  10. Segment(A, F) → i
  11. Line(D, F) → j
  12. Segment(F, D) → k
  13. Angle(A, F, D) → α
  14. Circle(F, 2) → e
  15. Intersect(e, j, 2) → G
  16. Angle(G, F, A) → β
  17. Circle(A, (0.15 * Min[i, k])) → p
  18. Circle(D, Radius[p]) → q
  19. Intersect(p, y = 0) → H, I
  20. Intersect(p, i, 1) → J
  21. Intersect(q, l, 1) → K
  22. Intersect(q, k, 1) → L
  23. Rotate(D, If[0 < a ≤ 1, (a * π), π], E) → D'
  24. CircleArc(E, D, D') → r
  25. Dilate(B, If[1 < a ≤ 2, 2 - a, 0], F) → F'
  26. Segment(B, F') → m
  27. Angle(F, B, A) → γ
  28. CircleSector(A, I, J) → s
  29. CircleSector(D, L, K) → t
  30. Dilate(A, If[3 < a ≤ 4, 4 - a, 0], F) → A'
  31. Dilate(D, If[3 < a ≤ 4, 4 - a, 0], F) → D'_1
  32. Segment(A, A') → n
  33. Segment(D, D'_1) → b
  34. Angle(B, A, F) → δ
  35. Angle(F, D, B) → ε
  36. Rotate(I, If[4 < a ≤ 5, ((a - 4) * δ), δ], A) → I'
  37. Rotate(K, If[4 < a ≤ 5, ((-(a - 4)) * ε), (-ε)], D) → K'
  38. CircleSector(D, K', K) → c_1
  39. CircleSector(A, I, I') → d_1
  40. Ray(F, G) → f_1
  41. Dilate(A, If[6 < a ≤ 7, 7 - a, 0], F) → A'_1
  42. Vector(A, A'_1) → u
  43. Translate(d_1, u) → e_1
  44. Rotate(e_1, If[7 < a ≤ 8, ((-(a - 7)) * π / 2), ((-π)) / 2], F) → g_1
  45. Dilate(D, If[8 < a ≤ 9, 9 - a, 0], F) → D'_2
  46. Vector(D, D'_2) → v
  47. Translate(c_1, v) → h_1
  48. Rotate(h_1, If[9 < a ≤ 10, ((a - 9) * π / 2), π / 2], F) → k_1
  49. Segment(A, B) → i_1
  50. Segment(B, D) → j_1