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Geometric Demonstration of High Power Differences

Geometric Demonstration of High Power Differences
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2019-06-25 05:23
FunctionTrigonometryIntegralTransformationGeometric Construction
This example demonstrates the geometric representation and transformation phenomena of high power differences. It involves core mathematical concepts such as power functions, geometric transformations, symmetry, and integral calculus. The construction utilizes GeoGebra commands like Circle, Point, Segment, Rotate, Angle, and Polygon. Suitable for high school and above mathematics learners to understand function graph transformations and geometric properties.

GeoGebra Commands & Parameters

  1. Circle(A, m) → c
  2. Point(c) → B
  3. Segment(A, B) → f
  4. Rotate(B, 18°, A) → B'
  5. Angle(B, A, B') → α
  6. Rotate(B', 18°, A) → B''
  7. Angle(B', A, B'') → β
  8. Rotate(B'', 18°, A) → B'''
  9. Angle(B'', A, B''') → γ
  10. Rotate(B''', 18°, A) → C
  11. Angle(B''', A, C) → δ
  12. Rotate(C, 18°, A) → C'
  13. Angle(C, A, C') → ε
  14. Rotate(C', 18°, A) → C''
  15. Angle(C', A, C'') → ζ
  16. Rotate(C'', 18°, A) → C'''
  17. Angle(C'', A, C''') → η
  18. Rotate(C''', 18°, A) → D
  19. Angle(C''', A, D) → θ
  20. Rotate(D, 18°, A) → D'
  21. Angle(D, A, D') → ι
  22. Rotate(D', 18°, A) → D''
  23. Angle(D', A, D'') → κ
  24. Rotate(D'', 18°, A) → D'''
  25. Angle(D'', A, D''') → λ
  26. Rotate(D''', 18°, A) → E
  27. Angle(D''', A, E) → μ
  28. Rotate(E, 18°, A) → E'
  29. Angle(E, A, E') → ν
  30. Rotate(E', 18°, A) → E''
  31. Angle(E', A, E'') → ξ
  32. Rotate(E'', 18°, A) → E'''
  33. Angle(E'', A, E''') → ο
  34. Rotate(E''', 18°, A) → F
  35. Angle(E''', A, F) → ρ
  36. Rotate(F, 18°, A) → F'
  37. Angle(F, A, F') → σ
  38. Rotate(F', 18°, A) → F''
  39. Angle(F', A, F'') → τ
  40. Rotate(F'', 18°, A) → F'''
  41. Angle(F'', A, F''') → υ
  42. Point(c) → G
  43. Segment(G, B') → h
  44. Segment(G, C') → l
  45. Segment(G, D') → q
  46. Segment(G, E') → b
  47. Segment(G, F') → g_1
  48. Polygon(B', F', E', D', C') → poly1, b', f', e', d', c'
  49. Circle(H, m) → d
  50. Point(d) → I
  51. Rotate(I, 72°, H) → I'
  52. Angle(I, H, I') → ϕ
  53. Rotate(I', 72°, H) → I''
  54. Angle(I', H, I'') → χ
  55. Rotate(I'', 72°, H) → I'''
  56. Angle(I'', H, I''') → ψ
  57. Rotate(I''', 72°, H) → J
  58. Angle(I''', H, J) → ω
  59. Polygon(I', I, J, I''', I'') → poly2, ı', ı, j, ı''', ı''
  60. Point(d) → K
  61. Segment(K, I) → g
  62. Segment(K, I') → i
  63. Segment(K, I'') → n
  64. Segment(K, I''') → p
  65. Segment(K, J) → r