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Dynamic & Modifiable Equilateral Polygon Illustrator

Dynamic & Modifiable Equilateral Polygon Illustrator
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2017-01-18 03:04
PolygonAngleGeometric ConstructionSlider Animation
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This example demonstrates the dynamic construction and modification of equilateral polygons with a definition writing prompt. It involves core mathematical concepts like polygon construction, ratios, angles, rotation, and transformation. Key GeoGebra commands/objects used include Circle, Segment, Point, Intersect, Polygon, Dilate, Angle, and Rotate. Suitable for high school mathematics teaching, aiding in geometric construction, transformation studies, and concept comprehension.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(A, B) → f
  3. Circle(B, f) → d
  4. Point(d) → C
  5. Circle(C, f) → e
  6. Segment(B, C) → g
  7. Point(e) → D
  8. Segment(C, D) → h
  9. Circle(D, f) → k
  10. Intersect(c, k, 1) → E
  11. Polygon(A, B, C, D, E) → poly1, a, b, c_1, d_1, e_1
  12. Segment(A, B) → i
  13. Segment(B, C) → j
  14. Segment(C, D) → l
  15. Segment(D, E) → m
  16. Segment(E, A) → n
  17. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], A) → A'
  18. Segment(B, A') → p
  19. Angle(B, A, E) → α
  20. Angle(A, E, D) → β
  21. Angle(E, D, C) → γ
  22. Angle(D, C, B) → δ
  23. Rotate(B, If[1 < o ≤ 2, ((o - 1) * α), α], A) → B'
  24. Rotate(A', If[1 < o ≤ 2, ((o - 1) * α), α], A) → A''
  25. Segment(B', A'') → p'
  26. Rotate(B', If[2 < o ≤ 3, ((o - 2) * β), β], E) → B''
  27. Rotate(A'', If[2 < o ≤ 3, ((o - 2) * β), β], E) → A'''
  28. Segment(B'', A''') → p''
  29. Rotate(B'', If[3 < o ≤ 4, ((o - 3) * γ), γ], D) → B'''
  30. Rotate(A''', If[3 < o ≤ 4, ((o - 3) * γ), γ], D) → F
  31. Segment(B''', F) → p'''
  32. Rotate(B''', If[4 < o ≤ 5, ((o - 4) * δ), δ], C) → G
  33. Rotate(F, If[4 < o ≤ 5, ((o - 4) * δ), δ], C) → F'
  34. Segment(G, F') → q