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Angles Fan Demo

Angles Fan Demo
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2020-05-31 00:39
CircleAngleVectorTrigonometryGeometric Construction
This example demonstrates the dynamic construction of an angle fan to illustrate the relationship between angles and arc lengths. It involves core mathematical concepts such as angles, circles, vectors, and geometric constructions. The construction uses commands like Circle, Point, Ray, Line, Intersect, OrthogonalLine, Segment, Vector, Mirror, CircleSector, and Angle in GeoGebra. It is suitable for high school mathematics teaching, explaining the calculation methods for angles, arc lengths, and sector areas.

GeoGebra Commands & Parameters

  1. Circle(A, 4) → c
  2. Point(c) → F
  3. Ray(A, F) → g
  4. Line(A, F) → i
  5. Intersect(c, i, 2) → J
  6. Intersect(c, xAxis, 1) → K
  7. Point(c) → L
  8. Line(A, xAxis) → j
  9. OrthogonalLine(A, j) → k
  10. Point(k) → M
  11. Point(k) → N
  12. Segment(M, N) → l
  13. Intersect(c, j, 2) → O
  14. Intersect(c, j, 1) → P
  15. Segment(O, P) → m
  16. Circle(Z, 2.75) → c_1
  17. Point(c_1) → A_1
  18. Segment(Z, A_1) → g_1
  19. Ray(A_1, Z) → s
  20. Intersect(c_1, s, 2) → V
  21. OrthogonalLine(Z, s) → n
  22. Line(A_1, n) → q
  23. Point(n) → C
  24. OrthogonalLine(C, n) → p
  25. Intersect(q, p) → Q
  26. OrthogonalLine(V, s) → r
  27. Intersect(p, r) → R
  28. Circle(A, 4.5) → d
  29. Point(d) → B
  30. Line(A, B) → f
  31. Point(c) → E
  32. Line(A, E) → h
  33. Vector(A, B) → u
  34. Vector(A, E) → v
  35. Intersect(d, h, 1) → H
  36. Vector(A, H) → b
  37. Intersect(c, f) → G, I
  38. Vector(A, G) → w
  39. Point(v) → S
  40. Mirror(S, A) → S'
  41. CircleSector(A, S, B) → e
  42. CircleSector(A, S', G) → t
  43. Angle(S, A, B) → α
  44. Point(b) → T
  45. Point(w) → U