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Sequence Fidget Spinner: Dynamic Sequence & Geometry Interaction

Sequence Fidget Spinner: Dynamic Sequence & Geometry Interaction
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2017-06-15 21:35
CirclePolygonSequenceGeometric ConstructionSlider Animation
① This example presents an interactive 'fidget spinner' style interface that dynamically illustrates the generation and variation of sequences, combining abstract sequence concepts with intuitive geometric visuals. ② Core mathematical concepts include arithmetic sequences, arithmetic operations, variance, fractions, and introductory hypothesis testing, along with geometric elements such as trapezoids and circumcircle arcs. ③ Construction highlights: Using GeoGebra commands such as If, Circle, Intersect, Midpoint, CircumcircleArc, and Textfield, the applet incorporates multiple buttons (button1 to button6) and sliders (r, f, d, a, h, α, m, n) to control sequence terms and geometric objects (points A-Q, segments, circles, arcs) in a linked dynamic manner. ④ Suitable for middle and high school mathematics (grades 8-12) for teaching sequences, exploring algebra-geometry connections, and for teacher demonstrations or student self-directed investigation of sequence patterns and geometric properties.

GeoGebra Commands & Parameters

  1. If(a ≟ 1, list_{arithmetic}, a ≟ 2, list_{geometric}) → list1
  2. Circle((0, 0), 1) → u
  3. Circle(P, 1.73) → c
  4. Intersect(c, u) → A, B, ,
  5. Midpoint(A, B) → D
  6. Midpoint(A, P) → E
  7. Midpoint(B, P) → F
  8. Midpoint(D, C) → G
  9. Midpoint(E, C) → H
  10. Midpoint(C, F) → I
  11. Circle(B, 0.25) → d_2
  12. Circle(P, 0.25) → e
  13. Circle(A, 0.25) → g_2
  14. Intersect(d_2, u) → J, K, ,
  15. Intersect(u, g_2) → L, M, ,
  16. Intersect(e, u) → O, Q, ,
  17. CircumcircleArc(M, G, K) → h_2
  18. CircumcircleArc(J, I, Q) → k
  19. CircumcircleArc(O, H, L) → p
  20. Circle(P, 0.4) → q
  21. Circle(B, 0.4) → t
  22. Circle(A, 0.4) → c_1
  23. Circle(N, 1.73) → d_1
  24. Intersect(d_1, u) → R, S, ,
  25. Circle(N, 0.25) → e_1
  26. Circle(S, 0.25) → f_1
  27. Circle(R, 0.25) → g_1
  28. Intersect(u, f_1) → T, U, ,
  29. Intersect(g_1, u) → V, W, ,
  30. Intersect(e_1, u) → Z, A_1, ,
  31. Midpoint(S, R) → B_1
  32. Midpoint(R, N) → C_1
  33. Midpoint(N, S) → D_1
  34. Midpoint(B_1, C) → E_1
  35. Midpoint(C_1, C) → F_1
  36. Midpoint(D_1, C) → G_1
  37. CircumcircleArc(T, E_1, V) → h_1
  38. CircumcircleArc(W, F_1, Z) → k_1
  39. CircumcircleArc(A_1, G_1, U) → p_1
  40. Circle(S, 0.4) → s_1
  41. Circle(R, 0.4) → r_1
  42. Circle(N, 0.4) → q_1
  43. Textfield(g) → InputBox1
  44. Textfield(g) → InputBox2
  45. Textfield(g) → InputBox3
  46. Textfield(g) → InputBox4
  47. Textfield(g) → InputBox5

AI Drawing Prompt Reference

Draw a dynamic fidget-spinner style geometric figure: start with a unit circle, place three equally spaced main points on its circumference, and construct circles of varying radii centered at these points and the center, creating overlapping circle families. Place small circles at intersection points as nodes, and connect adjacent nodes with three circular arcs to form rotating symmetric blades. The overall figure includes multiple concentric circles, intersection points, small circles, and arcs, exhibiting three-fold rotational symmetry, with several input boxes for parameter adjustment.
The prompt above was compiled from the original drawing commands and is for reference only.