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Rotating Sectors

Rotating Sectors
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2016-12-21 06:12
CircleFunctionTrigonometryCalculusParametric Equation
This example demonstrates rotating sectors inspired by a tacobank Tumblr animation. Core math concepts include circle, rotation, parametric curves, functions, and differential calculus. Construction uses GeoGebra commands like Circle, Point, CircleSector, Rotate, Sequence, Textfield; objects include A, B, c, C, d, a, d', N, D, list1, u, list2, list3, turn, button1, s, f, spc, stc, InputBox1, b, angc, u', list4. Suitable for high school mathematics teaching, demonstrating dynamic changes in parametric equations and function graphs.

GeoGebra Commands & Parameters

  1. Circle(B, A) → c
  2. Point(c) → C
  3. CircleSector(B, A, C) → d
  4. Rotate(d, a, B) → d'
  5. Point(Line[A, B]) → D
  6. Sequence(Rotate[d', ((i * 360) * ° / N), D], i, 1, N) → list1
  7. Sequence(Translate[list1, Vector[Rotate[u, ((i * 360) * ° / N)]]], i, 1, N) → list2
  8. Sequence(Translate[list1, Vector[Rotate[(2 * u), ((i * 360) * ° / ((2 * N)))]]], i, 1, (2 * N)) → list3
  9. Textfield(stc) → InputBox1
  10. Rotate(u, (((1 + f(N)) * 360) * ° / N)) → u'
  11. Sequence(Sequence[Translate[list1, Vector[(spc * ((i * u) + (j * Rotate[u, (((1 + f(N)) * 360) * ° / N)])))]], i, 0, 3], j, 0, 3) → list4