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Circle and Sequence Transformation Demo

Circle and Sequence Transformation Demo
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2017-03-12 13:02
CircleSequenceCoordinate GeometryGraphing
This example dynamically demonstrates the transformation relationship between circles and sequences, visually showing geometric translations and parameter changes. It involves core math concepts like exponent functions, parabolas, translation transformations, area calculation, coordinates, and histograms. The construction uses GeoGebra commands such as Circle and Sequence, controlled by sliders to achieve dynamic effects. Suitable for high school mathematics teaching to understand function graph transformations, parametric equations, and applications of analytical geometry.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 1) → r1
  2. Sequence(Rotate[Dilate[r1, f(a1), (1, 0)], (k * a1), (0, 0)], k, 0, n1 - 1) → r2
  3. Sequence(Rotate[Dilate[r2, f(a2), (1, 0)], (k * a2), (0, 0)], k, 0, n2 - 1) → r3
  4. Sequence(Rotate[Dilate[r3, f(a3), (1, 0)], (k * a3), (0, 0)], k, 0, n3 - 1) → r4
  5. Sequence(Rotate[Dilate[r4, f(a4), (1, 0)], (k * a4), (0, 0)], k, 0, n4 - 1) → r5
  6. Sequence(Rotate[Dilate[r5, f(a5), (1, 0)], (k * a5), (0, 0)], k, 0, n5 - 1) → r6
  7. Sequence(Rotate[Dilate[r1, f(a5), (1, 0)], (k * a5), (0, 0)], k, 0, n5 - 1) → C1
  8. Sequence(Rotate[Dilate[r1, f(a4), (1, 0)], (k * a4), (0, 0)], k, 0, n4 - 1) → C2
  9. Sequence(Rotate[Dilate[C2, f(a5), (1, 0)], (k * a5), (0, 0)], k, 0, n5 - 1) → C3
  10. Sequence(Rotate[Dilate[r1, f(a3), (1, 0)], (k * a3), (0, 0)], k, 0, n3 - 1) → C4
  11. Sequence(Rotate[Dilate[C4, f(a4), (1, 0)], (k * a4), (0, 0)], k, 0, n4 - 1) → C5
  12. Sequence(Rotate[Dilate[C5, f(a5), (1, 0)], (k * a5), (0, 0)], k, 0, n5 - 1) → C6
  13. Sequence(Rotate[Dilate[r1, f(a2), (1, 0)], (k * a2), (0, 0)], k, 0, n2 - 1) → C7
  14. Sequence(Rotate[Dilate[C7, f(a3), (1, 0)], (k * a3), (0, 0)], k, 0, n3 - 1) → C8
  15. Sequence(Rotate[Dilate[C8, f(a4), (1, 0)], (k * a4), (0, 0)], k, 0, n4 - 1) → C9
  16. Sequence(Rotate[Dilate[C9, f(a5), (1, 0)], (k * a5), (0, 0)], k, 0, n5 - 1) → C10