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Symmetry Sticks

Symmetry Sticks
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2016-05-10 01:17
PolygonSequenceTransformation
This example demonstrates how to generate complex polygonal patterns with symmetry through rotations and dilations. Core math concepts include transformations (rotation, dilation), polygon construction, symmetry, functions, and sequences. Key GeoGebra commands and objects used are Circle, PointIn, Sequence, Rotate, Dilate, and Element. Suitable for high school students studying geometric transformations, function graphs, and parametric equations to explore the generation rules and properties of shapes.

GeoGebra Commands & Parameters

  1. Circle(B, (2 * A) - B) → d
  2. PointIn(d) → C
  3. Circle(C, (2 * A) - C) → c
  4. Sequence(Rotate[B, ((i * 360) * ° / N), A], i, 1, N + 1) → list1
  5. PointIn(c) → B'
  6. PointIn(c) → C'
  7. Sequence(Segment[B + (i * (C - B) / M), B' + (i * (C' - B') / M)], i, 0, M) → list2
  8. Sequence(Rotate[list2, ((i * 360) * ° / N), A], i, 1, N) → list3
  9. Sequence(Dilate[list3, r^((sgn(k) * i)), A], i, 0, abs(k)) → list4
  10. Rotate(B, (360 * ° / N), A) → B_1
  11. Rotate(C, (360 * ° / N), A) → C_1
  12. Dilate(B, r, A) → C_0
  13. Element(list4, 1) → R_{1}
  14. Element(list4, 2) → R_{2}
  15. Element(list4, 3) → R_{3}
  16. Element(list4, 4) → R_{4}
  17. Element(list4, 5) → R_{5}
  18. Element(list4, 6) → R_{6}