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Repeated Dilation and Rotation

Repeated Dilation and Rotation
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2014-08-03 20:39
Coordinate GeometryTransformationGeometric ConstructionSlider AnimationLocus
In collections Symmetry, Transformation and Tessellation
This example demonstrates how complex geometric patterns are generated through repeated dilation and rotation operations. The core math concepts involved include dilation, rotation, coordinate geometry, and transformation. The construction utilizes GeoGebra commands like Polygon and Rotate, along with objects such as t, r, O, A, B, C, T0, c, a, b, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11, T12. It is suitable for high school mathematics education, helping students understand the effects of combined transformations on shapes, and can also be used for exploring parametric equations and loci.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → T0, c, a, b
  2. Rotate(Polygon[Dilate[A, r, O], Dilate[B, r, O], Dilate[C, r, O]], t, O) → T1
  3. Rotate(Dilate[T1, r, O], t, O) → T2
  4. Rotate(Dilate[T2, r, O], t, O) → T3
  5. Rotate(Dilate[T3, r, O], t, O) → T4
  6. Rotate(Dilate[T4, r, O], t, O) → T5
  7. Rotate(Dilate[T5, r, O], t, O) → T6
  8. Rotate(Dilate[T6, r, O], t, O) → T7
  9. Rotate(Dilate[T7, r, O], t, O) → T8
  10. Rotate(Dilate[T8, r, O], t, O) → T9
  11. Rotate(Dilate[T9, r, O], t, O) → T10
  12. Rotate(Dilate[T10, r, O], t, O) → T11
  13. Rotate(Dilate[T11, r, O], t, O) → T12

AI Drawing Prompt Reference

Draw a complex geometric pattern generated by repeated dilation and rotation. Start with a triangle, then repeatedly dilate and rotate it, keeping the rotation angle and dilation scale constant, for a total of twelve iterations, to observe the evolution of the pattern.
The prompt above was compiled from the original drawing commands and is for reference only.