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Cardioids in a Golden Spiral

Cardioids in a Golden Spiral
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2020-01-05 08:23
SequenceCoordinate GeometryTransformation
This example demonstrates the transformation of cardioids within a golden spiral. Key mathematical concepts include transformation, rotation, and dilation. Using GeoGebra commands such as Point, Rotate, Segment, and Sequence, the dynamic changes of cardioids within the golden spiral can be observed. Suitable for high school mathematics education, particularly in coordinate geometry and transformation geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → D
  2. Rotate(D + (r, 0), (anim * 360°), D) → B
  3. Rotate(B + (-1.5, 0), ((2 * anim) * 360°), B) → C
  4. Segment(A, B) → f
  5. Sequence(Rotate[Segment[Dilate[A, fact^(k)], Dilate[B, fact^(k)]], (k * α)], k, 0, 99) → l1
  6. Sequence(Rotate[Segment[Dilate[A, fact^(k)], Dilate[B, fact^(k)]], (k * α)], k, 0, 99) → l2

AI Drawing Prompt Reference

Draw multiple cardioid shapes within a golden spiral, showing dynamic transformations through rotation and scaling. Start by placing a point on the x-axis, then rotate and scale it to generate several cardioid shapes arranged along the golden spiral. The continuous rotation and scaling create a dynamic transformation effect.
The prompt above was compiled from the original drawing commands and is for reference only.