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Circle Rotation Illusion

Circle Rotation Illusion
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2017-06-28 07:26
CircleTrigonometryCoordinate GeometryParametric Equation
This example demonstrates the visual illusion created by rotating a circle, involving core mathematical concepts such as rotation, surface, fractal geometry, ratios, parametric curves, and coordinate geometry. It is constructed using GeoGebra commands like Circle, Rotate, Segment, OrthogonalLine, Intersect, and Sequence, making it suitable for high school and above students to explore spatial geometry and parametric equations applications.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 1) → c
  2. Rotate((1, 0), angle, (0, 0)) → A
  3. Segment(A, (0, 0)) → f
  4. OrthogonalLine(A, xAxis) → g
  5. Intersect(g, xAxis) → B
  6. Segment((0, 0), B) → h
  7. Sequence(Rotate[(1, 0), (i * π / 8), (0, 0)], i, 1, 8) → list1
  8. Sequence(Line[Element[list1, i], (0, 0)], i, 1, 8) → list2
  9. Sequence(OrthogonalLine[A, Element[list2, i]], i, 1, 8) → list3
  10. Sequence(Intersect[Element[list2, i], Element[list3, i]], i, 1, 8) → list4
  11. Sequence(Element[list4, i], i, 1, n) → list5