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Circle Rotating Around a Square

Circle Rotating Around a Square
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2015-10-26 00:29
CirclePolygonTransformationGeometric Construction
This example demonstrates a circle rotating around a square. Key mathematical concepts include the properties of circles and geometric transformations. Using GeoGebra commands such as Rotate, Polygon, and Circle, the dynamic process of the circle rotating around the square can be observed. Suitable for middle school and above students or teachers for teaching demonstrations.

GeoGebra Commands & Parameters

  1. Rotate(If[Mod[t, 1] < 1 / (1 + ratio), ((Mod[t, 1] * (1 + ratio)), ((-2) * ratio / π)), (1, 0) + (((sin((((Mod[t, 1] * (1 + ratio)) - 1) * π / ((2 * ratio)))), (-cos((((Mod[t, 1] * (1 + ratio)) - 1) * π / ((2 * ratio)))))) * 2) * ratio / π)], (90° * floor(t)), (0.5, 0.5)) → CenterOfCircle
  2. Polygon((0, 0), (1, 0), 4) → Square
  3. Circle(CenterOfCircle, (2 * ratio / π)) → Circle
  4. Circumference(Circle) → a
  5. Perimeter(Square) → b
  6. Locus(A, t) → Path
  7. Sequence(CenterOfCircle + ((((-sin(turn + (w * π / 3))), cos(turn + (w * π / 3))) * 2) * ratio / π), w, 1, 5) → Spokes
  8. Corner(5) → B
  9. Textfield(ratio) → InputBox1

AI Drawing Prompt Reference

Draw a square and a circle around it, making the circle rotate along the square's perimeter. Show the path of the circle's center as it moves around the square. Adjust the size ratio between the square and circle, and include an input box to control this ratio.
The prompt above was compiled from the original drawing commands and is for reference only.