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Rolling Circle Spirograph

Rolling Circle Spirograph
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2020-03-20 18:04
CircleTransformationGeometric Construction
This example demonstrates the process of drawing spirographs with a rolling circle. Key mathematical concepts include the properties of circles and rotation. Using GeoGebra commands such as Intersect, Circle, and Rotate, the construction of the spirograph is illustrated. Suitable for students at the junior high school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 2) → c
  3. Intersect(c, xAxis, 2) → B
  4. Circle(A, 1) → d
  5. Intersect(d, xAxis, 2) → C
  6. Rotate(C, α, A) → C'
  7. Circle(C', 1) → e
  8. Rotate(A, (-2 * α), C') → A'
  9. Line(C', A') → g
  10. Circle(C', 2) → f
  11. Intersect(f, g, 2) → D
  12. OrthogonalLine(C', g) → h
  13. Intersect(f, h, 2) → E
  14. Intersect(f, h, 1) → F
  15. Intersect(f, g, 1) → G
  16. Segment(F, E) → i
  17. Segment(D, G) → j
  18. Intersect(c, xAxis, 1) → H
  19. Intersect(c, yAxis, 2) → I
  20. Intersect(c, yAxis, 1) → J
  21. Intersect(e, j, 2) → K
  22. Segment(I, J) → k
  23. Segment(H, B) → l

AI Drawing Prompt Reference

Draw a spirograph created by a rolling circle. Start with a large circle centered at the origin and a smaller circle tangent to it on the positive x-axis. Rotate the smaller circle around the origin by an angle, then rotate the origin around the new small circle center by twice that angle in the opposite direction, and connect this point to the small circle center to form a line. With the small circle center as center, draw a larger circle; this line intersects it at two points. Draw a perpendicular line through the small circle center to the previous line, intersecting the larger circle at two points and the line at one point. Connect these intersection points with segments, and also take the intersections of the original large circle with the axes to form additional segments, building the spirograph framework.
The prompt above was compiled from the original drawing commands and is for reference only.