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A Circle Rolling on Another Circle

A Circle Rolling on Another Circle
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2015-08-07 20:00
CircleGeometric ConstructionLocus
In collections Rolling Circles and Polygons Rolling Circles and Polygons Rolling Circles and Polygons
This example demonstrates a small circle rolling on a larger circle. Key mathematical concepts include the properties of circles, geometric transformations, and loci. Using GeoGebra commands such as Point, Circle, Rotate, and Locus, the trajectory of the rolling circle can be constructed. Suitable for middle school and above students to learn about geometric transformations and loci.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Circle(A, B) → c
  3. Circle(C, B) → d
  4. Rotate(d, Roll) → d'
  5. Rotate(C, Roll) → C'
  6. Segment(C, B) → b
  7. Segment(A, B) → e
  8. Locus(D, Roll) → loc1
  9. CurveCartesian(((e - b) * cos(t)) + (b * cos(((e - b) / b * t))), ((e - b) * sin(t)) - (b * sin(((e - b) / b * t))), t, 0, Roll) → i

AI Drawing Prompt Reference

Draw a large circle and a small circle, where the small circle rolls along the large circle. First, draw a point on the y-axis as the center of the large circle, then draw the large circle. Next, draw a small circle with the same center as the large circle. Then, rotate the small circle around the center of the large circle, and rotate the center of the small circle. After that, draw a line segment between the centers of the two circles. Finally, draw the locus of the center of the small circle.
The prompt above was compiled from the original drawing commands and is for reference only.