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Rolling Sphere Demonstration

Rolling Sphere Demonstration
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2015-02-08 20:46
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the geometric patterns and phenomena formed by the contact point and vertex trajectory of a sphere rolling on a line, involving core mathematical concepts such as sphere, line segment, dilation, linear equations, cone, and rhombus. Key GeoGebra commands and objects used in the construction include Intersect, Polygon, Point, Element, OrthogonalLine, Rotate, Line, Translate, and Sphere, suitable for high school students studying solid geometry and analytical geometry to understand spatial transformations and geometric properties.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → E
  2. Polygon(E, F, n) → poly1, d, m, q, r, G, H, I, J, K, L, M, e, N, O, P, f, g, h, i, j, k, l
  3. Point(poly1, p) → A
  4. Element(pos, Length[pos] - 1) → B
  5. OrthogonalLine(B + (0, 0, 1), Segment[B + (0, 0, 1), C], xOyPlane) → a
  6. Rotate((0, 0, 0), (-Distance[B, A]), a) → D
  7. Line((0, 0, 1), a) → b
  8. Rotate(sp, (-Distance[B, A]), b) → sp'
  9. Translate(sp', Vector[A]) → sp''
  10. Sphere(C, 1) → c

AI Drawing Prompt Reference

Draw a diagram of a sphere rolling on a line. The trajectories of the contact point and vertex form geometric patterns. Include the sphere, line, contact point, and vertex to show spatial transformations and geometric properties.
The prompt above was compiled from the original drawing commands and is for reference only.