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Circle Animation and Transformations

Circle Animation and Transformations
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2016-06-20 10:19
CircleTransformationGeometric Construction
This example demonstrates the construction of a circle and its relationship with transformations through animation. Core mathematical concepts include circles, similarity transformations, and geometric constructions. Construction highlights involve commands like Segment, Midpoint, Circle, Intersect, Dilate, Rotate; suitable for high school mathematics to understand geometric transformations and circle properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Midpoint(f) → M
  3. Circle(M, (0.1 * f)) → c
  4. Intersect(c, f, 2) → D
  5. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], M) → A'
  6. Segment(A, A') → h
  7. Dilate(M, If[1 < a ≤ 2, 2 - a, 0], B) → C'
  8. Segment(M, C') → i
  9. Rotate(A, If[2 < a ≤ 3, ((-(a - 2)) * π), (-π)], M) → A'_1
  10. Rotate(A', If[2 < a ≤ 3, ((a - 2) * π), π], M) → A''
  11. Segment(A'_1, A'') → h'