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Animation 201: Geometric Transformations with Circles, Equilateral Triangles, an

Animation 201: Geometric Transformations with Circles, Equilateral Triangles, an
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2017-02-18 05:05
TriangleCircleSolid GeometryTransformationSlider Animation
This GeoGebra example demonstrates a dynamic animation combining circles, equilateral triangles, cones, linear functions, definite integrals, vectors, and curve sketching. The core mathematical concepts include geometric transformations (dilation and rotation), construction of a cone, properties of equilateral triangles, relationships between linear functions and definite integrals, and vector applications. The construction uses commands such as Dilate, Rotate, Circle, Segment, CircleArc, Intersect, and Polygon to create multiple points, segments, arcs, and polygons, with a button controlling the animation. It is suitable for high school and above students to explore geometric transformations, the interplay between 3D solids and 2D shapes, and to learn how to build dynamic mathematical demonstrations.

GeoGebra Commands & Parameters

  1. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], B) → A'
  2. Segment(A, A') → f
  3. Circle(A, B) → c
  4. Circle(B, A) → d
  5. Rotate(B, If[1 < b ≤ 2, (((b - 1) * 2) * π), (2 * π)], A) → B'
  6. CircleArc(A, B, B') → e
  7. Intersect(c, d, 1) → C
  8. Intersect(c, d, 2) → D
  9. Rotate(A, If[1 < b ≤ 2, (((b - 1) * 2) * π), (2 * π)], A) → A'_1
  10. Rotate(A', If[1 < b ≤ 2, (((b - 1) * 2) * π), (2 * π)], A) → A''
  11. Segment(A'_1, A'') → f'
  12. Rotate(A, If[2.5 < b ≤ 3.5, (((b - 2.5) * 2) * π), (2 * π)], B) → A'_2
  13. CircleArc(B, A, A'_2) → g
  14. Rotate(B, If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 3), π / 3], A) → B'_1
  15. Rotate(A, If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 3), π / 3], A) → A'_3
  16. Rotate(A', If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 3), π / 3], A) → A''_1
  17. Segment(A'_3, A''_1) → f'_1
  18. Rotate(A, If[4.5 < b ≤ 5.5, ((-(b - 4.5)) * π / 3), ((-π)) / 3], B) → A'_4
  19. Rotate(A', If[4.5 < b ≤ 5.5, ((-(b - 4.5)) * π / 3), ((-π)) / 3], B) → A''_2
  20. Segment(A'_4, A''_2) → f'_2
  21. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  22. Rotate(A, If[2.5 < b ≤ 3.5, (((b - 2.5) * 2) * π), (2 * π)], B) → A'_5
  23. Rotate(A', If[2.5 < b ≤ 3.5, (((b - 2.5) * 2) * π), (2 * π)], B) → A''_3
  24. Segment(A'_5, A''_3) → f'_3