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Rotation and Geometric Transformations Demo

Rotation and Geometric Transformations Demo
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2016-09-20 01:33
FunctionCalculusOptimizationGeometric Construction
This example demonstrates the construction of complex geometric figures through rotation and geometric transformations. Core math concepts involved include rotation, linear programming, piecewise functions, integral calculus, and symmetry. Key construction elements utilize GeoGebra commands and objects such as Circle, Point, Segment, Intersect, CircumcircleArc, and Dilate. Suitable for high school mathematics students and educators exploring visual representations of geometric transformations and optimization problems.

GeoGebra Commands & Parameters

  1. Circle(O, 1) → cm
  2. Point(cm) → M
  3. Segment(EE, M) → ee
  4. Segment(AA, M) → aa
  5. Segment(FF, M) → ff
  6. Intersect(Circle[I, 1], Line[I, ee], 1) → E
  7. Intersect(Circle[E, 1], Line[E, ff], 1) → F
  8. Segment(GG, M) → gg
  9. Intersect(Circle[F, 1], Line[F, gg], 1) → G
  10. Segment(F, G) → g
  11. Segment(E, F) → f
  12. Segment(HH, M) → hh
  13. Intersect(Circle[G, 1], Line[G, hh], 1) → H
  14. Segment(G, H) → h
  15. Segment(BB, M) → bb
  16. Intersect(Circle[I, 1], Line[I, aa], 1) → A
  17. Intersect(Circle[A, 0.7], Line[A, bb], 1) → B
  18. Segment(A, B) → b
  19. Segment(CC, M) → cc
  20. Intersect(Circle[B, 1.7], Line[B, cc], 1) → C
  21. Segment(B, C) → c
  22. Segment(DD, M) → dd
  23. Intersect(Circle[C, 0.5], Line[C, dd], 1) → D
  24. Segment(C, D) → d
  25. CircumcircleArc(E, I, A) → p
  26. Segment(TT, M) → tt
  27. Intersect(Circle[A, 1], Line[A, tt], 1) → T
  28. CircumcircleArc(I, A, T) → q
  29. Segment(QQ, M) → qq
  30. Intersect(Circle[E, 1.5], Line[E, qq], 1) → Q
  31. Dilate(T, -1 / 4, E) → T'
  32. CircumcircleArc(E, T', Q) → t