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Rotation Transformation Demo by Patrick Clément

Rotation Transformation Demo by Patrick Clément
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2013-08-31 18:16
VectorTrigonometryCoordinate GeometryTransformationGeometric Construction
In collections GCSE Higher Ch8 Transformations & Constructions
This example demonstrates the rotation transformation of a shape in two-dimensional space. It involves core math concepts like rotation, congruence, rhombus, cosine rule, 2D vectors, and secant line. The construction uses GeoGebra commands such as CurveCartesian, Sequence, and Element to create axes, points, vectors, and curves. Suitable for high school mathematics education to understand the geometric meaning and algebraic representation of rotation transformations.

GeoGebra Commands & Parameters

  1. CurveCartesian(ax * cos(t * 2 * π / px), ay * sin(t * 2 * π / py + π / 4 + d), t, 0, fin) → h
  2. Sequence(Rotate[h, i], i, 0, 6.283185307179586, 2 * π / n) → liste1
  3. Element(liste1, 1) → hr1
  4. Element(liste1, 2) → hr2
  5. Element(liste1, 3) → hr3
  6. Element(liste1, 4) → hr4
  7. Element(liste1, 5) → hr5
  8. Element(liste1, 6) → hr6
  9. Element(liste1, 7) → hr7
  10. Element(liste1, 8) → hr8
  11. Element(liste1, 9) → hr9
  12. Element(liste1, 10) → hr10
  13. Element(liste1, 11) → hr11
  14. Element(liste1, 12) → hr12
  15. Element(liste1, 13) → hr13
  16. Element(liste1, 14) → hr14
  17. Element(liste1, 15) → hr15
  18. Element(liste1, 16) → hr16
  19. Element(liste1, 17) → hr17
  20. Element(liste1, 18) → hr18
  21. Element(liste1, 19) → hr19
  22. Element(liste1, 20) → hr20
  23. Element(liste1, 21) → hr21
  24. Element(liste1, 22) → hr22
  25. Element(liste1, 23) → hr23
  26. Element(liste1, 24) → hr24
  27. Element(liste1, 25) → hr25
  28. Element(liste1, 26) → hr26
  29. Element(liste1, 27) → hr27
  30. Element(liste1, 28) → hr28
  31. Element(liste1, 29) → hr29
  32. Element(liste1, 30) → hr30
  33. Element(liste1, 31) → hr31

AI Drawing Prompt Reference

Draw a demonstration of rotation transformation in 2D space showing a shape rotating around a point at specific angles, creating a sequence of rotated shapes to form a continuous rotation path, illustrating concepts like rotation, congruence, rhombus, cosine rule, 2D vectors, and secant lines, suitable for high school education to understand the geometric and algebraic representation of rotation transformations.
The prompt above was compiled from the original drawing commands and is for reference only.