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Homer Transformed

Homer Transformed
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2015-04-02 14:02
Coordinate GeometryTransformationGeometric Construction
This example demonstrates how reflections compose to form arbitrary transformations by dragging points. Core math concepts include reflection, kite, ellipse, orthocenter, integral calculus, and roots. It is constructed using GeoGebra commands like Line, Mirror, Segment, LineBisector, OrthogonalLine, Intersect, and Polygon. Suitable for high school and above, exploring geometric transformations and their combinations.

GeoGebra Commands & Parameters

  1. Line(D, E) → a
  2. Line(F, G) → b
  3. Line(I, J) → c
  4. Mirror(pic1, a) → pic1'
  5. Mirror(pic1', b) → pic1''
  6. Mirror(pic1'', c) → pic1'''
  7. Segment(H, H_2) → d
  8. LineBisector(d) → e
  9. Mirror(pic1, e) → pic1'_1
  10. Mirror(O, e) → O'
  11. Segment(O', O_2) → f
  12. LineBisector(f) → g
  13. Mirror(pic1'_1, g) → pic2
  14. Mirror(M, e) → M'
  15. Mirror(M', g) → M''
  16. Segment(M'', M_2) → h
  17. LineBisector(h) → i
  18. Mirror(pic2, i) → pic2'
  19. Segment(A, B) → j
  20. Line(C, j) → k
  21. OrthogonalLine(B, j) → l
  22. Intersect(k, l) → K
  23. Polygon(A, C, K, B) → poly1, a_1, c_1, k_1, b_1
  24. Mirror(A, a) → A'
  25. Mirror(C, a) → C'
  26. Mirror(K, a) → K'
  27. Mirror(B, a) → B'
  28. Polygon(A', C', K', B') → poly1', a', c', k', b'
  29. Mirror(A', b) → A''
  30. Mirror(C', b) → C''
  31. Mirror(K', b) → K''
  32. Mirror(B', b) → B''
  33. Polygon(A'', C'', K'', B'') → poly1'', a'', c'', k'', b''
  34. Mirror(A'', c) → A'''
  35. Mirror(C'', c) → C'''
  36. Mirror(K'', c) → K'''
  37. Mirror(B'', c) → B'''
  38. Polygon(A''', C''', K''', B''') → poly1''', a''', c''', k''', b'''

AI Drawing Prompt Reference

Draw a geometric transformation showing how reflections compose to form arbitrary transformations. Start by drawing two line segments and their perpendicular bisectors, then reflect the initial shape three times using each line segment as a mirror. Next, connect specific points to form a quadrilateral and reflect it three times using different line segments as mirrors. Finally, combine all the reflected shapes to display the complex geometric transformation.
The prompt above was compiled from the original drawing commands and is for reference only.