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Logo Picasa Geometric Construction

Logo Picasa Geometric Construction
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2019-05-13 16:36
PolygonVectorTransformationGeometric Construction
This example demonstrates the geometric construction of the Logo Picasa using GeoGebra. It involves core mathematical concepts such as polygons, rotation, vectors, and reflection. Key GeoGebra commands and objects used in the construction include Polygon, Line, Intersect, LineBisector, Circle, Vector, Mirror, Rotate, CircleArc, and Segment. It is suitable for high school mathematics education, showcasing geometric transformations and the construction of complex shapes.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → polígono1, f, g, h, i, j, C, D, E
  2. Line(A, B) → k
  3. Line(D, C) → l
  4. Intersect(l, k) → F
  5. LineBisector(A, B) → m
  6. LineBisector(A, E) → n
  7. Intersect(m, n) → G
  8. Circle(G, F) → c
  9. Vector(G, F) → u
  10. Circle(G, H) → d
  11. Vector(A, B) → v
  12. Line(I, g) → p
  13. Vector(B, C) → w
  14. Line(J, l) → q
  15. Mirror(p, m) → p'
  16. Mirror(q, m) → q'
  17. Rotate(p, (-(72°)), G) → p'_1
  18. Mirror(l, m) → l'
  19. Line(A, E) → r
  20. Mirror(r, m) → r'
  21. Intersect(d, q) → K, L
  22. Intersect(d, r') → M, N
  23. CircleArc(G, N, K) → e
  24. Polygon(K, N, J) → t1, j_1, k_1, n_1
  25. Rotate(e, 72°, G) → e'
  26. Rotate(K, 72°, G) → K'
  27. Rotate(N, 72°, G) → N'
  28. Rotate(J, 72°, G) → J'
  29. Polygon(K', N', J') → t1', j', k', n'
  30. Rotate(e, (-(72°)), G) → e'_1
  31. Rotate(K, (-(72°)), G) → K'_1
  32. Rotate(N, (-(72°)), G) → N'_1
  33. Rotate(J, (-(72°)), G) → J'_1
  34. Polygon(K'_1, N'_1, J'_1) → t1'_1, j'_1, k'_1, n'_1
  35. Rotate(e'_1, (-(72°)), G) → s
  36. Rotate(K'_1, (-(72°)), G) → O
  37. Rotate(N'_1, (-(72°)), G) → P
  38. Rotate(J'_1, (-(72°)), G) → Q
  39. Polygon(O, P, Q) → t2, q_1, o_1, p_1
  40. Rotate(s, (-(72°)), G) → s'
  41. Rotate(O, (-(72°)), G) → O'
  42. Rotate(P, (-(72°)), G) → P'
  43. Rotate(Q, (-(72°)), G) → Q'
  44. Polygon(O', P', Q') → t2', t, o', a
  45. Segment(P, O) → b

AI Drawing Prompt Reference

Draw a pentagon and construct a complex geometric pattern using rotations and reflections, incorporating segments, perpendicular bisectors, circles, and vectors to demonstrate core mathematical concepts like polygons, rotation, and reflection, resembling a Picasa Logo.
The prompt above was compiled from the original drawing commands and is for reference only.