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Last Propositions of Decagon

Last Propositions of Decagon
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2019-03-16 06:31
PolygonVectorGeometric Construction
This example illustrates the last few propositions of a decagon, involving geometric transformations and vectors. Using GeoGebra commands such as Circle, Point, Segment, and Rotate, the construction of a decagon's elements is demonstrated. Suitable for high school geometry, aiding students in understanding the properties and transformations of a decagon.

GeoGebra Commands & Parameters

  1. Circle(C, m_0) → g_1
  2. Point(g_1) → G
  3. Point(g_1) → D
  4. Segment(G, D) → f
  5. Rotate(D, 36°, C) → D'
  6. Segment(G, D') → g
  7. Rotate(D', 36°, C) → D''
  8. Segment(G, D'') → h
  9. Rotate(D'', 36°, C) → D'''
  10. Segment(G, D''') → u
  11. Rotate(D''', 36°, C) → E
  12. Segment(G, E) → w
  13. Rotate(E, 36°, C) → E'
  14. Segment(G, E') → a
  15. Rotate(E', 36°, C) → E''
  16. Segment(G, E'') → b
  17. Rotate(E'', 36°, C) → E'''
  18. Segment(G, E''') → c
  19. Rotate(E''', 36°, C) → F
  20. Segment(G, F) → d
  21. Rotate(F, 36°, C) → F'
  22. Segment(G, F') → e
  23. Segment(C, D) → m
  24. Circle(A, m_0) → hhh
  25. Point(hhh) → B
  26. Rotate(B, (-(60°)), A) → B'_1
  27. Rotate(B, 60°, A) → B'
  28. Rotate(B', 60°, A) → B''
  29. Rotate(B'', 60°, A) → B'''
  30. Rotate(B''', 60°, A) → K
  31. AttachCopyToView(PolyLine[(12.100000000000005,0.2599999999999979), (12.100000000000005,0.2599999999999979), (NaN,NaN), (12.100000000000005,0.2599999999999979), (12.080000000000004,0.19999999999999787), (12.020000000000005,0.2199999999999979), (12.020000000000005,0.29999999999999793), (12.020000000000005,0.379999999999998), (12.020000000000005,0.4599999999999981), (12.080000000000004,0.41999999999999804), (12.140000000000004,0.359999999999998), (12.160000000000004,0.29999999999999793), (12.160000000000004,0.2199999999999979), (12.140000000000004,0.15999999999999784), (12.060000000000004,0.15999999999999784), (12.000000000000004,0.17999999999999786), (11.960000000000004,0.2399999999999979), (11.960000000000004,0.31999999999999795), (11.960000000000004,0.399999999999998), (12.040000000000004,0.399999999999998), (12.140000000000004,0.399999999999998), (12.220000000000004,0.399999999999998), (12.260000000000005,0.33999999999999797), (12.280000000000005,0.2599999999999979), (12.280000000000005,0.17999999999999786), (12.220000000000004,0.2599999999999979), (12.220000000000004,0.33999999999999797), (12.200000000000005,0.4599999999999981), (12.160000000000004,0.5399999999999981), (12.120000000000005,0.5999999999999982), (12.040000000000004,0.5999999999999982), (11.960000000000004,0.5799999999999982), (11.880000000000004,0.5999999999999982), (11.880000000000004,0.6799999999999982), (11.800000000000004,0.7399999999999982), (11.880000000000004,0.6799999999999982), (11.920000000000005,0.6199999999999982), (11.940000000000005,0.5599999999999982), (12.040000000000004,0.5399999999999981), (12.160000000000004,0.49999999999999806), (12.220000000000004,0.4599999999999981), (12.180000000000005,0.399999999999998), (12.140000000000004,0.33999999999999797), (12.180000000000005,0.399999999999998), (12.240000000000004,0.41999999999999804), (12.280000000000005,0.33999999999999797), (12.280000000000005,0.2599999999999979), (12.320000000000004,0.15999999999999784), (12.340000000000005,0.2199999999999979), (12.260000000000005,0.2199999999999979), (12.180000000000005,0.2199999999999979), (12.100000000000005,0.19999999999999787), (12.000000000000004,0.19999999999999787), (11.900000000000004,0.19999999999999787), (11.860000000000005,0.2599999999999979), (11.840000000000005,0.31999999999999795), (11.800000000000004,0.379999999999998), (11.880000000000004,0.379999999999998), (11.940000000000005,0.33999999999999797), (12.000000000000004,0.29999999999999793), (12.060000000000004,0.359999999999998), (12.040000000000004,0.2799999999999979), (NaN,NaN), (7.460000000000003,-1.7000000000000035), (7.460000000000003,-1.7000000000000035), true], 1, (-5.120000000000001, -5.000000000000006), (18.720000000000006, 6.620000000000003), (0, 581), (1192, 0)) → stroke1
  32. Segment(C, D') → h_1
  33. Segment(C, D'') → i
  34. Segment(C, D''') → j
  35. Segment(C, E) → l
  36. Segment(C, E') → p
  37. Segment(C, E'') → q
  38. Segment(C, E''') → r
  39. Segment(C, F) → s
  40. Segment(F', C) → t
  41. Polygon(E', E'', E''', F, F', D, D', D'', D''', E) → poly1, e', e_2, e'', e''', f_2, f', d_1, d', d'', d'''
  42. Polygon(E', E'', E''', F, F', D, D', D'', D''', E) → poly2, e'_1, e_3, e''_1, e'''_1, f_3, f'_1, d_2, d'_1, d''_1, d'''_1

AI Drawing Prompt Reference

Draw a decagon starting from point C, rotating 36 degrees each time to generate points D, D', D'', D''', E, E', E'', E''', F, and connect these points to form the decagon. Additionally, rotate 60 degrees from point C to generate points B, B', B'', B''', and connect these points to form a hexagon. Finally, connect point C to all generated points to form polygons.
The prompt above was compiled from the original drawing commands and is for reference only.