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Sara (Germany) – Polygon and Function Combined Construction

Sara (Germany) – Polygon and Function Combined Construction
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2020-02-27 23:55
PolygonFunctionCoordinate GeometryGeometric ConstructionGraphing
In collections Polygons: first steps (GER)
This example demonstrates a comprehensive geometric construction that combines polygons, midpoints, centroids, and function graphs, built using GeoGebra commands to create a complex figure with numerous points, segments, and polygon objects. The core mathematical concepts involve power functions, linear functions, fractions, and geometric properties such as centroids and midpoints. The construction uses commands like Polygon to create polygons, Midpoint to find midpoints, Segment to connect points, Centroid to compute centroids, and Intersect to find intersection points, defining many point objects (A, B, C, D, etc.) and function or segment objects (f, g, h, etc.), resulting in the figure named 'Sara (Germany)'. This is suitable for upper secondary or early university students to explore the interplay between geometry and functions, and can also serve as a teaching demonstration for combining geometric constructions with function graphing.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 7) → Vieleck1, f, E, F, G, g, h, i, j, k, l, C, D
  2. Midpoint(F, E) → H
  3. Midpoint(D, C) → I
  4. Midpoint(E, D) → J
  5. Midpoint(B, C) → K
  6. Midpoint(A, B) → L
  7. Midpoint(A, G) → M
  8. Midpoint(G, F) → N
  9. Segment(N, H) → m
  10. Segment(H, J) → n
  11. Segment(I, J) → p
  12. Segment(M, L) → q
  13. Segment(L, K) → r
  14. Segment(K, I) → s
  15. Segment(M, N) → t
  16. Centroid(Vieleck1) → O
  17. Segment(H, O) → a
  18. Segment(O, J) → b
  19. Segment(O, I) → c
  20. Segment(O, L) → d
  21. Segment(O, K) → e
  22. Segment(O, M) → f_1
  23. Segment(N, O) → g_1
  24. Segment(O, D) → h_1
  25. Segment(O, C) → i_1
  26. Segment(O, B) → j_1
  27. Segment(O, A) → k_1
  28. Segment(O, G) → l_1
  29. Segment(O, F) → m_1
  30. Segment(E, O) → n_1
  31. Midpoint(t) → P
  32. Midpoint(q) → Q
  33. Midpoint(r) → S
  34. Midpoint(s) → T
  35. Midpoint(p) → U
  36. Midpoint(n) → V
  37. Midpoint(m) → W
  38. Midpoint(L, O) → R
  39. Midpoint(M, O) → Z
  40. Midpoint(N, O) → A_1
  41. Midpoint(H, O) → B_1
  42. Midpoint(J, O) → C_1
  43. Midpoint(O, I) → D_1
  44. Midpoint(O, K) → E_1
  45. Segment(A_1, W) → p_1
  46. Segment(W, B_1) → q_1
  47. Segment(B_1, V) → r_1
  48. Segment(V, F_1) → s_1
  49. Segment(F_1, C_1) → t_1
  50. Segment(F_1, U) → a_1
  51. Segment(U, D_1) → b_1
  52. Segment(D_1, T) → c_1
  53. Segment(T, E_1) → d_1
  54. Segment(E_1, S) → e_1
  55. Segment(S, R) → f_2
  56. Segment(R, Q) → g_2
  57. Segment(Q, Z) → h_2
  58. Segment(Z, P) → i_2
  59. Segment(P, A_1) → j_2
  60. Intersect(j, m) → G_1
  61. Intersect(f_1, g_1) → H_1
  62. Segment(G_1, H_1) → k_2

AI Drawing Prompt Reference

Draw a figure combining a polygon and function graphs. Start by drawing a polygon Vieleck1, then find the midpoints of its sides and connect them to form a new polygon. Next, calculate the centroid O of polygon Vieleck1 and connect it to the midpoints of its sides to form several segments. Finally, find the midpoints of these segments and connect them to form an even smaller polygon.
The prompt above was compiled from the original drawing commands and is for reference only.