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Geometric Construction of Kemal Ataturk Portrait

Geometric Construction of Kemal Ataturk Portrait
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2020-01-21 14:32
CirclePolygonSolid GeometryTransformationGeometric Construction
This GeoGebra example constructs a geometric composition themed around Kemal Ataturk, primarily demonstrating the integrated construction and transformation of a 3D cube with 2D polygons, circles, and line segments. Core mathematical concepts include faces and edges of a cube, centroid (barycenter), midpoint, circumcircle, general quadrilaterals, symmetry, and geometric transformations such as translation and rotation. The construction uses commands like Point, Cube, Polygon, Centroid, Midpoint, Circle, Intersect, Line, Segment, and PointIn, creating six faces of the cube (e.g., faceABCD, faceADHE) and twelve edges (e.g., edgeAD, edgeAB), while auxiliary points (J, K, L) are derived from intersections, midpoints, and centroids, resulting in a symmetric geometric pattern. This example is suitable for middle school to early university geometry education, helping students understand the connection between solid and plane geometry, applications of geometric transformations, and how to build complex geometric models through procedural construction.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Polygon(E, F, B, A) → q1, e, f_1, b, a_1
  4. Polygon(H, E, A, D) → q2, h, e_1, a_2, d
  5. Centroid(q1) → J
  6. Centroid(q2) → K
  7. Midpoint(E, A) → L
  8. Midpoint(E, F) → M
  9. Midpoint(F, B) → N
  10. Circle(L, M, N) → c
  11. Midpoint(D, A) → O
  12. Midpoint(H, D) → P
  13. Midpoint(H, E) → Q
  14. Circle(P, Q, L) → k
  15. Intersect(b, c) → R, S
  16. Point(k) → I
  17. Line(I, K) → g
  18. Intersect(g, k, 1) → T
  19. Segment(I, T) → j
  20. Point(c) → U
  21. Line(U, J) → f
  22. Intersect(f, c, 1) → V
  23. Segment(U, V) → l
  24. PointIn(q2) → Pointq2_1
  25. PointIn(q2) → Pointq2_2
  26. PointIn(q2) → Pointq2_3
  27. PointIn(q2) → Pointq2
  28. Polygon(G, H, D, C) → q3, g_1, h_1, d_1, c_1
  29. Polygon(F, G, C, B) → q4, f_2, g_2, c_2, b_1
  30. Centroid(q3) → W
  31. Centroid(q4) → Z
  32. Midpoint(F, G) → A_1
  33. Midpoint(B, C) → B_1
  34. Circle(A_1, N, B_1) → p
  35. Midpoint(G, C) → C_1
  36. Midpoint(G, H) → D_1
  37. Circle(C_1, D_1, P) → q
  38. Point(q) → E_1
  39. Line(E_1, W) → i
  40. Intersect(i, q, 1) → F_1
  41. Segment(E_1, F_1) → m
  42. Point(p) → G_1
  43. Line(G_1, Z) → n
  44. Intersect(n, p, 1) → H_1
  45. Segment(G_1, H_1) → r
  46. Segment(G_1, I_1) → s
  47. Segment(H_1, I_1) → t
  48. Segment(E_1, I_1) → i_1
  49. Segment(F_1, I_1) → j_1
  50. Segment(U, I_1) → k_1
  51. Segment(V, I_1) → l_1
  52. Segment(T, I_1) → m_1
  53. Segment(I, I_1) → n_1

AI Drawing Prompt Reference

Draw a cube with six faces (e.g., faceABCD, faceADHE) and twelve edges (e.g., edgeAD, edgeAB), and construct a symmetric geometric pattern. Start by creating points A and B, then create a circle with A and B as the edge, and use points A, B, and C to create the cube. Next, create quadrilaterals EFB and HAE, calculate their centroids J and K, and the midpoint L of edge EF. Create circle c with L, M, and N, and create circle k with midpoints O (of DA) and P (of HD). Calculate the intersection points R, S of circle c and circle k, and another intersection point I of circle k. Create line g through I and K, calculate the intersection point T of g and k, and create line segment IT. Continue creating other key objects, such as line segments UV, EF, GH, and so on, to form a symmetric geometric pattern.
The prompt above was compiled from the original drawing commands and is for reference only.