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Exploring Tangram Geometric Construction and Transformations

Exploring Tangram Geometric Construction and Transformations
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2023-09-09 18:41
TrianglePolygonTransformationGeometric Construction
In collections MateTangram
This example demonstrates how to construct the classic Tangram puzzle using GeoGebra. The core mathematical concepts include polygon decomposition, area calculation, and geometric transformations (rotation, translation). Construction key points: Use Polygon command to draw basic triangles and quadrilaterals, Segment command for edges, Midpoint command to find midpoints, Line command for auxiliary lines, Intersect command to determine intersections, and Rotate command for rotation and assembly. Objects include points A to M, polygons poli1 to poli4, segments b_1 to g_2, etc. Suitable for upper elementary to middle school mathematics classes, for understanding basic geometric shapes, area conservation principles, and exploring geometric transformation rules.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poli1, frame3, frame4, frame1, frame2, C, D
  2. Segment(A, C) → frame12
  3. Midpoint(D, C) → E
  4. Midpoint(D, A) → F
  5. Segment(F, E) → frame5
  6. Midpoint(A, C) → G
  7. Segment(B, G) → frame9
  8. Midpoint(F, E) → H
  9. Midpoint(G, C) → I
  10. Segment(H, I) → frame7
  11. Segment(G, H) → frame8
  12. Line(F, frame8) → j
  13. Intersect(j, frame12) → J
  14. Segment(F, J) → frame11
  15. Polygon(A, G, B) → poli2, b_1, a_1, g_1
  16. Point(Circle[N, b_1]) → O
  17. Rotate(O + (a_1, 0), Angle[B - G] + Angle[O - N] - Angle[G - A], O) → P
  18. Polygon(N, O, P) → poli4, p, n, o
  19. Polygon(B, G, C) → poli3, c_1, b_2, g_2
  20. Point(Circle[K, c_1]) → L
  21. Rotate(L + (b_2, 0), Angle[C - G] + Angle[L - K] - Angle[G - B], L) → M
  22. Polygon(K, L, M) → poli5, m, k_1, l
  23. Polygon(H, E, C, I) → poli6, h_1, e_1, c_2, i_1
  24. Point(Circle[Q, h_1]) → R
  25. Rotate(R + (e_1, 0), Angle[C - E] + Angle[R - Q] - Angle[E - H], R) → S
  26. Rotate(S + (c_2, 0), Angle[I - C] + Angle[S - R] - Angle[C - E], S) → T
  27. Polygon(Q, R, S, T) → poli7, q, r, s, t
  28. Polygon(H, G, I) → poli8, i_2, h_2, g_3
  29. Point(Circle[U, i_2]) → V
  30. Rotate(V + (h_2, 0), Angle[I - G] + Angle[V - U] - Angle[G - H], V) → W
  31. Polygon(U, V, W) → poli9, w, u, v
  32. Polygon(F, H, G, J) → poli10, f_1, h_3, g_4, j_1
  33. Point(Circle[Z, f_1]) → A_1
  34. Rotate(A_1 + (h_3, 0), Angle[G - H] + Angle[A_1 - Z] - Angle[H - F], A_1) → B_1
  35. Rotate(B_1 + (g_4, 0), Angle[J - G] + Angle[B_1 - A_1] - Angle[G - H], B_1) → C_1
  36. Polygon(Z, A_1, B_1, C_1) → poli11, z, a_2, b_3, c_3
  37. Polygon(F, J, A) → poli12, a_3, f_2, j_2
  38. Point(Circle[D_1, a_3]) → E_1
  39. Rotate(E_1 + (f_2, 0), Angle[A - J] + Angle[E_1 - D_1] - Angle[J - F], E_1) → F_1
  40. Polygon(D_1, E_1, F_1) → poli13, f_3, d_1, e_2
  41. Polygon(F, D, E) → poli14, e_3, f_4, d_2
  42. Point(Circle[G_1, e_3]) → H_1
  43. Rotate(H_1 + (f_4, 0), Angle[E - D] + Angle[H_1 - G_1] - Angle[D - F], H_1) → I_1
  44. Polygon(G_1, H_1, I_1) → poli15, i_3, g_5, h_4

AI Drawing Prompt Reference

Draw a tangram puzzle consisting of seven different polygons. Start by drawing basic triangles and quadrilaterals using the polygon command. Then, use segment, midpoint, line, intersect, and rotate commands to construct each polygon. Finally, combine and rotate these polygons to form the complete tangram pattern.
The prompt above was compiled from the original drawing commands and is for reference only.