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Cookie Cutters - Extra Fun!

Cookie Cutters - Extra Fun!
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2020-03-13 23:43
VectorCoordinate GeometryTransformationGeometric Construction
In collections Developing games and puzzles with 3D printing for STEAM
This example demonstrates the creation of cookie cutter shapes using 2D vectors, reflections, and geometric transformations. It involves core mathematical concepts like 2D vectors, reflections, standard deviation, hypergeometric distribution, and geometric transformations. The construction utilizes GeoGebra commands and objects such as Point, Polygon, Segment, Midpoint, Centroid, Circle, Intersect, Vector, Translate, and Prism. It is suitable for high school mathematics education, showcasing applications of vector operations and geometric transformations.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  5. Segment(H, F) → n
  6. Segment(E, G) → p
  7. Midpoint(i) → I
  8. Midpoint(m) → J
  9. Midpoint(l) → K
  10. Midpoint(k) → L
  11. Midpoint(j) → M
  12. Midpoint(n) → N
  13. Midpoint(h) → O
  14. Midpoint(g) → P
  15. Centroid(poly1) → Q
  16. Centroid(poly1) → R
  17. Midpoint(f) → S
  18. Polygon(D, I, J, E, N, H, K, O) → poly3, d, i_1, j_1, e, n_1, h_1, k_1, o
  19. Polygon(O, K, H, N, G, L, P, C) → poly4, o_1, k_2, h_2, n_2, g_1, l_1, p_1, c
  20. Polygon(L, G, N, F, M, S, B, P) → poly5, l_2, g_2, n_3, f_1, m_1, s, b, p_2
  21. Polygon(I, A, S, M, F, N, E, J) → poly6, i_2, a, s_1, m_2, f_2, n_4, e_1, j_2
  22. Circle(N, r) → q
  23. Intersect(q, h_2) → T,
  24. Intersect(q, g_2) → U,
  25. Vector(N, T) → u
  26. Vector(N, U) → v
  27. Translate(O, v) → O'
  28. Translate(K, v) → K'
  29. Translate(H, v) → H'
  30. Translate(N, v) → N'
  31. Translate(G, v) → G'
  32. Translate(L, v) → L'
  33. Translate(P, v) → P'
  34. Translate(C, v) → C'
  35. Polygon(O', K', H', N', G', L', P', C') → poly4', o', k', h', n', g', l', p', c'
  36. Translate(D, u) → D'
  37. Translate(I, u) → I'
  38. Translate(J, u) → J'
  39. Translate(E, u) → E'
  40. Translate(N, u) → N'_1
  41. Translate(H, u) → H'_1
  42. Translate(K, u) → K'_1
  43. Translate(O, u) → O'_1
  44. Polygon(D', I', J', E', N'_1, H'_1, K'_1, O'_1) → poly3', d', i', j', e', n'_1, h'_1, k'_1, o'_1
  45. Translate(I, Vector[(-v)]) → I'_1
  46. Translate(A, Vector[(-v)]) → A'
  47. Translate(S, Vector[(-v)]) → S'
  48. Translate(M, Vector[(-v)]) → M'
  49. Translate(F, Vector[(-v)]) → F'
  50. Translate(N, Vector[(-v)]) → N'_2
  51. Translate(E, Vector[(-v)]) → E'_1
  52. Translate(J, Vector[(-v)]) → J'_1
  53. Polygon(I'_1, A', S', M', F', N'_2, E'_1, J'_1) → poly6', i'_1, a', s', m', f', n'_2, e'_1, j'_1
  54. Translate(L, Vector[(-u)]) → L'_1
  55. Translate(G, Vector[(-u)]) → G'_1
  56. Translate(N, Vector[(-u)]) → N'_3
  57. Translate(F, Vector[(-u)]) → F'_1
  58. Translate(M, Vector[(-u)]) → M'_1
  59. Translate(S, Vector[(-u)]) → S'_1
  60. Translate(B, Vector[(-u)]) → B'
  61. Translate(P, Vector[(-u)]) → P'_1
  62. Polygon(L'_1, G'_1, N'_3, F'_1, M'_1, S'_1, B', P'_1) → poly5', l'_1, g'_1, n'_3, f'_1, m'_1, s'_1, b', p'_1
  63. Prism(poly3', a_1) → b_1, F_1, face10, face11, face12, face13, face14, face15, face9, face16, edge12, edge13, G_1, edge14, edge15, edge16, edge17, edge18, edge19, edge20, edge22, edge23, edge24, H_1, edge25, edge26, edge27, edge21, I_1, J_1, K_1, L_1, M_1, face8
  64. Prism(poly4', q_1) → r_1, V_1, face28, face29, face30, face31, face32, face33, face27, face34, edge28, edge45, W_1, edge46, edge47, edge48, edge49, edge50, edge51, edge52, edge54, edge55, edge56, Z_1, edge57, edge58, edge59, edge53, A_2, B_2, C_2, D_2, E_2, face17
  65. Prism(poly6', d_1) → t_1, N_1, face21, face22, face23, face24, face25, face26, face20, face35, edge30, edge31, O_1, edge32, edge33, edge34, edge35, edge36, edge37, edge38, edge40, edge41, edge42, P_1, edge43, edge44, edge60, edge39, Q_1, R_1, S_1, T_1, U_1, face19
  66. Prism(poly5', u_1) → v_1, F_2, face39, face40, face41, face42, face43, face44, face38, face45, edge63, edge64, G_2, edge65, edge66, edge67, edge68, edge69, edge70, edge71, edge73, edge74, edge75, H_2, edge76, edge77, edge78, edge72, I_2, J_2, K_2, L_2, M_2, face37

AI Drawing Prompt Reference

Draw a complex decorative pattern starting with two squares. Use their vertices, midpoints, and centroids to create multiple new shapes through vector operations and geometric transformations. Include points determined by the intersection of a circle with lines, then apply translation to these points, resulting in a intricate design that highlights the use of 2D vectors and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.