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Christmas Card 6

Christmas Card 6
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2021-09-13 03:49
FunctionTrigonometrySolid Geometry
In collections STEAM like Leonardo
This example demonstrates a 3D geometric shape using concepts such as circles, polygons, and trigonometric functions to create a beautiful Christmas card. Construction highlights include the use of Segment, Sequence, and Point commands in GeoGebra. Suitable for high school students and teachers for teaching solid geometry and function graphs.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(A, C) → g
  3. Sequence(A + (i / n * (B - A)), i, 1, n) → l1, {(-6, 10.8), (-6, 9.6), (-6, 8.4), (-6, 7.199999999999999), (-6, 6), (-6, 4.800000000000001), (-6, 3.6000000000000014), (-6, 2.3999999999999986), (-6, 1.1999999999999993), (-6, 0)}
  4. Sequence(A + (i / n * (C - A)), i, 1, n) → l2, {(-4.8, 12), (-3.5999999999999996, 12), (-2.4000000000000004, 12), (-1.1999999999999993, 12), (0, 12), (1.1999999999999993, 12), (2.3999999999999986, 12), (3.6000000000000014, 12), (4.800000000000001, 12), (6, 12)}
  5. Sequence(Segment[Element[l1, i], Element[l2, n - i]], i, 1, n) → l3, {10.8664621657649, 9.895453501482386, 9.138927727036688, 8.653323061113573, 8.485281374238571, 8.653323061113573, 9.138927727036688, 9.895453501482386, 10.8664621657649, NaN}
  6. Segment(D, E) → h
  7. Segment(D, F) → i
  8. Sequence(D + (i / a * (E - D)), i, 1, a) → l4, {(-4.8, -12), (-3.5999999999999996, -12), (-2.4000000000000004, -12), (-1.1999999999999993, -12), (0, -12), (1.1999999999999993, -12), (2.3999999999999986, -12), (3.6000000000000014, -12), (4.800000000000001, -12), (6, -12)}
  9. Sequence(D + (i / a * (F - D)), i, 1, a) → l5, {(-6, -10.8), (-6, -9.6), (-6, -8.4), (-6, -7.199999999999999), (-6, -6), (-6, -4.800000000000001), (-6, -3.6000000000000014), (-6, -2.3999999999999986), (-6, -1.1999999999999993), (-6, 0)}
  10. Sequence(Segment[Element[l4, i], Element[l5, a - i]], i, 1, a) → l6, {10.8664621657649, 9.895453501482386, 9.138927727036688, 8.653323061113573, 8.485281374238571, 8.653323061113573, 9.138927727036688, 9.895453501482386, 10.8664621657649, NaN}
  11. Segment(G, H) → j
  12. Segment(G, I) → k
  13. Sequence(G + (i / b * (H - G)), i, 1, b) → l7, {(16.8, -12), (15.6, -12), (14.4, -12), (13.2, -12), (12, -12), (10.8, -12), (9.600000000000001, -12), (8.399999999999999, -12), (7.199999999999999, -12), (6, -12)}
  14. Sequence(G + (i / b * (I - G)), i, 1, b) → l8, {(18, -10.8), (18, -9.6), (18, -8.4), (18, -7.199999999999999), (18, -6), (18, -4.800000000000001), (18, -3.6000000000000014), (18, -2.3999999999999986), (18, -1.1999999999999993), (18, 0)}
  15. Sequence(Segment[Element[l7, i], Element[l8, b - i]], i, 1, b) → l9, {10.8664621657649, 9.895453501482386, 9.138927727036688, 8.653323061113573, 8.485281374238571, 8.653323061113573, 9.138927727036688, 9.895453501482386, 10.8664621657649, NaN}
  16. Segment(J, K) → l
  17. Segment(J, L) → m
  18. Sequence(J + (i / c * (K - J)), i, 1, c) → l10, {(16.8, 12), (15.6, 12), (14.4, 12), (13.2, 12), (12, 12), (10.8, 12), (9.600000000000001, 12), (8.399999999999999, 12), (7.199999999999999, 12), (6, 12)}
  19. Sequence(J + (i / c * (L - J)), i, 1, c) → l11, {(18, 10.8), (18, 9.6), (18, 8.4), (18, 7.199999999999999), (18, 6), (18, 4.800000000000001), (18, 3.6000000000000014), (18, 2.3999999999999986), (18, 1.1999999999999993), (18, 0)}
  20. Sequence(Segment[Element[l10, i], Element[l11, c - i]], i, 1, c) → l12, {10.8664621657649, 9.895453501482386, 9.138927727036688, 8.653323061113573, 8.485281374238571, 8.653323061113573, 9.138927727036688, 9.895453501482386, 10.8664621657649, NaN}
  21. Segment(M, N) → p
  22. Segment(M, O) → q
  23. Sequence(M + (i / d * (N - M)), i, 1, d) → l13, {(6.45, 0.45), (6.9, 0.9), (7.35, 1.3499999999999999), (7.8, 1.8), (8.25, 2.25), (8.7, 2.6999999999999997), (9.15, 3.15), (9.6, 3.6), (10.05, 4.05), (10.5, 4.5), (10.95, 4.95), (11.399999999999999, 5.3999999999999995), (11.850000000000001, 5.8500000000000005), (12.3, 6.3), (12.75, 6.75), (13.2, 7.2), (13.649999999999999, 7.6499999999999995), (14.1, 8.1), (14.549999999999999, 8.549999999999999), (15, 9)}
  24. Sequence(M + (i / d * (O - M)), i, 1, d) → l14, {(5.55, 0.45), (5.1, 0.9), (4.65, 1.3499999999999999), (4.2, 1.8), (3.75, 2.25), (3.3000000000000003, 2.6999999999999997), (2.85, 3.15), (2.4, 3.6), (1.9500000000000002, 4.05), (1.5, 4.5), (1.0499999999999998, 4.95), (0.6000000000000005, 5.3999999999999995), (0.14999999999999947, 5.8500000000000005), (-0.2999999999999998, 6.3), (-0.75, 6.75), (-1.2000000000000002, 7.2), (-1.6499999999999995, 7.6499999999999995), (-2.0999999999999996, 8.1), (-2.549999999999999, 8.549999999999999), (-3, 9)}
  25. Sequence(Segment[Element[l13, i], Element[l14, d - i]], i, 1, d) → l15, {12.108261642366339, 11.525623627379128, 10.985900054160332, 10.495713410721542, 10.062305898749054, 9.69329665284211, 9.396275858019496, 9.178235124467014, 9.0448880590088, 9, 9.0448880590088, 9.178235124467012, 9.396275858019498, 9.69329665284211, 10.062305898749054, 10.495713410721542, 10.98590005416033, 11.525623627379128, 12.108261642366339, NaN}
  26. Segment(P, Q) → r
  27. Segment(P, R) → s
  28. Sequence(A + (i / n * (B - A)), i, 1, n) → l16, {(-6, 10.8), (-6, 9.6), (-6, 8.4), (-6, 7.199999999999999), (-6, 6), (-6, 4.800000000000001), (-6, 3.6000000000000014), (-6, 2.3999999999999986), (-6, 1.1999999999999993), (-6, 0)}
  29. Sequence(P + (i / e * (Q - P)), i, 1, e) → l17, {(5.55, -0.45), (5.1, -0.9), (4.65, -1.3499999999999999), (4.2, -1.8), (3.75, -2.25), (3.3000000000000003, -2.6999999999999997), (2.85, -3.15), (2.4, -3.6), (1.9500000000000002, -4.05), (1.5, -4.5), (1.0499999999999998, -4.95), (0.6000000000000005, -5.3999999999999995), (0.14999999999999947, -5.8500000000000005), (-0.2999999999999998, -6.3), (-0.75, -6.75), (-1.2000000000000002, -7.2), (-1.6499999999999995, -7.6499999999999995), (-2.0999999999999996, -8.1), (-2.549999999999999, -8.549999999999999), (-3, -9)}
  30. Sequence(P + (i / e * (R - P)), i, 1, e) → l18, {(6.45, -0.45), (6.9, -0.9), (7.35, -1.3499999999999999), (7.8, -1.8), (8.25, -2.25), (8.7, -2.6999999999999997), (9.15, -3.15), (9.6, -3.6), (10.05, -4.05), (10.5, -4.5), (10.95, -4.95), (11.399999999999999, -5.3999999999999995), (11.850000000000001, -5.8500000000000005), (12.3, -6.3), (12.75, -6.75), (13.2, -7.2), (13.649999999999999, -7.6499999999999995), (14.1, -8.1), (14.549999999999999, -8.549999999999999), (15, -9)}
  31. Sequence(Segment[Element[l17, i], Element[l18, e - i]], i, 1, e) → l19, {12.108261642366339, 11.525623627379128, 10.98590005416033, 10.495713410721542, 10.062305898749054, 9.69329665284211, 9.396275858019498, 9.178235124467012, 9.0448880590088, 9, 9.0448880590088, 9.178235124467014, 9.396275858019496, 9.69329665284211, 10.062305898749054, 10.495713410721542, 10.985900054160332, 11.525623627379128, 12.108261642366339, NaN}
  32. Segment(S, T) → t
  33. Segment(S, U) → f_1
  34. Sequence(S + (i / o * (T - S)), i, 1, o) → l20, {(6, -0.6000000000000001), (6, -1.2000000000000002), (6, -1.7999999999999998), (6, -2.4000000000000004), (6, -3), (6, -3.5999999999999996), (6, -4.199999999999999), (6, -4.800000000000001), (6, -5.4), (6, -6), (6, -6.6000000000000005), (6, -7.199999999999999), (6, -7.800000000000001), (6, -8.399999999999999), (6, -9), (6, -9.600000000000001), (6, -10.2), (6, -10.8), (6, -11.399999999999999), (6, -12)}
  35. Sequence(S + (i / o * (U - S)), i, 1, o) → l21, {(5.4, 0), (4.8, 0), (4.2, 0), (3.5999999999999996, 0), (3, 0), (2.4000000000000004, 0), (1.8000000000000007, 0), (1.1999999999999993, 0), (0.5999999999999996, 0), (0, 0), (-0.6000000000000005, 0), (-1.1999999999999993, 0), (-1.8000000000000007, 0), (-2.3999999999999986, 0), (-3, 0), (-3.6000000000000014, 0), (-4.199999999999999, 0), (-4.800000000000001, 0), (-5.399999999999999, 0), (-6, 0)}
  36. Sequence(Segment[Element[l20, i], Element[l21, o - i]], i, 1, o) → l22, {11.415778554264266, 10.8664621657649, 10.357605900979241, 9.895453501482386, 9.486832980505138, 9.138927727036688, 8.858893836140041, 8.653323061113573, 8.527602242131138, 8.485281374238571, 8.527602242131138, 8.653323061113573, 8.858893836140041, 9.138927727036688, 9.486832980505138, 9.895453501482386, 10.357605900979241, 10.8664621657649, 11.415778554264266, NaN}
  37. Segment(V, W) → g_1
  38. Segment(V, Z) → h_1
  39. Sequence(V + (i / u * (W - V)), i, 1, u) → l23, {(6, 0.6000000000000001), (6, 1.2000000000000002), (6, 1.7999999999999998), (6, 2.4000000000000004), (6, 3), (6, 3.5999999999999996), (6, 4.199999999999999), (6, 4.800000000000001), (6, 5.4), (6, 6), (6, 6.6000000000000005), (6, 7.199999999999999), (6, 7.800000000000001), (6, 8.399999999999999), (6, 9), (6, 9.600000000000001), (6, 10.2), (6, 10.8), (6, 11.399999999999999), (6, 12)}
  40. Sequence(V + (i / u * (Z - V)), i, 1, u) → l24, {(5.4, 0), (4.8, 0), (4.2, 0), (3.5999999999999996, 0), (3, 0), (2.4000000000000004, 0), (1.8000000000000007, 0), (1.1999999999999993, 0), (0.5999999999999996, 0), (0, 0), (-0.6000000000000005, 0), (-1.1999999999999993, 0), (-1.8000000000000007, 0), (-2.3999999999999986, 0), (-3, 0), (-3.6000000000000014, 0), (-4.199999999999999, 0), (-4.800000000000001, 0), (-5.399999999999999, 0), (-6, 0)}
  41. Sequence(Segment[Element[l23, i], Element[l24, u - i]], i, 1, u) → l25, {11.415778554264266, 10.8664621657649, 10.357605900979241, 9.895453501482386, 9.486832980505138, 9.138927727036688, 8.858893836140041, 8.653323061113573, 8.527602242131138, 8.485281374238571, 8.527602242131138, 8.653323061113573, 8.858893836140041, 9.138927727036688, 9.486832980505138, 9.895453501482386, 10.357605900979241, 10.8664621657649, 11.415778554264266, NaN}
  42. Segment(A_1, B_1) → i_1
  43. Segment(A_1, C_1) → j_1
  44. Sequence(A + (i / v * (B - A)), i, 1, v) → l26, {(-6, 11.4), (-6, 10.8), (-6, 10.2), (-6, 9.6), (-6, 9), (-6, 8.4), (-6, 7.800000000000001), (-6, 7.199999999999999), (-6, 6.6), (-6, 6), (-6, 5.3999999999999995), (-6, 4.800000000000001), (-6, 4.199999999999999), (-6, 3.6000000000000014), (-6, 3), (-6, 2.3999999999999986), (-6, 1.8000000000000007), (-6, 1.1999999999999993), (-6, 0.6000000000000014), (-6, 0)}
  45. Sequence(A_1 + (i / v * (B_1 - A_1)), i, 1, v) → l27, {(6, 0.6000000000000001), (6, 1.2000000000000002), (6, 1.7999999999999998), (6, 2.4000000000000004), (6, 3), (6, 3.5999999999999996), (6, 4.199999999999999), (6, 4.800000000000001), (6, 5.4), (6, 6), (6, 6.6000000000000005), (6, 7.199999999999999), (6, 7.800000000000001), (6, 8.399999999999999), (6, 9), (6, 9.600000000000001), (6, 10.2), (6, 10.8), (6, 11.399999999999999), (6, 12)}
  46. Sequence(A_1 + (i / v * (C_1 - A_1)), i, 1, v) → l28, {(6.6, 0), (7.2, 0), (7.8, 0), (8.4, 0), (9, 0), (9.6, 0), (10.2, 0), (10.8, 0), (11.4, 0), (12, 0), (12.600000000000001, 0), (13.2, 0), (13.8, 0), (14.399999999999999, 0), (15, 0), (15.600000000000001, 0), (16.2, 0), (16.8, 0), (17.4, 0), (18, 0)}
  47. Sequence(Segment[Element[l27, i], Element[l28, v - i]], i, 1, v) → l29, {11.415778554264266, 10.8664621657649, 10.357605900979241, 9.895453501482386, 9.486832980505138, 9.138927727036688, 8.858893836140041, 8.653323061113573, 8.527602242131138, 8.485281374238571, 8.527602242131138, 8.653323061113573, 8.858893836140041, 9.138927727036688, 9.486832980505138, 9.895453501482386, 10.357605900979241, 10.8664621657649, 11.415778554264266, NaN}
  48. Segment(D_1, E_1) → k_1
  49. Segment(D_1, F_1) → l_1
  50. Sequence(D_1 + (i / w * (E_1 - D_1)), i, 1, w) → l30, {(6, -0.6000000000000001), (6, -1.2000000000000002), (6, -1.7999999999999998), (6, -2.4000000000000004), (6, -3), (6, -3.5999999999999996), (6, -4.199999999999999), (6, -4.800000000000001), (6, -5.4), (6, -6), (6, -6.6000000000000005), (6, -7.199999999999999), (6, -7.800000000000001), (6, -8.399999999999999), (6, -9), (6, -9.600000000000001), (6, -10.2), (6, -10.8), (6, -11.399999999999999), (6, -12)}
  51. Sequence(D_1 + (i / w * (F_1 - D_1)), i, 1, w) → l31, {(6.6, 0), (7.2, 0), (7.8, 0), (8.4, 0), (9, 0), (9.6, 0), (10.2, 0), (10.8, 0), (11.4, 0), (12, 0), (12.600000000000001, 0), (13.2, 0), (13.8, 0), (14.399999999999999, 0), (15, 0), (15.600000000000001, 0), (16.2, 0), (16.8, 0), (17.4, 0), (18, 0)}
  52. Sequence(Segment[Element[l30, i], Element[l31, w - i]], i, 1, w) → l32, {11.415778554264266, 10.8664621657649, 10.357605900979241, 9.895453501482386, 9.486832980505138, 9.138927727036688, 8.858893836140041, 8.653323061113573, 8.527602242131138, 8.485281374238571, 8.527602242131138, 8.653323061113573, 8.858893836140041, 9.138927727036688, 9.486832980505138, 9.895453501482386, 10.357605900979241, 10.8664621657649, 11.415778554264266, NaN}
  53. Segment(G_1, H_1) → m_1
  54. Segment(G_1, I_1) → n_1
  55. Sequence(A + (i / n * (B - A)), i, 1, n) → l33, {(-6, 10.8), (-6, 9.6), (-6, 8.4), (-6, 7.199999999999999), (-6, 6), (-6, 4.800000000000001), (-6, 3.6000000000000014), (-6, 2.3999999999999986), (-6, 1.1999999999999993), (-6, 0)}
  56. Sequence(G_1 + (i / a_1 * (H_1 - G_1)), i, 1, a_1) → l34, {(5.55, -0.45), (5.1, -0.9), (4.65, -1.3499999999999999), (4.2, -1.8), (3.75, -2.25), (3.3000000000000003, -2.6999999999999997), (2.85, -3.15), (2.4, -3.6), (1.9500000000000002, -4.05), (1.5, -4.5), (1.0499999999999998, -4.95), (0.6000000000000005, -5.3999999999999995), (0.14999999999999947, -5.8500000000000005), (-0.2999999999999998, -6.3), (-0.75, -6.75), (-1.2000000000000002, -7.2), (-1.6499999999999995, -7.6499999999999995), (-2.0999999999999996, -8.1), (-2.549999999999999, -8.549999999999999), (-3, -9)}
  57. Sequence(G_1 + (i / a_1 * (I_1 - G_1)), i, 1, a_1) → l35, {(5.55, 0.45), (5.1, 0.9), (4.65, 1.3499999999999999), (4.2, 1.8), (3.75, 2.25), (3.3000000000000003, 2.6999999999999997), (2.85, 3.15), (2.4, 3.6), (1.9500000000000002, 4.05), (1.5, 4.5), (1.0499999999999998, 4.95), (0.6000000000000005, 5.3999999999999995), (0.14999999999999947, 5.8500000000000005), (-0.2999999999999998, 6.3), (-0.75, 6.75), (-1.2000000000000002, 7.2), (-1.6499999999999995, 7.6499999999999995), (-2.0999999999999996, 8.1), (-2.549999999999999, 8.549999999999999), (-3, 9)}
  58. Sequence(Segment[Element[l34, i], Element[l35, a_1 - i]], i, 1, a_1) → l36, {12.108261642366335, 11.525623627379128, 10.985900054160332, 10.495713410721542, 10.062305898749054, 9.69329665284211, 9.396275858019496, 9.178235124467014, 9.0448880590088, 9, 9.0448880590088, 9.178235124467014, 9.396275858019496, 9.69329665284211, 10.062305898749054, 10.495713410721542, 10.985900054160332, 11.525623627379128, 12.108261642366335, NaN}
  59. Segment(J_1, K_1) → p_1
  60. Segment(J_1, L_1) → q_1
  61. Sequence(J_1 + (i / n_2 * (K_1 - J_1)), i, 1, n_2) → l37, {(6.45, 0.45), (6.9, 0.9), (7.35, 1.3499999999999999), (7.8, 1.8), (8.25, 2.25), (8.7, 2.6999999999999997), (9.15, 3.15), (9.6, 3.6), (10.05, 4.05), (10.5, 4.5), (10.95, 4.95), (11.399999999999999, 5.3999999999999995), (11.850000000000001, 5.8500000000000005), (12.3, 6.3), (12.75, 6.75), (13.2, 7.2), (13.649999999999999, 7.6499999999999995), (14.1, 8.1), (14.549999999999999, 8.549999999999999), (15, 9)}
  62. Sequence(J_1 + (i / n_2 * (L_1 - J_1)), i, 1, n_2) → l38, {(6.45, -0.45), (6.9, -0.9), (7.35, -1.3499999999999999), (7.8, -1.8), (8.25, -2.25), (8.7, -2.6999999999999997), (9.15, -3.15), (9.6, -3.6), (10.05, -4.05), (10.5, -4.5), (10.95, -4.95), (11.399999999999999, -5.3999999999999995), (11.850000000000001, -5.8500000000000005), (12.3, -6.3), (12.75, -6.75), (13.2, -7.2), (13.649999999999999, -7.6499999999999995), (14.1, -8.1), (14.549999999999999, -8.549999999999999), (15, -9)}
  63. Sequence(Segment[Element[l37, i], Element[l38, n_2 - i]], i, 1, n_2) → l39, {12.108261642366335, 11.525623627379128, 10.985900054160332, 10.495713410721539, 10.062305898749054, 9.69329665284211, 9.396275858019496, 9.178235124467014, 9.0448880590088, 9, 9.0448880590088, 9.178235124467014, 9.396275858019496, 9.69329665284211, 10.062305898749054, 10.495713410721539, 10.985900054160332, 11.525623627379128, 12.108261642366335, NaN}
  64. Point(q) → M_1
  65. Point(f) → N_1
  66. Point(r) → O_1
  67. Point(h) → P_1
  68. Point(s) → Q_1
  69. Point(k) → R_1
  70. Point(p) → S_1
  71. Point(g) → T_1
  72. Point(f_1) → U_1

AI Drawing Prompt Reference

Create a 3D Christmas-card style geometric figure. Start by choosing several key endpoints and drawing boundary line segments that act as the left/right limits of different faces. Along each chosen direction, sample points in equal steps between the endpoints to form multiple layer polylines. For every layer, interpolate points between the two corresponding boundary segments so the resulting outlines are symmetric and smooth by segments. Repeat the same construction for adjacent faces using the other pair of endpoints and connect the corresponding layers across the top and bottom to produce visible folded surfaces, giving a stacked multi-face solid appearance with slanted edges and gradually varying profile heights.
The prompt above was compiled from the original drawing commands and is for reference only.