MathPlotAI Logo MathPlotAI

Arco Rampante (Rampant Arch) Geometric Construction

Arco Rampante (Rampant Arch) Geometric Construction
Loading the math board and drawing, please wait…
2023-03-17 22:41
CircleCoordinate GeometryTransformationGeometric ConstructionLocus
In collections geometriadinamica.es
This example demonstrates a geometric figure named 'Arco Rampante' (Rampant Arch), which combines lines, circles, arcs, and various transformations to create a symmetric, mirrored arch-like structure. The core mathematical concepts include geometric construction, circle intersections and tangents, orthogonal lines, midpoints, reflection and translation transformations, and arc drawing. The construction uses GeoGebra commands such as Line, Circle, Intersect, OrthogonalLine, Segment, If, Midpoint, Mirror, Vector, Translate, CircleArc, Distance, and Min, involving objects like line q, circle a, intersection points A_1/B_1, segment b, point C, circle k, point D, lines h/g, point F, line l, point G, line p, function f, point H, segment s, point r, point J, segment t, point L, circle c_1, points M/N, line a_1, point K, variable zz, circle c, point ε, line u, point e, point K_1, lines j/i, circle c1, point d, line i1, point m1, point m, and point n. It is suitable for senior high school or early university students to study comprehensive geometric construction and transformations, and can also serve as a reference for mathematical modeling or artistic geometric design.

GeoGebra Commands & Parameters

  1. Line(A_1, C) → k
  2. Line(B_1, D) → h
  3. Circle(D, q) → g
  4. Intersect(g, h, 2) → F
  5. OrthogonalLine(F, h) → l
  6. Intersect(k, l) → G
  7. Circle(C, G) → p
  8. Segment(C, D) → f
  9. Intersect(p, f, 1) → H
  10. Circle(H, D) → s
  11. OrthogonalLine(H, f) → r
  12. Intersect(s, r, 2) → J
  13. OrthogonalLine(J, r) → t
  14. Intersect(k, t) → L
  15. Circle(J, L) → c_1
  16. Intersect(c_1, r) → M, N
  17. OrthogonalLine(M, r) → a_1
  18. Intersect(a_1, k) → K
  19. If(zz < 0, 10, zz) → c
  20. Segment(D, B_1) → e
  21. Midpoint(C, D) → K_1
  22. Segment(A_1, C) → d
  23. Circle(K_1, C) → c_2
  24. Line(T, T1) → n_1
  25. Segment(T1, T) → a_2
  26. Mirror(A_1, a_2) → A'
  27. Mirror(C, a_2) → B
  28. Segment(A', B) → d'
  29. Mirror(D, a_2) → A
  30. Mirror(B_1, a_2) → B'
  31. Segment(A, B') → e'
  32. Vector(A_1, B') → v
  33. Translate(pic1, v) → pic1'_1
  34. Translate(pic1, v) → pic1'
  35. Intersect(g, f, 1) → E
  36. Intersect(l, r) → I
  37. Intersect(a_1, k) → O
  38. CircleArc(H, D, J) → d_1
  39. CircleArc(M, J, O) → e_1
  40. Segment(O, C) → b_1
  41. Segment(O, M) → f_1
  42. Segment(M, F) → g_1
  43. Segment(J, D) → h_1
  44. Distance(D, J) → distanciaDJ
  45. Min(Distance[D, J], ((c - 2) * Distance[D, J] / 3)) → p1
  46. Circle(D, p1) → k_1
  47. Min(Distance[K, J], ((c - 5) * Distance[K, J] / 2)) → p2
  48. Circle(J, p2) → p_1
  49. Min(Distance[C, O], ((c - 7) * Distance[C, O] / 2)) → p3
  50. Intersect(s, d_1) → U, , ,
  51. Intersect(k_1, d_1) → V, D_1, ,
  52. Intersect(p_1, e_1) → W, , ,
  53. Segment(V, H) → i_1
  54. CircleArc(H, D, V) → r_1
  55. Segment(W, M) → j_1
  56. CircleArc(M, J, W) → s_1
  57. Circle(O, p3) → q_1
  58. Intersect(q_1, b_1) → R, Z
  59. Segment(O, R) → l_1
  60. CircleArc(H, D, D_1) → t_1
  61. Segment(K, Z) → m_1
  62. Segment(H, D_1) → b_2
  63. CircleArc(D, F, E) → d_2
  64. CircleArc(H, D, J) → e_2
  65. CircleArc(M, J, O) → f_2
  66. Segment(O, C) → g_2
  67. Segment(W, R) → i_2
  68. Segment(W, R) → j_2
  69. Segment(O, R) → h_2

AI Drawing Prompt Reference

Draw a geometric figure called 'Arco Rampante', which combines lines, circles, arcs and various transformations to create a symmetric, mirrored arch-like structure. The core mathematical concepts include geometric construction, circle intersections and tangents, orthogonal lines, midpoints, reflection and translation transformations, and arc drawing. The figure should have a central axis, with lines and arcs radiating from it, and should be symmetrical about a central point. The arcs should be smooth and continuous, with no sharp corners or edges. The figure should also have a sense of depth and dimensionality, with the lines and arcs appearing to recede into the distance. The overall shape should be dynamic and visually appealing, with a sense of movement and energy. The figure should be constructed using a combination of straight lines, circular arcs, and curved lines, with the arcs and curves blending smoothly into each other. The figure should also have a sense of balance and harmony, with the different elements working together to create a cohesive and visually appealing whole. The construction should involve a series of transformations, including reflections, rotations, and translations, to create the desired shape and symmetry. The figure should be drawn in a way that creates a sense of tension and release, with the lines and arcs seeming to push and pull against each other. The overall effect should be a dynamic and visually striking image that captures the essence of the Arco Rampante figure.
The prompt above was compiled from the original drawing commands and is for reference only.