MathPlotAI Logo MathPlotAI

Randomized geometric construction via rotation: a “yellow submarine” style diagr

Randomized geometric construction via rotation: a “yellow submarine” style diagr
Loading the math board and drawing, please wait…
2020-08-07 22:50
CirclePolygonSequenceTransformationGeometric Construction
This GeoGebra example demonstrates how to build a complex plane figure by composing geometric primitives—circles, segments, and polygons—then applying rotation-based transformations. The “yellow submarine” theme is used to make the assembly process intuitive while showcasing mathematical mechanisms behind the artwork. Key math concepts include coordinate geometry and geometric construction (points, orthogonal lines, intersections, circles, segments, polygons) as well as rigid motions (Rotate) to generate repeated or rotated parts. It also introduces a stochastic/algorithmic flavor through Random, together with conditional logic (If) and modular arithmetic (Mod) to control how parameters evolve. From the construction summary, it uses commands such as OrthogonalLine to create perpendicular lines, Intersect to compute intersection points, Segment/Circle/Polygon to form the main shapes, Point and Sequence to organize key coordinates and parameter lists, and Rotate to position components consistently. Interface-oriented objects (text labels and interactive elements like Bouton1, plus image/icon placeholders) support an engaging classroom or creative-coding workflow. Suitable for secondary school geometry lessons, GeoGebra construction practice, and introductory algorithmic visualization projects.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, yAxis) → a
  2. OrthogonalLine(A, xAxis) → h
  3. Intersect(yAxis, a) → B
  4. Intersect(h, xAxis) → C
  5. Segment(B, A) → i
  6. Segment(A, C) → j
  7. OrthogonalLine(A, yAxis) → l
  8. Circle(A, 1.5) → k
  9. Intersect(a, i) → D
  10. Intersect(k, a) → E, F
  11. Polygon(G, H, I, J) → poly1, g_1, h_1, i_1, j_1
  12. Point(h_1) → L
  13. Sequence(Segment[G + (i, 0), J + (i, 0)], i, 0, 21) → liste2
  14. Sequence(Segment[J + (0, i), I + (0, i)], i, 0, 21) → liste1
  15. Segment((-11, 0), (11, 0)) → m
  16. Segment((0, -10), (0, 11.25)) → n
  17. Sequence((-11, 0) + (i, 0), i, 1, 21, 1) → liste3
  18. Sequence((0, -10) + (0, i), i, 1, 20) → liste4
  19. Sequence(Text[-10 + i, Element[liste3, i + 1] - (0.32, 0.75)], i, 0, 20) → liste5
  20. Sequence(Text[-9 + i, Element[liste4, i + 1] - (0.82, 0.2)], i, 0, 20) → liste6
  21. Sequence(Segment[Element[liste3, i] + (0, 0.2), Element[liste3, i] - (0, 0.2)], i, 1, Length[liste3]) → liste7
  22. Sequence(Segment[Element[liste4, i] + (0.2, 0), Element[liste4, i] - (0.2, 0)], i, 1, Length[liste4]) → liste8
  23. Polygon(M + (-6, -6), M + (6, -6), M + (6, 6), M + (-6, 6)) → poly2, p, q, s, a_1
  24. Circle(M, 5) → c_1
  25. Rotate(P, o, M) → P'
  26. Segment(M, P') → b_1
  27. Random(1, 4) → aa
  28. If(aa ≤ 2, 1, -1) → signe1
  29. Random(1, 4) → bb
  30. If(bb ≤ 2, -1, 1) → signe2
  31. Circle(M, 5) → d_1
  32. Segment(M - (5, 0), M + (5, 0)) → e_1
  33. Segment(M - (0, 5), M + (0, 5)) → f_1
  34. Random(0, 360) → cc
  35. Circle(W, 0.5) → k_1
  36. Circle(W, 0.5) → p_1
  37. Circle(Z, 0.5) → q_1
  38. Circle(A_1, 0.5) → r_1
  39. Mod(round(o), 2) → tt

AI Drawing Prompt Reference

Draw a yellow submarine-style geometric figure by first creating vertical and horizontal lines on the coordinate axes, then finding their intersections to construct a quadrilateral. Rotate this quadrilateral around a central point using random numbers to control the rotation angle, generating a series of repeated rotated shapes. Finally, add some auxiliary lines and text labels to complete the figure.
The prompt above was compiled from the original drawing commands and is for reference only.