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Weiden's Descent: Geometric and Function Construction

Weiden's Descent: Geometric and Function Construction
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2023-03-20 19:47
TriangleFunctionGeometric Construction
In collections geometriadinamica.es
This example demonstrates the Weiden's descent phenomenon, involving triangles, step functions, and geometry. Key mathematical concepts include right triangles, piecewise functions, and angle calculations. Construction involves using GeoGebra commands like Line, Point, OrthogonalLine, and Midpoint, along with Circle and Polygon tools. Suitable for middle or high school mathematics education to understand the integration of geometry and functions.

GeoGebra Commands & Parameters

  1. Line(A, T) → a
  2. Point(a) → B
  3. OrthogonalLine(A, a) → b
  4. Line(A, C) → c
  5. Line(A, B) → d
  6. OrthogonalLine(C, c) → e
  7. OrthogonalLine(B, d) → f
  8. Intersect(e, f) → D
  9. Point(c) → E
  10. Polygon(E, A, 4) → poly1, n, p, q, r, F, G
  11. Midpoint(A, G) → H
  12. Midpoint(E, G) → I
  13. Circle(H, I) → s
  14. Segment(G, A) → t
  15. Point(e) → J
  16. Segment(J, A) → a1
  17. Rotate(I, 72°, H) → K
  18. Point(s) → L
  19. Polygon(L, K, 5) → poly2, b1, c1, d1, e1, o, M, N, O
  20. Midpoint(B, A) → P
  21. OrthogonalLine(P, d) → f1
  22. Mirror(L, f1) → L'
  23. Mirror(K, f1) → K'
  24. Mirror(M, f1) → M'
  25. Mirror(N, f1) → N'
  26. Mirror(O, f1) → O'
  27. Polygon(L', K', M', N', O') → poly2', l', k', m', n', o'
  28. Mirror(J, f1) → J'
  29. Mirror(A, f1) → A'
  30. Segment(J', A') → g1
  31. Mirror(s, f1) → h1
  32. Intersect(e, f1) → Q
  33. Vector(I, Q) → v
  34. Translate(s, v) → k1
  35. Translate(L, v) → L'_1
  36. Translate(K, v) → K'_1
  37. Translate(M, v) → M'_1
  38. Translate(N, v) → N'_1
  39. Translate(O, v) → O'_1
  40. Polygon(L'_1, K'_1, M'_1, N'_1, O'_1) → poly2'_1, l'_1, k'_1, m'_1, n'_1, o'_1
  41. Circle(O'_1, J') → p1
  42. Point(p1) → R
  43. Intersect(k1, p1, 2) → S
  44. CircumcircleArc(J', R, S) → q1
  45. Mirror(f1, f1) → i1
  46. Mirror(G, f1) → G'
  47. Mirror(A, f1) → A'_1
  48. Segment(G', A'_1) → j1
  49. Intersect(j1, t) → U
  50. OrthogonalLine(U, f1) → l1
  51. Intersect(k1, l1) → V, W
  52. Segment(W, V) → m1

AI Drawing Prompt Reference

Create a geometric figure on the plane by first fixing a base point and drawing a reference line through another point. From the base point, draw a perpendicular line and additional lines so that several right-angle relations are formed; compute the intersections to obtain the main vertices. Use these key points to construct one polygon based on the triangle-like structure. Next, take midpoints of relevant segments to define a circle (using the midpoint as center and another midpoint as the radius). Determine an intersection on the circle region and build a circular arc through the circle points. Then rotate a constructed point around the circle center by a fixed angle to create a second set of points, mirror the rotated configuration across the same auxiliary line, and form a corresponding second polygon. Finish by drawing segments connecting the matched rotated and mirrored points and include the arc obtained from the circle.
The prompt above was compiled from the original drawing commands and is for reference only.