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Trammel of Archimedes

Trammel of Archimedes
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2016-03-14 21:54
Coordinate Geometry
This example demonstrates the principle of the trammel of Archimedes, constructing an ellipse using three key points to specify the center, major axis, and minor axis. Key mathematical concepts include the geometric properties and construction of ellipses. GeoGebra commands used include Line, OrthogonalLine, Point, Circle, Intersect, Ellipse, Ray, and Segment. Suitable for high school mathematics education and learning about ellipses.

GeoGebra Commands & Parameters

  1. Line(B, A) → a
  2. OrthogonalLine(A, a) → b
  3. Point(b) → C
  4. Circle(B, Segment[A, C]) → c
  5. Intersect(c, b) → D, E
  6. Ellipse(D, E, B) → d
  7. Point(a) → F
  8. Circle(F, Segment[C, A]) → e
  9. Circle(F, Segment[B, A]) → f
  10. Intersect(f, a, 1) → G
  11. Intersect(e, a, 1) → H
  12. Circle(F, Segment[H, G]) → g
  13. Intersect(g, b) → I, J
  14. Ray(F, J) → h
  15. Ray(F, I) → i
  16. Intersect(e, i) → K,
  17. Intersect(e, h) → L,
  18. Segment(K, F) → j
  19. Segment(F, L) → k
  20. Point(b) → M
  21. Circle(M, Segment[C, A]) → p
  22. Intersect(p, b, 2) → N
  23. Circle(N, Segment[B, A]) → q
  24. Intersect(q, b, 2) → O
  25. Circle(M, Segment[M, O]) → r
  26. Intersect(r, a) → P, Q
  27. Segment(P, M) → l
  28. Circle(M, Segment[O, N]) → s
  29. Segment(M, Q) → m
  30. Intersect(s, l) → R,
  31. Intersect(s, m) → S,