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Poncelet's Porism for 2 Ellipses (order 5)

Poncelet's Porism for 2 Ellipses (order 5)
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2015-04-27 21:08
Trigonometry
This example illustrates Poncelet's porism for two ellipses with order 5. Key mathematical concepts include ellipses, quadrilaterals, cosine, and kite. It is constructed using GeoGebra commands such as Conic, Tangent, Point, etc. Suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. Conic(A, B, C, D, E) → c
  2. Tangent(F, c) → a, b
  3. Point(b) → G
  4. Tangent(G, c) → d, e
  5. Point(e) → I
  6. Tangent(I, c) → f, g
  7. Point(g) → J
  8. Tangent(J, c) → h, i
  9. Intersect(i, a) → K
  10. Conic(G, I, J, K, F) → k
  11. Ray(O, O + (cos(α), sin(α))) → j
  12. Intersect(k, j) → H, R
  13. Tangent(H, c) → l, m
  14. Intersect(k, l, 2) → L
  15. Intersect(k, m, 2) → M
  16. Tangent(M, c) → n, p
  17. Intersect(k, p, 2) → N
  18. Tangent(N, c) → q, r
  19. Intersect(k, r) → P, Q
  20. Segment(Q, L) → s
  21. Segment(L, H) → t
  22. Segment(H, M) → a_1
  23. Segment(M, P) → b_1
  24. Segment(P, Q) → c_1

AI Drawing Prompt Reference

Draw two ellipses, with one ellipse having five points connected to form a pentagon, each point having a tangent line to the ellipse. Use these tangents and points to construct a figure with multiple intersections and segments, ultimately forming a closed polygon with these segments.
The prompt above was compiled from the original drawing commands and is for reference only.