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Scissors Model for an Ellipse

Scissors Model for an Ellipse
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2020-12-07 17:23
Coordinate GeometryParametric EquationGeometric Construction
This example demonstrates a scissors model for an ellipse, involving parametric equations and tangent lines. Using commands like Intersect, Segment, and OrthogonalLine, the construction of tangent lines and related geometric elements is shown. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(d, xAxis) → M, N
  2. Intersect(d, yAxis) → K, L
  3. Segment(A, B) → a
  4. Segment(D, E) → b
  5. Segment(F, G) → c
  6. OrthogonalLine(D, b) → f
  7. Intersect(d, f) → H, I
  8. Circle(D, C) → g
  9. Ray(D, I) → h
  10. Intersect(g, h) → J,
  11. CurveCartesian(x(D + ((0.2 * cos(k)) * Vector[D, J]) + ((0.25 * sin(k)) * Vector[D, C])), y(D + ((0.2 * cos(k)) * Vector[D, J]) + ((0.25 * sin(k)) * Vector[D, C])), k, 0, (2 * π)) → e
  12. Intersect(b, e) → O, P, O_{1}, O_{2}
  13. Circle(C, 0.1) → k
  14. Mirror(e, a) → e'
  15. OrthogonalLine(C, b) → i
  16. Intersect(k, i) → Q, R
  17. Midpoint(D, O) → S
  18. Midpoint(S, O) → T
  19. Midpoint(O, T) → U
  20. Midpoint(U, O) → V
  21. OrthogonalLine(V, b) → j
  22. Intersect(j, e) → W, Z
  23. Polygon(E, Q, Z, W, R) → poly1, e_1, q, z_1, w, r
  24. Mirror(E, a) → E'
  25. Mirror(Q, a) → Q'
  26. Mirror(Z, a) → Z'
  27. Mirror(W, a) → W'
  28. Mirror(R, a) → R'
  29. Polygon(E', Q', Z', W', R') → poly1', l, q', z', w', r'
  30. Mirror(D, a) → D'

AI Drawing Prompt Reference

Draw a scissors model for an ellipse, demonstrating parametric equations and tangent lines. Start by intersecting a line with the x-axis and y-axis to find points, then connect these points to form segments. Next, find the perpendicular lines to these segments and calculate their intersections. Use these intersections to draw a circle and a ray, and plot the ellipse based on a parametric equation. Finally, sketch the tangent lines to the ellipse and create multiple symmetric shapes to showcase the model's symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.