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Interactive Hyperbola with Paper Folding

Interactive Hyperbola with Paper Folding
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2016-04-30 03:14
FunctionCoordinate GeometryGeometric ConstructionSlider AnimationLocus
This example demonstrates the formation and properties of a hyperbola through interactive paper folding. It involves core mathematical concepts like hyperbola, isosceles triangles, median line, rational numbers, multiplication, and expected value. Construction highlights include commands such as Circle, Point, Segment, LineBisector, Line, Intersect, Hyperbola, Midpoint, Rotate, OrthogonalLine, and Polygon. Suitable for high school mathematics teaching or geometric exploration activities.

GeoGebra Commands & Parameters

  1. Circle(F_1, r) → c
  2. Point(c) → A
  3. Segment(A, F_2) → f
  4. LineBisector(f) → g
  5. Line(A, F_1) → h
  6. Intersect(g, h) → B
  7. Line(F_2, B) → i
  8. Hyperbola(F_1, F_2, B) → d
  9. Segment(F_1, A) → j
  10. Segment(A, B) → k
  11. Segment(B, F_2) → l
  12. Segment(B, F_2) → m
  13. Segment(F_1, F_2) → n
  14. Midpoint(F_1, F_2) → C
  15. Intersect(d, n, 2) → V_1
  16. Intersect(d, n, 1) → V_2
  17. Segment(C, V_2) → p
  18. Segment(V_1, C) → q
  19. Segment(F_1, C) → s
  20. Circle(V_1, b) → e
  21. Rotate(F_1, (-(90°)), C) → D
  22. Rotate(F_2, (-(90°)), C) → E
  23. Segment(D, E) → n'
  24. Intersect(e, n', 1) → F
  25. Line(V_1, n') → t
  26. OrthogonalLine(F, t) → a
  27. Line(V_2, t) → f_1
  28. Rotate(F_1, 90°, C) → G
  29. Rotate(F_2, 90°, C) → H
  30. Segment(G, H) → n'_1
  31. Intersect(e, n'_1) → I, J
  32. Line(I, a) → g_1
  33. Intersect(t, a) → K
  34. Intersect(a, f_1) → L
  35. Intersect(f_1, g_1) → M
  36. Intersect(t, g_1) → N
  37. Polygon(N, K, L, M) → poly1, n_1, k_1, l_1, m_1
  38. Line(N, L) → h_1
  39. Line(K, M) → i_1
  40. Line(K, L) → j_1
  41. Line(M, N) → p_1