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Interactive Hyperbola with Paper Folding by Tatia Totorica

Interactive Hyperbola with Paper Folding by Tatia Totorica
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2016-04-30 03:13
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the properties of hyperbolas through paper folding. It involves concepts such as hyperbolas, integers, parabolas, and fractions. Using GeoGebra commands like Circle, Point, Segment, LineBisector, Line, Intersect, Hyperbola, Midpoint, Rotate, OrthogonalLine, and Polygon, the construction of a hyperbola model is achieved. Suitable for high school mathematics education, particularly for learning about coordinate geometry and hyperbolas.

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

AI Drawing Prompt Reference

Draw a hyperbola by paper folding to demonstrate its properties. Start by defining two foci and a line segment passing through one focus. Find the intersection of the perpendicular bisector of the segment with the segment itself. Construct the hyperbola using the two foci and the intersection point. Then, add auxiliary lines, segments, and circles related to the hyperbola, rotating certain elements to show symmetry. Finally, connect some lines and points to form polygons, completing the model display.
The prompt above was compiled from the original drawing commands and is for reference only.