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Discrete to Continuous Hyperbola

Discrete to Continuous Hyperbola
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2019-03-08 05:29
Coordinate GeometryGeometric Construction
This example demonstrates the transition from discrete points to a continuous hyperbola. It involves core mathematical concepts such as hyperbola, prism, conic sections, trapezoid, standard deviation, and logarithm. The construction uses GeoGebra commands like Segment, Point, Mirror, Circle, and Intersect. Suitable for high school mathematics teaching or understanding the geometric properties and continuity of hyperbolas.

GeoGebra Commands & Parameters

  1. Segment((1, 0), (5, 0)) → f
  2. Point(f) → C
  3. Segment((x(C) + 1, 0), (x(C) + 5, 0)) → g
  4. Point(g) → D
  5. Mirror(C, O) → C'
  6. Mirror(D, O) → D'
  7. Circle(D, p) → d
  8. Circle(D', (2 * x(C)) + p) → e
  9. Intersect(d, e) → E, F, ,
  10. Circle(D', p - 15) → h
  11. Circle(D, (2 * x(C)) + p - 15) → k
  12. Intersect(k, h) → G, H, ,