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Witch of Agnesi

Witch of Agnesi
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2020-02-18 21:01
FunctionCoordinate GeometryGraphing
This GeoGebra example demonstrates the Witch of Agnesi curve, a special type of function curve involving function concepts. Using commands like Ray, Point, Circle, etc., the curve can be dynamically constructed. Suitable for high school mathematics education, particularly in coordinate geometry and function graphing.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Ray(O, B) → f
  3. Point(f) → C_1
  4. Midpoint(C_1, O) → a
  5. Circle(a, C_1) → c
  6. OrthogonalLine(C_1, f) → h
  7. Point(g) → E
  8. Rotate(E, α, O) → E'
  9. Angle(E, O, E') → β
  10. Ray(O, E') → i
  11. Intersect(c, i, 2) → A
  12. Intersect(h, i) → C
  13. OrthogonalLine(C, h) → j
  14. OrthogonalLine(A, j) → k
  15. Intersect(j, k) → P
  16. Segment(C, O) → l
  17. Segment(A, P) → m
  18. Segment(P, C) → n
  19. Distance(O, a) → a_1
  20. CurveCartesian(((2 * a_1) * cot(t)), ((2 * a_1) * sin(t)^(2)), t, 0, (2 * π)) → b
  21. Angle(C, P, A) → γ