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Mangold Ellipse Construction

Mangold Ellipse Construction
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2020-06-28 00:42
VectorCoordinate GeometryGeometric Construction
This example demonstrates how to generate a Mangold Ellipse by constructing a rectangle and points. Core mathematical concepts include the definition of an ellipse, coordinate geometry, and vector operations. It utilizes GeoGebra commands such as Corner, Rect, Point, and Conic. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Corner(1) → C1
  2. Corner(2) → C2
  3. Corner(3) → C3
  4. Corner(4) → C4
  5. Rect(A, C1) → q1
  6. Point(Segment[A, (x(C1), y(A))]) → B
  7. Rect(C4, B) → q2
  8. Point(Segment[B, (x(B), y(C4))]) → C
  9. Rect(C, C3) → q3
  10. Point(Segment[(x(A), y(C)), (x(C3), y(C))]) → D
  11. Rect(D, C2) → q4
  12. Point(Segment[(x(D), y(A)), (x(D), y(C2))]) → E
  13. Rect((x(A), y(C1)), E) → q5
  14. Conic(B, C, D, E, F) → c