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Ibn Sanin's Parabola Geometric Construction

Ibn Sanin's Parabola Geometric Construction
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2015-10-29 03:37
AngleCoordinate GeometryGeometric ConstructionLocus
This GeoGebra example demonstrates Ibn Sanin's geometric construction method for parabolas. Key mathematical concepts include the geometric definition of parabolas, angle relationships, and segment proportions. The construction utilizes GeoGebra commands such as Segment, Point, OrthogonalLine, Midpoint, Circle, Intersect, and Line to dynamically visualize the process. It is suitable for high school or university students and math enthusiasts interested in analytic geometry and historical mathematical methods.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Point(a) → C
  3. OrthogonalLine(C, a) → b
  4. Point(a) → H
  5. Segment(A, H) → c
  6. Midpoint(c) → E
  7. Segment(A, B) → d
  8. Circle(E, H) → e
  9. OrthogonalLine(H, d) → f
  10. Intersect(e, b, 2) → F
  11. Line(F, c) → g
  12. Intersect(f, g) → G
  13. Intersect(e, b, 1) → H_1
  14. Line(H_1, d) → h
  15. Intersect(f, h) → I

AI Drawing Prompt Reference

Draw a parabola with points A and B as foci. First, draw segment a between points A and B. Choose point C on segment a and draw the perpendicular line b to segment a. Choose point H on segment a and draw segment c from A to H. The midpoint of segment c is E, and draw circle e with E as the center and H as the radius. Draw the perpendicular line f to segment d, where segment d is the extension of segment a. Find the intersection of lines b and e, which is point F. Draw line g parallel to segment c through point F. Find the intersection of lines g and f, which is point G. Draw line h parallel to segment d through point G. Find the intersection of lines h and f, which is point I.
The prompt above was compiled from the original drawing commands and is for reference only.