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Parabola by Folding

Parabola by Folding
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2017-10-19 21:18
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to generate a parabola by folding paper. Key mathematical concepts include the geometric properties and symmetry of parabolas. Using GeoGebra commands such as Line, Point, Segment, Midpoint, LineBisector, OrthogonalLine, and Intersect, the focus, directrix, and envelope of the parabola can be constructed. Suitable for high school mathematics education and learning coordinate geometry.

GeoGebra Commands & Parameters

  1. Line(B, C) → directrix
  2. Point(directrix) → T
  3. Segment(Focus, T) → b
  4. Midpoint(b) → E
  5. LineBisector(b) → envelope
  6. OrthogonalLine(T, directrix) → a
  7. Intersect(envelope, a) → A
  8. Segment(A, Focus) → c
  9. Segment(A, T) → e

AI Drawing Prompt Reference

Draw a parabola by folding paper. Start by drawing a line as the directrix, then take a point T on the line as an auxiliary point. Connect the focus to T, find the midpoint as the vertex of the parabola. Draw a perpendicular line from the vertex to the directrix, and find the intersection with the envelope line to get a point A on the parabola. Finally, connect the focus to A, and A to T to form part of the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.