MathPlotAI Logo MathPlotAI

Shannon's Parabola of Wonder 2

Shannon's Parabola of Wonder 2
Loading the math board and drawing, please wait…
2019-10-11 03:50
AngleCoordinate Geometry
This example demonstrates Shannon's Parabola of Wonder 2. It involves parabolas, angles, curve sketching, and conic sections. Using GeoGebra commands such as Segment, Point, OrthogonalLine, LineBisector, and Intersect, a dynamic model of the parabola can be constructed. Suitable for high school mathematics education and learning, particularly for coordinate geometry and curve sketching.

GeoGebra Commands & Parameters

  1. Segment(A, F) → Directrix
  2. Point(Directrix) → G
  3. OrthogonalLine(G, Directrix) → n
  4. LineBisector(G, Focus) → p
  5. Segment(G, Focus) → q
  6. Intersect(n, p) → I
  7. Segment(I, Focus) → r
  8. Segment(I, G) → s

AI Drawing Prompt Reference

Draw a horizontal segment as the directrix, pick an arbitrary point on it, and construct a perpendicular line through that point. Place a fixed point as the focus, connect the focus to the point on the directrix, and draw the perpendicular bisector of this segment. The intersection of this bisector with the perpendicular line gives a point on the parabola. Finally, connect this intersection point to the focus and to the directrix point, forming two segments. The figure shows the geometric construction of a parabola with directrix, focus, perpendicular, bisector, and connecting segments.
The prompt above was compiled from the original drawing commands and is for reference only.