MathPlotAI Logo MathPlotAI

Hippias' Quadratrix

Hippias' Quadratrix
Loading the math board and drawing, please wait…
2015-07-14 13:33
FunctionCoordinate GeometryGeometric Construction
In collections Geometric Constructions Geometric Constructions Geometric Constructions-MINE Geometric Constructions
This example demonstrates Hippias' Quadratrix, a special plane curve related to geometric means and area problems. By constructing points, line segments, and loci, the dynamic generation of the curve can be shown. The example uses GeoGebra commands such as Point, Segment, If, and Locus. Suitable for high school mathematics education, particularly in coordinate geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Segment(A, B) → a
  3. Point(xAxis) → C
  4. Segment(A, B) → c
  5. Segment(A, D) → b
  6. Segment(D, C) → d
  7. Segment(C, B) → e
  8. Segment(B, A) → f
  9. Segment((0, 1 - t), (1, 1 - t)) → xx
  10. Segment(B, E) → yy
  11. If(t < 1, Intersect[xx, yy], (0.6366197723675814, 0)) → F
  12. Locus(F, t) → zz