MathPlotAI Logo MathPlotAI

Ruled Surface

Ruled Surface
Loading the math board and drawing, please wait…
2017-08-07 03:54
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the concept of a ruled surface, which is a surface that can be formed by moving a straight line. Using GeoGebra commands such as Point, Plane, OrthogonalPlane, IntersectPath, CurveCartesian, and Surface, a ruled surface can be constructed. Suitable for high school mathematics education, particularly in solid and coordinate geometry.

GeoGebra Commands & Parameters

  1. Point(yAxis) → B
  2. Plane(zAxis, xAxis) → d
  3. Plane(zAxis, yAxis) → c
  4. Point(zAxis) → C
  5. OrthogonalPlane(C, zAxis) → b
  6. IntersectPath(b, d) → g
  7. Point(g) → D
  8. IntersectPath(b, c) → f
  9. Point(f) → E
  10. Point(xAxis) → A
  11. CurveCartesian((x(D) * cos(t - shift)), (y(E) * sin(t - shift)), z(C), t, 0, (2 * π)) → e
  12. CurveCartesian((x(A) * cos(t)), (y(B) * sin(t)), 0, t, 0, (2 * π)) → a
  13. Surface((u * x(a(t))) + ((1 - u) * x(e(t))), (u * y(a(t))) + ((1 - u) * y(e(t))), (u * z(a(t))) + ((1 - u) * z(e(t))), t, 0, (2 * π), u, 0, 1) → h