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Graphs of Functions of Two Variables (Version 3)

Graphs of Functions of Two Variables (Version 3)
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2017-02-16 02:06
FunctionCoordinate GeometrySolid Geometry
This example demonstrates the graphs of functions of two variables. It involves key mathematical concepts such as functions, coordinate geometry, and solid geometry. Using GeoGebra commands like Surface, CurveCartesian, and IntersectPath, the construction of the three-dimensional graph of a function of two variables is illustrated. Suitable for high school mathematics education, particularly in coordinate geometry and solid geometry.

GeoGebra Commands & Parameters

  1. Textfield(f) → PoleTekstowe1
  2. Simplify(f) → fupr
  3. CurveCartesian(x0, t, f(x0, t), t, -5, 5) → xsection
  4. CurveCartesian(t, y0, f(t, y0), t, -5, 5) → ysection
  5. Surface(x0 + (x(v) * t), y0 + (y(v) * t), s, t, -5, 5, s, -10, 10) → dsectionPlane
  6. CurveCartesian(x0 + (x(v) * t), y0 + (y(v) * t), f(x0 + (x(v) * t), y0 + (y(v) * t)), t, -5, 5) → dsection
  7. Segment(P, S) → odcinekPS
  8. IntersectPath(ySectionPlane, xOyPlane) → prostaYsection
  9. IntersectPath(xsectionPlane, xOyPlane) → prostaXsection
  10. CurveCartesian(x0 + (x(v) * t), y0 + (y(v) * t), t, -5, 5) → prostaDsection
  11. CurveCartesian(t, g(t), f(t, g(t)), t, -5, 5) → krzywaDsection
  12. Surface(t, g(t), s, t, -5, 5, s, -10, 10) → dsectionSurface
  13. Textfield(g) → PoleTekstowe2
  14. Segment(A, B) → i