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Elliptic Paraboloid

Elliptic Paraboloid
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2015-09-13 17:42
FunctionCoordinate GeometrySolid GeometryGraphing
This example demonstrates the 3D elliptic paraboloid surface and its variations. Key math concepts include surface, continuity, unit circle, function graph, algebra, and exponential functions. Construction involves commands like Surface, CurveCartesian, and parameters a, b, c, along with objects O, ox, oy, oz, and text elements. Suitable for high school and above students studying solid geometry, function graphs, and parametric equations.

GeoGebra Commands & Parameters

  1. Surface(((a * sqrt(w)) * cos(v)) + x(O), ((b * sqrt(w)) * sin(v)) + y(O), w + z(O), v, 0, 6.28319, w, 0, 6) → d
  2. CurveCartesian(((a * cos(t)) * sqrt(3)) + ox, ((b * sin(t)) * sqrt(3)) + oy, 3 + oz, t, 0, 6.28319) → h
  3. CurveCartesian(ox, (b * t) + oy, t^(2) + oz, t, -2.449489742783178, 2.449489742783178) → i
  4. CurveCartesian((a * t) + ox, oy, t^(2) + oz, t, -2.449489742783178, 2.449489742783178) → j

AI Drawing Prompt Reference

Draw a 3D elliptic paraboloid surface, showing its relation with the unit circle and function graphs, with variations controlled by parameters a, b, c, and include curves along the coordinate axes, start by plotting the elliptic paraboloid, then add the unit circle and two parabolas as references, finally label key points and coordinate axes.
The prompt above was compiled from the original drawing commands and is for reference only.