MathPlotAI Logo MathPlotAI

Surface of Revolution of 3D Parametric Curve about LINE

Surface of Revolution of 3D Parametric Curve about LINE
Loading the math board and drawing, please wait…
2018-02-11 02:29
VectorCoordinate GeometrySolid GeometryCalculusParametric Equation
In collections Calculus C07_Apps Of Integration
This example demonstrates the surface of revolution generated by rotating a 3D parametric curve around a line. It involves core mathematical concepts such as calculus, rotation surfaces, vector operations, and 3D coordinate geometry. The construction uses GeoGebra commands like CurveCartesian, Surface, and Textfield, along with InputBoxes for dynamic parameter adjustments, making it suitable for high school and above learning calculus and solid geometry.

GeoGebra Commands & Parameters

  1. CurveCartesian(cos(t), sin(t) + 1.5, cos((3 * t)), t, low, up) → a
  2. Surface(a, α, g) → b
  3. Textfield(b) → InputBox1
  4. Textfield(a) → InputBox2
  5. Textfield(g) → InputBox3

AI Drawing Prompt Reference

Create a 3D surface of revolution. Start with a parametric curve in 3D space, where the x-coordinate follows a cosine function, the y-coordinate is a sine function plus a constant offset, and the z-coordinate is the cosine of a triple angle. Then revolve this curve around a straight line to form a smooth surface. The surface shape is controlled by the parameter range of the curve. Include three input boxes to adjust the curve's parameter range, the rotation angle, and another related parameter, allowing dynamic observation of the surface changes. The final graphic should show both the original curve and the resulting surface clearly in space.
The prompt above was compiled from the original drawing commands and is for reference only.