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Create a 3D Surface of Revolution by Rotating Any 2D Figure about Any Line

Create a 3D Surface of Revolution by Rotating Any 2D Figure about Any Line
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2019-07-03 23:34
Coordinate GeometrySolid GeometryTransformation
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources
This example demonstrates how to create a 3D surface of revolution by rotating any 2D figure about any line. Core mathematical concepts include coordinate geometry and solid geometry. Commands used include Line, Vector, CurveCartesian, Surface, and Rotate. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Vector(C, D) → u
  3. CurveCartesian(x(C) + (k * x(u)), y(C) + (k * y(u)), z(C) + (k * z(u)), k, 0, 1) → a
  4. Surface(a, n, f) → b
  5. Rotate(a, n, f) → a'

AI Drawing Prompt Reference

Create a 3D surface of revolution by rotating any 2D figure about any line to demonstrate core concepts in coordinate and solid geometry, start by drawing a line as the axis of rotation, define a vector to determine the rotation center, generate a 2D figure based on the vector, then rotate it around the line to form the 3D surface, and visualize the rotation process.
The prompt above was compiled from the original drawing commands and is for reference only.