Creating 3D Surfaces of Revolution

Creating 3D Surfaces of Revolution
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2020-07-15 22:26
This example demonstrates how to create 3D surfaces of revolution from a modifiable cross section. It involves core mathematical concepts such as solids of revolution, cross-sections, 3D geometry, and function fitting. The construction uses GeoGebra commands like PointIn, IndexOf, FitPoly, Surface, Line, and objects including B, A, l2, c, b, d, A_1, B_1, C, D, degree, f, g, angle, a, l1, e, h, i, j, k. Suitable for high school and above students studying solid geometry and calculus.

GeoGebra Commands & Parameters

  1. PointIn(d) → A_1
  2. PointIn(d) → B_1
  3. PointIn(d) → C
  4. PointIn(d) → D
  5. IndexOf(SelectedElement[l2], l2) → degree
  6. FitPoly({A_1, B_1, C, D}, degree) → f
  7. Surface(g, angle, xAxis) → a
  8. Surface(g, angle, yAxis) → e
  9. Line(A, B) → h
  10. Surface(g, angle, h) → i
  11. IndexOf(SelectedElement[l1], l1) → j
  12. Line(A, B) → k