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Surface of Revolution: Another Vase

Surface of Revolution: Another Vase
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2017-09-21 02:24
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how to generate a surface of revolution by rotating a curve. Key mathematical concepts include curves and surfaces in coordinate geometry. The construction uses Spline, CurveCartesian, and Surface commands to create a vase shape. Suitable for high school mathematics education, particularly in coordinate geometry and solid geometry.

GeoGebra Commands & Parameters

  1. Spline({C, D, E, F, G, H, I, J, K, L, M, N}, 3) → a
  2. CurveCartesian((x(N) * cos(t)), y(N), (x(N) * sin(t)), t, 0, b) → d
  3. Surface((x(a(t)) * cos(u)), y(a(t)), (x(a(t)) * sin(u)), t, 0, 1, u, 0, b) → c
  4. Surface((u * x(d(t))), y(d(t)), (u * z(d(t))), t, 0, b, u, 0, 1) → e