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Surface of Revolution by cbishop

Surface of Revolution by cbishop
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2016-03-03 11:39
Coordinate GeometrySolid GeometryParametric Equation
This example demonstrates the generation of a surface of revolution. Key mathematical concepts include rotation, parametric equations, and coordinate geometry. Using GeoGebra commands such as Surface and CurveCartesian, a surface of revolution can be constructed. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox2
  2. Point(xAxis) → A
  3. Point(xAxis) → B
  4. Segment(A, B) → m
  5. Point(m) → C
  6. Point(m) → D
  7. Sequence(Cylinder[(x(C) + ((x(D) - x(C)) * (j - 1) / n), 0, 0), (x(C) + ((x(D) - x(C)) * j / n), 0, 0), f(x(C) + ((x(D) - x(C)) * j / n))], j, 1, n) → list1
  8. Sequence(Cylinder[(x(C) + ((x(D) - x(C)) * j / n), 0, 0), (x(C) + ((x(D) - x(C)) * (j + 1) / n), 0, 0), f(x(C) + ((x(D) - x(C)) * j / n))], j, 0, n - 1) → list2
  9. CurveCartesian(t, 0, f(t), t, x(C), x(D)) → c
  10. Surface(u, (cos(v) * f(u)), (sin(v) * f(u)), u, x(C), x(D), v, 0, T) → d
  11. Surface(u, (cos(v) * f(u)), (sin(v) * f(u)), u, x(C), x(D), v, 0, 6.28319) → a
  12. CurveCartesian(u, g(u), h(u), u, x(C) - 1, x(D) + 1) → b