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Surface of Revolution by Andrew Knauft

Surface of Revolution by Andrew Knauft
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2016-04-02 05:58
Solid GeometryCalculusIntegralTransformationGraphing
This example demonstrates the generation of a surface of revolution by rotating the region bounded by functions f(x) and g(x) around a horizontal line. Key math concepts include calculus, definite integrals, linear equations, and coordinate transformations. It utilizes GeoGebra commands like Point, Rotate, Locus, Surface, and Textfield to construct the visualization. Suitable for high school students and math enthusiasts exploring the principles of surface generation and integral calculations.

GeoGebra Commands & Parameters

  1. Point(Segment[A, B]) → E
  2. Rotate(C, α, rot) → C'
  3. Rotate(D, α, rot) → D'
  4. Locus(D', E) → loc3
  5. Locus(C', E) → loc4
  6. Surface(t, ((f(t) - R) * cos(u)) + R, ((f(t) - R) * sin(u)), t, a, b, u, (-α), 0) → e
  7. Surface(t, ((g(t) - R) * cos(u)) + R, ((g(t) - R) * sin(u)), t, a, b, u, (-α), 0) → i
  8. Surface(t, ((f(t) - R) * cos(u)) + R, ((f(t) - R) * sin(u)), t, x(C), x(C) + dx, u, (-α), 0) → l
  9. Surface(t, ((g(t) - R) * cos(u)) + R, ((g(t) - R) * sin(u)), t, x(D), x(D) + dx, u, (-α), 0) → d
  10. Surface(x(C), R - ((R - ((y(C) * (1 - t)) + (y(D) * t))) * cos(v)), ((R - ((y(C) * (1 - t)) + (y(D) * t))) * sin(v)), t, 0, 1, v, 0, α) → c
  11. Surface(x(C) + dx, R - ((R - ((g(x(C) + dx) * (1 - t)) + (f(x(C) + dx) * t))) * cos(v)), ((R - ((g(x(C) + dx) * (1 - t)) + (f(x(C) + dx) * t))) * sin(v)), t, 0, 1, v, 0, α) → k
  12. Surface(a, R - ((R - ((g(a) * (1 - t)) + (f(a) * t))) * cos(v)), ((R - ((g(a) * (1 - t)) + (f(a) * t))) * sin(v)), t, 0, 1, v, 0, α) → m
  13. Surface(b, R - ((R - ((g(b) * (1 - t)) + (f(b) * t))) * cos(v)), ((R - ((g(b) * (1 - t)) + (f(b) * t))) * sin(v)), t, 0, 1, v, 0, α) → n
  14. Surface(t, (g(t) * u) + (f(t) * (1 - u)), 0, t, a, b, u, 0, 1) → p
  15. Surface(t, R + (((f(t) * u) + (g(t) * (1 - u)) - R) * cos(α)), ((((R - f(t)) * u) + ((R - g(t)) * (1 - u))) * sin(α)), t, a, b, u, 0, 1) → o
  16. Surface(t, R + (((f(t) * u) + (g(t) * (1 - u)) - R) * cos(α)), ((((R - f(t)) * u) + ((R - g(t)) * (1 - u))) * sin(α)), t, x(C), x(C) + dx, u, 0, 1) → q
  17. Surface(t, (g(t) * u) + (f(t) * (1 - u)), 0, t, x(C), x(C) + dx, u, 0, 1) → r
  18. Textfield(f) → InputBox1
  19. Textfield(g) → InputBox2
  20. Textfield(R) → InputBox3
  21. Textfield(a) → InputBox4
  22. Textfield(b) → InputBox5