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Rotation Body III

Rotation Body III
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2015-10-27 20:40
Solid GeometryTransformationGeometric Construction
This example demonstrates the rotation of a body around the y-axis. It involves solid geometry and rotation transformation. Using GeoGebra commands such as Point, Ray, Sequence, Surface, etc., students can intuitively understand the process of generating a rotation body.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Ray(A, E) → a
  3. Point(a) → B
  4. Sequence(A + ((B - A) * ((2 * i) - 1) / ((2 * n))), i, 1, n) → punkter
  5. RectangleSum(f, x(A), x(B), n, 0.5) → middelsum
  6. Distance(A, B) → d
  7. Sequence(Surface[((x(punkter(i)) + d / ((2 * n))) * cos(v)), u, ((x(punkter(i)) + d / ((2 * n))) * sin(v)), u, 0, f(x(punkter(i))), v, 0, t], i, 1, n) → indersider
  8. Sequence(Surface[((x(punkter(i)) - d / ((2 * n))) * cos(v)), u, ((x(punkter(i)) - d / ((2 * n))) * sin(v)), u, 0, f(x(punkter(i))), v, 0, t], i, 1, n) → ydersider
  9. Sequence(Surface[(u * cos(v)), f(x(punkter(i))), (u * sin(v)), u, x(punkter(i)) - d / ((2 * n)), x(punkter(i)) + d / ((2 * n)), v, 0, t], i, 1, n) → toppe
  10. Surface((u * cos(v)), 0, (u * sin(v)), u, x(A), x(B), v, 0, t) → list5
  11. Integral(f, x(A), x(B)) → integral
  12. Sequence(Rotate[Polygon[punkter(i) - (d / ((2 * n)), 0), punkter(i) + (d / ((2 * n)), 0), punkter(i) + (d / ((2 * n)), f(punkter(i))), punkter(i) + (((-d)) / ((2 * n)), f(punkter(i)))], (-t), yAxis], i, 1, n) → rotmiddelsummer
  13. Surface((cos(t) * u), (v * f(u)), (sin(t) * u), u, x(A), x(B), v, 0, 1) → punktmaengde
  14. Surface((u * cos(v)), f(u), (u * sin(v)), u, x(A), x(B), v, 0, t) → omdrejning
  15. Surface((x(B) * cos(v)), u, (x(B) * sin(v)), u, 0, f(x(B)), v, 0, t) → yderside
  16. Surface((x(A) * cos(v)), u, (x(A) * sin(v)), u, 0, f(x(A)), v, 0, t) → inderside
  17. Surface((u * cos(v)), 0, (u * sin(v)), u, x(A), x(B), v, 0, t) → bund

AI Drawing Prompt Reference

Create a solid body rotated around the y-axis. Start by creating a point A on the x-axis, then draw a ray a from A. Create another point B on the ray. Generate a sequence of points to form the middle and top surfaces of a rectangle. Finally, use rotation and surface commands to create the side and top surfaces of the rotated body.
The prompt above was compiled from the original drawing commands and is for reference only.