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Surface of Revolution-1

Surface of Revolution-1
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2016-01-16 05:46
Coordinate GeometrySolid Geometry
This example demonstrates the surface formed by rotating an n-segment polyline around a line. Key mathematical concepts include rotation, surface, and geometric construction. Using GeoGebra commands such as RotateText, Sequence, and Segment, the rotation process is dynamically illustrated. Suitable for high school and above students to learn about rotation and related concepts in solid geometry.

GeoGebra Commands & Parameters

  1. RotateText("uStas\;\&\,Т.С.", 90°) → надпись01
  2. Sequence(U + (0, (r * ((2 * i) + 1)), 0), i, 0, q1 - 1) → s1
  3. Sequence(Q + (0, ((r * 2) * i), 0), i, 0, q2) → s2
  4. Sequence(Segment[Element[s2, i], Element[s1, i]], i, 1, q1) → s3
  5. Sequence(Segment[Element[s1, i], Element[s2, i + 1]], i, 1, q2) → s4
  6. Sequence(Surface[(v * sin(u)), (v * cos(u)), z(U) - (k * ((r * ((2 * i) - 1)) - v)), u, 0, λ, v, (r * ((2 * i) - 2)), (r * ((2 * i) - 1))], i, 1, q1) → φ
  7. Sequence(Surface[(v * sin(u)), (v * cos(u)), z(Q) + (k * (((r * 2) * i) - v)), u, 0, λ, v, (r * ((2 * i) - 1)), ((r * 2) * i)], i, 1, q2) → ψ
  8. Sequence(Surface[(v * sin(u)), (v * cos(u)), z(U) + (h * (i - 2)) - (k * ((r * (i - 1)) - v)), u, 0, λ, v, (r * (i - 1)), (r * i)], i, 1, n) → Ω
  9. Sequence(Circle[U + (0, 0, (h * i)), (r * (i + 1)), zAxis], i, 0, n - 1) → ω
  10. Segment(U + (0, 0, (0.4 * m)), Q + (0, 0, (-0.4 * m))) → d
  11. Point(Ray[A, A + (1, 0)]) → B