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Cones & Cylinders from Revolution

Cones & Cylinders from Revolution
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2016-05-12 19:27
TrigonometryCoordinate GeometrySolid GeometryCalculusGeometric Construction
This example demonstrates the generation of 3D solids like cones and cylinders by revolving 2D shapes. Key math concepts include solids of revolution, 3D geometry, and coordinate geometry. Construction highlights the use of commands like Vector, Polygon, Sequence, and CurveCartesian in GeoGebra. Suitable for high school and above students learning about rotational geometry and 3D modeling.

GeoGebra Commands & Parameters

  1. Vector(((1.1 * d) * W_x)) → u
  2. Vector(((1.1 * d) * W_y)) → v
  3. Vector(((1.1 * d) * W_z)) → w
  4. Polygon(((1.1 * d) * (W_x + W_y)), ((1.1 * d) * ((-W_x) + W_y)), ((1.1 * d) * ((-W_x) - W_y)), ((1.1 * d) * (W_x - W_y))) → poly1, g, i, j, l
  5. Sequence(((r * cos((0.125 * i))) * W_x) + ((r * sin((0.125 * i))) * W_y), i, 0, p) → list1
  6. Sequence(((r * cos((0.125 * i))) * W_x) + ((r * sin((0.125 * i))) * W_y) + (k * W_z), i, 0, p) → list3
  7. CurveCartesian(x(((r * cos((0.125 * i))) * W_x) + ((r * sin((0.125 * i))) * W_y)), y(((r * cos((0.125 * i))) * W_x) + ((r * sin((0.125 * i))) * W_y)), i, 0, p) → e_1
  8. CurveCartesian(x(((r * cos((0.125 * t))) * W_x) + ((r * sin((0.125 * t))) * W_y) + (k * W_z)), y(((r * cos((0.125 * t))) * W_x) + ((r * sin((0.125 * t))) * W_y) + (k * W_z)), t, 0, p) → e_2
  9. Sequence(Segment[A, Element[list1, i]], i, 1, p + 1) → list2
  10. Sequence(Segment[Element[list1, i], Element[list3, i]], i, 1, p + 1) → list4
  11. Sequence(Segment[(0, 0) + (k * W_z), Element[list3, i]], i, 1, p + 1) → list5