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Hyperboloids Demonstration

Hyperboloids Demonstration
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2016-02-16 17:24
FunctionSolid GeometryTransformation
In collections Conic Section Collection
This example demonstrates the generation process of hyperboloids. Key mathematical concepts include the definition and properties of hyperboloids. Using GeoGebra commands such as Circle, Point, Rotate, and CurveCartesian, the formation of hyperboloids can be dynamically shown. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Circle(zAxis, (2, 0, -2)) → c
  2. Point(c) → A
  3. Rotate(A, 120°, zAxis) → A'
  4. CurveCartesian(sec(t) - 0.25, 0, (1.15 * tan(t)), t, ((-π)) / 2, π / 2) → a
  5. Segment(A, A' + (0, 0, 4)) → f
  6. CurveCartesian(sec(t) + 0.25, 0, (1.15 * tan(t)), t, ((-π)) / 2, π / 2) → b
  7. Sequence((x(a(t)), 0, z(a(t))), t, ((-π)) / 3, (2 * π / 5), 0.2) → list1
  8. Sequence((x(b(t)), 0, z(b(t))), t, ((-π)) / 3, (2 * π / 5), 0.2) → list2
  9. Append(list1, (0, 0, 2.59)) → list3
  10. Append(list3, (0, 0, -1.99)) → list4
  11. Polygon(list4) → poly1
  12. Append(list2, (4, 0, 2.59)) → list5
  13. Append(list5, (4, 0, -1.99)) → list6
  14. Polygon(list6) → poly2