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Hyperboloid via Segments

Hyperboloid via Segments
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2023-09-11 05:37
TrigonometrySolid GeometryParametric EquationGeometric Construction
In collections Conic Section Collection
This example demonstrates how to construct a hyperboloid as a ruled surface by sweeping a straight line through space. It involves core math concepts like hyperbola, straight lines, solid geometry, surface, rhombus, trigonometry, real numbers, plane figures, and geometric distribution. The construction uses GeoGebra commands and objects such as Sequence, Translate, a, R2, N, R1, H, list2, list1, θ, list3, list4, list5, list6, b, speed, view, button1, spin, button2. Suitable for high school and above students studying solid geometry, coordinate geometry, and spatial geometric constructions.

GeoGebra Commands & Parameters

  1. Sequence(((If[a, R2, R1] * cos(((2 * pi / N) * t))), (If[a, R2, R1] * sin(((2 * pi / N) * t))), 0), t, 0, N - 1) → list2
  2. Sequence(((R1 * cos(((2 * pi / N) * t))), (R1 * sin(((2 * pi / N) * t))), 0), t, 0, N - 1) → list1
  3. Translate(Rotate[list1, θ, zAxis], Vector[(0, 0, H)]) → list3
  4. Translate(Rotate[list2, (-θ), zAxis], Vector[(0, 0, H)]) → list4
  5. Sequence(Segment[Element[list1, t], Element[list3, t]], t, 1, N) → list5
  6. Sequence(Segment[Element[list2, t], Element[list4, t]], t, 1, N) → list6

AI Drawing Prompt Reference

Construct a hyperboloid by sweeping a circle with radius R1 and another with R2 around the z-axis and translating them. Then, connect corresponding points on the two surfaces with line segments to form the hyperboloid's surface.
The prompt above was compiled from the original drawing commands and is for reference only.