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Hyperboloid of One Sheet and Merry Christmas

Hyperboloid of One Sheet and Merry Christmas
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2016-01-05 07:08
Coordinate GeometrySolid GeometryGeometric Construction
This GeoGebra example demonstrates a one-sheet hyperboloid, a type of surface in solid geometry. Using commands like Sequence, Surface, Circle, and RotateText, the example constructs the hyperboloid. Suitable for high school math education or students learning solid geometry.

GeoGebra Commands & Parameters

  1. Sequence((0, u, (-u^(2)) + (6 * u) - 1 + Lift), u, 0.3, 3, 0.1) → s1
  2. Length(s1) → ds1
  3. Surface((r * (cos(u) - (v * sin(u)))), (r * (sin(u) + (v * cos(u)))), (h * (v + Lift)), u, 0, (6.28319 * k), v, 0, h1) → e
  4. Circle(zAxis, A) → p
  5. Circle(zAxis, B) → c
  6. Surface((r * (cos(u) - (v * sin(u)))), ((-r) * (sin(u) + (v * cos(u)))), ((-h) * (v - Lift)), u, (-6.28319 * k), 0, v, 0, h1) → f
  7. Sequence(((r * (cos((a * n)) - (h1 * sin((a * n))))), (r * (sin((a * n)) + (h1 * cos((a * n))))), ((-h) * (h1 - Lift))), n, 1, i + i_3) → список2
  8. Sequence(((r * (cos((a * n)) - (h1 * sin((a * n))))), (r * (sin((a * n)) + (h1 * cos((a * n))))), (h * (h1 + Lift))), n, 1, i) → список1
  9. Sequence(((r * (cos((a * n)) - (h1 * sin((a * n))))), (r * (sin((a * n)) + (h1 * cos((a * n))))), ((-h) * (h1 - Lift))), n, 1, i + i_3) → список4
  10. Sequence(((r * (cos((a * n)) - (h1 * sin((a * n))))), (r * (sin((a * n)) + (h1 * cos((a * n))))), (h * (h1 + Lift))), n, 1, i + i_3) → список5
  11. Sequence(Segment[Element[список1, u], Element[список2, u + i_3]], u, 1, Length[список1]) → список3
  12. Sequence(Translate[Element[s1, u], Vector[(0, 0, 0), (0.2 - δ, 0.2 + δ, 0.3)]], u, 1, ds1) → s2
  13. Sequence(Segment[Element[список4, u], Element[список5, u + i_3]], u, 1, Length[список4]) → список6
  14. Sequence(Segment[Element[s1, u], Element[s2, u]], u, 1, ds1) → u1
  15. Sequence(Rotate[Element[u1, u], 72°, Element[s1, u]], u, 1, ds1) → u2
  16. Sequence(Rotate[Element[u1, u], 144°, Element[s1, u]], u, 1, ds1) → u3
  17. Sequence(Rotate[Element[u1, u], 216°, Element[s1, u]], u, 1, ds1) → u4
  18. Sequence(Rotate[Element[u1, u], 288°, Element[s1, u]], u, 1, ds1) → u5
  19. RotateText("uStas\;\&\,T.C.", 90°) → надпись01
  20. CurveCartesian(0, u, (-u^(2)) + (6 * u) - 1 + Lift, u, -0.25, 3) → φ
  21. Sphere(Z, δ + ((0.5 * δ) * (-1)^(j))) → Ω_1
  22. Sphere(Z, δ - ((0.5 * δ) * (-1)^(j))) → Ω_2