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Holed Torus Construction

Holed Torus Construction
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2019-04-08 03:22
CircleVectorTrigonometrySolid GeometryParametric Equation
This example demonstrates the construction and visualization of a three-dimensional torus with circular holes. It involves core mathematical concepts such as solid geometry, circles, trigonometry, vectors, and parametric equations. The construction utilizes GeoGebra commands and objects like Segment, Point, Max, Min, Line, Vector, Length, Surface, CurveCartesian, Sequence, Circle, and Textfield. It is suitable for high school students and math enthusiasts studying solid geometry and parametric modeling.

GeoGebra Commands & Parameters

  1. Segment((0, 0, π / 2), (0, 0, ((-π)) / 2)) → segInfSup
  2. Point(segInfSup) → P2
  3. Point(segInfSup) → P1
  4. Max(z(P1), z(P2)) → vMax
  5. Min(z(P1), z(P2)) → vInf
  6. Point(yAxis) → A
  7. Line(A, A + (1, 0, 0)) → rOp2
  8. Point(rOp2) → B
  9. Vector(A, B) → v2
  10. Length(v2) → r1
  11. Vector(A) → v
  12. Length(v) → r
  13. Surface((((cos((s * f(t))) * r1) * cos(t)) + (sin((s * f(t))) * r), (((-sin((s * f(t)))) * r1) * cos(t)) + (cos((s * f(t))) * r), (r1 * sin(t))), t, vInf, vMax, s, 0, (2 * π / n)) → parteSuperficie
  14. CurveCartesian(((r1 * cos(t)), r, (r1 * sin(t))), t, (-π), π) → circ1T
  15. Sequence(Rotate[circ1T, ((t * 360 / n))°, zAxis], t, 0, n - 1) → Circ
  16. Sequence(Rotate[parteSuperficie, ((t * 360 / n))°, zAxis], t, 0, n - 1) → sup
  17. Circle((0, 0, r1), r, zAxis) → Tapa1
  18. Textfield(n) → CasillaDeEntrada1
  19. Vector(P1) → vA
  20. Vector(P2) → vB