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Various Pipe Constructions

Various Pipe Constructions
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2016-12-31 01:43
VectorFunctionSolid GeometryCalculus
This example demonstrates the construction of various types of pipes. It involves core mathematical concepts such as functions, derivatives, and continuity. Using GeoGebra commands like CurveCartesian, Surface, and Vector, different pipe shapes can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Textfield(f_1) → CampEntradaSortida1
  2. Textfield(f_2) → CampEntradaSortida2
  3. Textfield(f_3) → CampEntradaSortida3
  4. Derivative(f_1) → g_1
  5. Derivative(f_2) → g_2
  6. Derivative(f_3) → g_3
  7. CurveCartesian(f_1(ss) - (c1(ss) * e_1(t)) - (c5(ss) * e_2(t)), f_2(ss) + (c2(ss) * e_1(t)) - (c4(ss) * e_2(t)), f_3(ss) + (c3(ss) * e_2(t)), t, 0, (2 * π)) → j
  8. Surface(f_1(s) - (c1(s) * e_1(t)) - (c5(s) * e_2(t)), f_2(s) + (c2(s) * e_1(t)) - (c4(s) * e_2(t)), f_3(s) + (c3(s) * e_2(t)), t, 0, (2 * π), s, 0, (2 * π)) → o
  9. Surface(f_1(s) - (c1(s) * e_1(t)) - (c5(s) * e_2(t)), f_2(s) + (c2(s) * e_1(t)) - (c4(s) * e_2(t)), f_3(s) + (c3(s) * e_2(t)), t, 0, (2 * π), s, 0, ss) → q
  10. CurveCartesian(f_1(0) - (c1(0) * e_1(t)) - (c5(0) * e_2(t)), f_2(0) + (c2(0) * e_1(t)) - (c4(0) * e_2(t)), f_3(0) + (c3(0) * e_2(t)), t, 0, (2 * π)) → s
  11. CurveCartesian((aa * cos(t)), (bb * sin(t)), 0, t, 0, (2 * π)) → e_0
  12. CurveCartesian(f_1(t), f_2(t), f_3(t), t, 0, (2 * π)) → ac
  13. Derivative(ac) → ac'
  14. Derivative(ac') → ac''
  15. Vector((0, 0, 0), A) → w
  16. Vector(P, P + UnitVector[w]) → t
  17. CurvatureVector(P, ac) → n
  18. OrthogonalPlane(P, t) → a