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Geometric constructions of cylinder intersections

Geometric constructions of cylinder intersections
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2016-08-24 00:21
Coordinate GeometrySolid GeometryParametric EquationGeometric ConstructionGraphing
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates the geometric construction of the curve of intersection between two cylinders. Key math concepts include coordinate geometry, solid geometry, and curve drawing. Construction highlights the use of GeoGebra commands like ImplicitCurve, Point, CurveCartesian, Textfield, LaTeX, and objects such as b, a, i, c, A, f1, f2, etc., controlled by sliders and parameters to shape the intersection curve. Suitable for high school students and math enthusiasts studying spatial geometry and curve constructions.

GeoGebra Commands & Parameters

  1. ImplicitCurve(x^(2) - y^(2) - (b^(2) - a^(2))) → c
  2. Point(c, i) → A
  3. CurveCartesian((b * cos(t)), (b * sin(t)), sqrt(a^(2) - (b^(2) * sin(t)^(2))), t, 0, (2 * π)) → f1
  4. CurveCartesian((b * cos(t)), (b * sin(t)), (-sqrt(a^(2) - (b^(2) * sin(t)^(2)))), t, 0, (2 * π)) → f2
  5. Textfield(v) → InputBox1
  6. LaTeX(f1, false, false) → text6
  7. LaTeX(f2, false, false) → text7