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Curve of Cylinder-Sphere Intersection-Viviani's Curve

Curve of Cylinder-Sphere Intersection-Viviani's Curve
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2016-08-29 16:41
TrigonometryCoordinate GeometrySolid GeometryParametric Equation
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 Viviani's curve formed by the intersection of a cylinder and a sphere, involving spatial geometry, analytical geometry, quadratic surfaces, and curves. It utilizes commands like Sequence, LaTeX, and Point in GeoGebra for construction. Suitable for high school and above, focusing on solid geometry and analytical geometry concepts.

GeoGebra Commands & Parameters

  1. Sequence(CurveCartesian[fx_z(t), (i * sqrt(R^(2) - t^(2) - fx_z(t)^(2))), t, t, (-R), R], i, -1, 1, 2) → listxyz
  2. Sequence(CurveCartesian[(i * sqrt(R^(2) - t^(2) - fx_z(t)^(2))), t, t, (-R), R], i, -1, 1, 2) → list2
  3. LaTeX(a, false, false) → text5
  4. LaTeX(i, false, false) → text6
  5. Point(c) → A