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Intersection of Cylinder and Cos Surfaces

Intersection of Cylinder and Cos Surfaces
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2016-08-29 18:17
TrigonometryCoordinate 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 intersection of a cylinder and cosine surfaces in the interval [-π, π]. Key mathematical concepts include surface intersection and trigonometric functions. Constructed using GeoGebra commands like Sequence, Textfield, and InputBox, it is suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Textfield(x0) → InputBox1
  2. Textfield(y0) → InputBox2
  3. Sequence((i * acos((-cos(x)) - cos(y))), i, -1, 1, 2) → l_f
  4. Textfield(z0) → InputBox3
  5. Sequence(CurveCartesian[t, (i * acos((-cos(f1(t))) - cos(t))), f1(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l1
  6. Sequence(CurveCartesian[t, (i * acos((-cos(f2(t))) - cos(t))), f2(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l2
  7. Sequence(CurveCartesian[x0, (i * acos((-cos(f1(t))) - cos(t))), f1(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l1_{x}
  8. Sequence(CurveCartesian[t, y0, f1(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l1_{y}
  9. Sequence(CurveCartesian[t, (i * acos((-cos(f1(t))) - cos(t))), z0, t, (-t_{max}), t_{max}], i, -1, 1, 2) → l1_{z}
  10. Sequence(CurveCartesian[x0, (i * acos((-cos(f2(t))) - cos(t))), f2(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l2_{x}
  11. Sequence(CurveCartesian[t, y0, f2(t), t, (-t_{max}), t_{max}], i, -1, 1, 2) → l2_{y}
  12. Sequence(CurveCartesian[t, (i * acos((-cos(f2(t))) - cos(t))), z0, t, (-t_{max}), t_{max}], i, -1, 1, 2) → l2_{z}

AI Drawing Prompt Reference

Draw the intersection of a cylinder and cosine surfaces in the interval [-π, π]. First, input the offsets for the x-axis, y-axis, and z-axis of the cylinder. Then, based on these offsets, draw two cosine surfaces, each with positive and negative branches. Finally, draw the projections of each surface on the x-axis, y-axis, and z-axis.
The prompt above was compiled from the original drawing commands and is for reference only.