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Bicylinder (Mouhefanggai)

Bicylinder (Mouhefanggai)
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2014-10-19 15:38
Coordinate GeometrySolid GeometryCalculusGeometric ConstructionSlider Animation
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve Parametric Surfaces
This example demonstrates the intersection of two cylinders intersecting at right angles, known as a bicylinder or Mouhefanggai in Chinese. It involves core mathematical concepts in solid geometry, coordinate geometry, and calculus. The construction uses GeoGebra commands like Point, Cylinder, CurveCartesian, and Surface. Suitable for high school and above students to explore spatial geometric solids and their intersection properties.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Cylinder(A, B, 1) → a, c, d, b
  4. Point(yAxis) → C
  5. Point(yAxis) → D
  6. Cylinder(C, D, 1) → e, f, g, h
  7. CurveCartesian(sqrt(1 - t^(2)), sqrt(1 - t^(2)), t, t, -1, 1) → m
  8. CurveCartesian((-sqrt(1 - t^(2))), sqrt(1 - t^(2)), t, t, -1, 1) → n
  9. CurveCartesian((-sqrt(1 - t^(2))), (-sqrt(1 - t^(2))), t, t, -1, 1) → o
  10. CurveCartesian(sqrt(1 - t^(2)), (-sqrt(1 - t^(2))), t, t, -1, 1) → p
  11. Surface(sqrt(1 - t^(2)), (s * sqrt(1 - t^(2))), t, s, -1, 1, t, -1, 1) → i
  12. Surface((s * sqrt(1 - t^(2))), sqrt(1 - t^(2)), t, s, -1, 1, t, -1, 1) → j
  13. Surface((-sqrt(1 - t^(2))), (s * sqrt(1 - t^(2))), t, s, -1, 1, t, -1, 1) → k
  14. Surface((s * sqrt(1 - t^(2))), (-sqrt(1 - t^(2))), t, s, -1, 1, t, -1, 1) → l

AI Drawing Prompt Reference

Draw a geometric shape formed by the intersection of two cylinders intersecting at right angles, highlighting their intersection curve. Start by plotting two cylinders with radius 1, centered on the x-axis and y-axis respectively. Then, sketch four curves connecting the edges of the top and bottom faces of the cylinders, forming a square cross-section. Finally, generate four surfaces corresponding to the four quadrants of the square cross-section, fully presenting the solid structure created by the intersection of the two cylinders.
The prompt above was compiled from the original drawing commands and is for reference only.