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Intersection of Two Cylinders by Jose Manuel Arranz

Intersection of Two Cylinders by Jose Manuel Arranz
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2018-02-15 07:54
Coordinate GeometrySolid GeometryTransformation
This example demonstrates the intersection of two cylinders. Key mathematical concepts include solid geometry and coordinate geometry. Using GeoGebra commands such as Surface, Vector, Circle, Mirror, Intersect, CurveCartesian, and Rotate, the intersection of two cylinders can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Surface((r * cos(u)), v, (r * sin(u)), u, 0, (2 * π), v, ((-p) * r), (p * r)) → cily
  2. Surface(v, (r * cos(u)), (r * sin(u)), u, 0, (2 * π), v, ((-p) * r), (p * r)) → cilx
  3. Vector((((-p) * r), 0, 0), ((p * r), 0, 0)) → ux
  4. Circle((((-p) * r), 0, 0) + (t * ux), r, xAxis) → c
  5. Vector((0, ((-p) * r), 0), (0, (p * r), 0)) → uy
  6. Circle((0, ((-p) * r), 0) + (t * uy), r, yAxis) → d
  7. Mirror(c, (0, 0, 0)) → c'
  8. Mirror(d, (0, 0, 0)) → d'
  9. Intersect(d, c') → E, F, ,
  10. Intersect(c, d) → G, H, ,
  11. Intersect(d', c) → I, J, ,
  12. Intersect(d', c') → K, L, ,
  13. CurveCartesian((r * cos(t)), (r * cos(t)), (r * sin(t)), t, (-π), π) → h
  14. Rotate(h, 90°, zAxis) → h'
  15. Surface((r * sqrt(1 - t^(2))), ((r * s) * sqrt(1 - t^(2))), (r * t), s, -1, 1, t, -1, 1) → a
  16. Surface(((-r) * sqrt(1 - t^(2))), ((r * s) * sqrt(1 - t^(2))), (r * t), s, -1, 1, t, -1, 1) → e
  17. Surface(((r * s) * sqrt(1 - t^(2))), (r * sqrt(1 - t^(2))), (r * t), s, -1, 1, t, -1, 1) → f
  18. Surface(((r * s) * sqrt(1 - t^(2))), ((-r) * sqrt(1 - t^(2))), (r * t), s, -1, 1, t, -1, 1) → i

AI Drawing Prompt Reference

Draw two intersecting cylinders, one along the x-axis and the other along the y-axis. First, create two cylinder surfaces, then create unit vectors in the x-axis and y-axis directions. Next, create two circles, one on the x-axis and the other on the y-axis. Use mirroring to get the mirrors of these circles. Then find the intersections of these circles and cylinder surfaces to get four intersection points. Finally, draw two tilted cylinder surfaces through rotation and mirroring to get the final shape.
The prompt above was compiled from the original drawing commands and is for reference only.