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Intersection of Two Cylinders by Tomáš Vysloužil

Intersection of Two Cylinders by Tomáš Vysloužil
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2015-02-04 03:25
Coordinate GeometrySolid GeometryGeometric Construction
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 two cylinders. Key mathematical concepts include solid geometry, specifically cylinders and spatial geometry. Construction highlights include using the Cylinder command to create cylinders and the IntersectPath command to find the intersection. Suitable for high school or university-level solid geometry education.

GeoGebra Commands & Parameters

  1. Cylinder((0, 0, 0), (-3, 0, 5), r2) → e, f, g, h
  2. Cylinder((5, 0, 0), (-7, 0, 0), r1) → a, c, d, b
  3. Sphere((0, 0, 0), r) → i
  4. Circle(xAxis, ((-sqrt(r^(2) - 3^(2))), 0, (-3))) → k
  5. IntersectPath(j, e) → p
  6. Corner(p) → A, B, C, D
  7. IntersectPath(j, a) → q
  8. Corner(q) → E, F, G, H
  9. Intersect
  10. Intersect(p, q) → I, J, K, L
  11. Line((0, 0, 0), (-3, 0, 5)) → m
  12. Intersect(zAxis, xAxis) → M
  13. Segment(M, L) → l
  14. Intersect(xAxis, yAxis) → N
  15. Sphere(M, vs) → n
  16. Intersect(m, n) → O, P
  17. OrthogonalPlane(P, m) → o
  18. Line(B, L) → s
  19. Intersect(s, o) → Q
  20. Circle(m, Q) → t
  21. Intersect
  22. Intersect(k, t) → R, S, ,
  23. Circle(xAxis, (sqrt(r^(2) - 3^(2)), 0, (-3))) → c_1
  24. Intersect
  25. Intersect
  26. Intersect(t, c_1) → T, U, ,

AI Drawing Prompt Reference

Draw two intersecting cylinders, one centered at the origin and the other at (5,0,0). Use the cylinder command to create the cylinders and then use the intersect path command to find their intersection. Next, draw a sphere centered at the origin and a circle on the x-axis. Use the intersect path command to find the intersection of the circle and the intersection line, and construct the corner points. Finally, draw a line segment between the intersection points, and a vertical plane through the intersection points, find the intersection points on the plane, and construct the final intersection line.
The prompt above was compiled from the original drawing commands and is for reference only.