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7 Mutually Touching Cylinders

7 Mutually Touching Cylinders
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2014-03-21 23:49
Coordinate GeometrySolid GeometryGeometric Construction
In collections 3D Geometry & Cross Sections GeoGebra goes 3D
This example demonstrates 7 mutually touching cylinders. The core mathematical concepts involved include the problem of touching cylinders in solid geometry. Using GeoGebra commands Line and InfiniteCylinder, 7 mutually touching cylinders are constructed. Suitable for high school students and math enthusiasts.

GeoGebra Commands & Parameters

  1. Line((A1, B1, C1), Vector[(D1, E1, F1)]) → G1
  2. Line((A2, B2, C2), Vector[(D2, E2, F2)]) → G2
  3. Line((A3, B3, C3), Vector[(D3, E3, F3)]) → G3
  4. InfiniteCylinder(G1, 1) → H1
  5. InfiniteCylinder(G2, 1) → H2
  6. InfiniteCylinder(G3, 1) → H3
  7. Line((A4, B4, C4), Vector[(D4, E4, F4)]) → G4
  8. InfiniteCylinder(G4, 1) → H4
  9. Line((A5, B5, C5), Vector[(D5, E5, F5)]) → G5
  10. InfiniteCylinder(G5, 1) → H5
  11. Line((A6, B6, C6), Vector[(D6, E6, F6)]) → G6
  12. Line((A7, B7, C7), Vector[(D7, E7, F7)]) → G7
  13. InfiniteCylinder(G6, 1) → H6
  14. InfiniteCylinder(G7, 1) → H7

AI Drawing Prompt Reference

Create a 3D geometric figure consisting of seven mutually touching cylinders, all with equal radius of 1. Define seven spatial lines, each specified by a point and a direction vector, serving as the central axes of the cylinders. Construct seven infinite cylinders along these axes so that every cylinder touches each of the other six exactly. The final arrangement shows seven cylinders closely packed in space, demonstrating the mutual tangency relationship among them.
The prompt above was compiled from the original drawing commands and is for reference only.