Hyperbolic Slot

Spin the straight rod so that it passes through a curved slot. It’s maths, not magic.

Explanation

When you spin the rod around, it traces out a 3-dimensional shape called a hyperboloid. The edges of this hyperboloid form the branches of a hyperbola.

The curved slot you see is cut in the exact shape of one branch of the hyperbola so that the rod passes straight through.

Extras for Experts

Hyperbolas are conic sections. If you take two cones that are standing tip-to-tip and slice straight down through them, the curves on the resulting flat faces will form the branches of a hyperbola.

If you hold two circular bubble frames together and dip them into bubble solution, then slowly pull them apart, you will find that the bubble film between them pinches together in the centre to make a hyperboloid. This reduces the surface area of the shape.

If you look at the area of light made by a lamp with a cylindrical shade, it forms a hyperbola.

Further Reading

• Hyperbola at Wolfram Mathworld
  http://mathworld.wolfram.com/Hyperbola.html
• Hyperboloid at Wolfram Mathworld
  http://mathworld.wolfram.com/Hyperboloid.html

Hyperbolic Slot
Can you make a straight rod pass through a curved slot?

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