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Gallery 2

# Hyperbolic Slot

Pass a straight rod through a curved (part-parabolic) slot in this surprising mathematical-visual illusion.

## How it works

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

## Things to try or ask around the exhibition

• How does the rod pass through the curve?
• Does it still work if we swing the rod backwards?

## Background

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.

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.

## Finding the science in your world

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