## Straight curves

By David Shaw, 31 August 2022

This curvy shape is made from straight lines!

Skewers are straight and pretty tough. But put just the right twist on them, and you can make something surprisingly curvy!

## You will need

- Sponge cloth – ours was about 0.5 centimetres (cm) thick and about 20 cm wide
- 16 bamboo skewers
- Marker
- Mug or other circular object to trace
- Ruler (optional)

## What to do

- Trace 2 circles onto the sponge cloth.
- Leave a gap around each circle and cut them out.
- Draw a vertical line through the centre of one circle, cutting it in half.
- Draw a horizontal line through the circle, dividing it into 4 equal quarters.
- Now divide each quarter in half to make 8 equal pizza slice segments.
- Finally, divide each of these slices in half once again. You will end up with 16 equal segments.
- Starting at the top of the circle, number each point where a straight line meets the circle.
- Repeat steps 3–7 on the other circle.
- Line up the point of a skewer with point 1 on one of the circles.
- Roll the skewer between your fingers to make it spin a bit like a drill and gently poke it through the sponge cloth. Don’t force it! Keep going until most of the skewer has poked through.
- Take your second circle, and do the same thing, gently drilling through the point marked 1.
- Adjust the 2 sponge circles so they are about 3 cm from each end of the skewer.
- Take a new skewer and gently drill it through point 2 on the first circle, then the second circle. The 2 skewers should be parallel.
- Repeat this process for each number around your circles. You will end up with a cylinder shape made of skewers.
- Hold one sponge in each hand and twist them in different directions. What shape do the skewers make?

## What’s happening?

You may be surprised to make a curvy shape out of straight skewers. But such shapes are not as rare as you might think.

A 3D shape that can be made out of straight lines is called a ruled surface. There are many different types of ruled surface, including cylinders and helixes – like the underside of a spiral staircase.

Sydney Tower has a hyperboloid shape

*Image: ©iStock.com/JamersonG*

The shape in this activity is called a hyperboloid. It is a doubly ruled surface, because there are 2 ways of making a hyperboloid out of straight lines. You could twist the lines clockwise, or you could twist them anticlockwise. Sydney Tower, or Centrepoint, is supported by cables that make a hyperboloid shape. These cables run both clockwise and anticlockwise – showing the doubly ruled surface.

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