Ring of Fire
Place the shapes in the ring of fire to reveal their cross section.
|Which shapes contain a circle? Which shapes contain a triangle?|
|Can you use the cube to find a hexagon?|
|Which shape contains the ten-sided decagon?|
The ring of fire takes a slice through 3-dimensional shapes to reveal hidden 2-dimensional shapes. For example, in the cone you will find a circle, an ellipse (a slightly squashed circle), and a parabola (the arc of a ball thrown through the air).
Some shapes contain surprises, for example did you know that the cylinder contains a rectangle, or that a cube contains a hexagon!
If a cube fell into a 2-dimensional world, the people of that world might see a square, or a triangle or a hexagon. In the same way, it might be difficult for you to imagine what a 4-dimensional shape looks like, but different slices will look like different 3-dimensional shapes.
Cross-sections have been studied since the ancient Greek mathematicians. In particular, the Greek mathematicians studied slices of the cones, known as conic sections, in which you can find circles, ellipses and parabolas.
Cross sections was an early way to work out the volume of shape. If two shapes could be compared so that each slice have the same cross-section, then they would have the same volume.
Flatland is a famous Victorian novella that describes a square living in a 2-dimensional world, who is visited by a sphere. The novel is useful in picturing what shapes look like in different dimensions, such as shapes in four dimensions.
A lot of ideas in physics, such as Einstein’s theory of relativity, uses 4-dimensional geometry. It is very difficult to picture 4-dimensional geometry, but it helps if you start by thinking how 3-dimensional shapes look in other dimensions.
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