Grades 6 to 12 Sierpinski Number and Shape Patterns

by TONI on JUNE 10, 2013 · 1 COMMENT

The smallest pyramid (tetrahedron) is made from 6 balloons, each 25 cm long, although it can also be made from two longer balloons twisted together.

The next pyramid is made from 4 of the small pyramids and it has edges of  length 50 centimetres.

Then 4 of these bigger pyramids are used to make the next one and 4 of those to make the next one and so on, and so on. Imagine this going on for ever.

At each stage of the construction 4 pyramids are used to make a bigger pyramid and the lengths of the edges of each pyramid are double the lengths of the edges at the previous stage.

It is also interesting to note that at each stage a "space" is created.

This picture shows a pyramid with edges of length 2 metres made up of 16 of the 50 cm pyramids. The picture of the 1 metre pyramid is not shown.

This is a pyramid with edges of length 4 metres made with 4 of the 2 metre pyramids.

If none of the balloons burst how many 25 cm balloons will be used at each stage? How many of the smallest 25 cm pyramids will be used?

The Guinness World Record breaking Balloon Modelling Sculpture will be a pyramid with edge lengths of 16 metres and it will be over 13 metres high.

If none of the balloons burst, how many 25 cm balloons will be used? How many of the smallest 25 cm pyramids will be used?

There are many other questions about number patterns and geometry that you can investigate based on this structure.  Let us know what you find out.