# Years 6 – 12 Sierpinski Number and Shape Patterns

*By toni On 11 September, 2019 · 2 Comments*

In March 2014 and February 2015 Bubblz the Mathematical Clown and the Pyraloons built Guinness World Record breaking Balloon Model Sierpinski Pyramids to raise funds for AIMSSEC. The photo shows the triumphant team in a shopping mall in Cambridge, UK and their 6.5 metre high pyramid.

The smallest pyramid is made from 6 balloons, each 25 centimetres long.

The next pyramid, made from 4 small pyramids. In a perfect model it has edges of length 50 centimetres. The balloon model was not a perfect shape. Why?

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

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.

This pyramid has 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 needed at each stage?

If none of the balloons burst, how many of the smallest 25 cm pyramids would be used to make the record breaking pyramid with edges of 8 metres?

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.

Click here to download AIMSSEC Teacher Notes SIERPINSKI NUMBER & SHAPE PATTERNS.

These pyramids are on a glass table so you can see their reflections. Describe what you see. You can also play the Youtube video entitled Sierpinski Dream by Mehrdad Garousi.

Thanks to Mehrdad Garousi for the video and to Gayla Chandler for the image from her webpage

http://www.fractalnature.com/sierpinskitetrahedron.html

### 2 Responses to *Years 6 – 12 Sierpinski Number and Shape Patterns*

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Starting with a 1 metre tetrahedron, how many stages would you need before you reached the moon – from one tip (vertex) touching Earth to the other tip (vertex) touching the moon?

The moon is approximately 385,000,000 metres away.

I have found this software very much interesting.there lots are of activities i could use during my teaching and learning