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In June of this year I bought a 60cm ruler from eBay. It arrived promptly – in a HUGE cardboard box measuring 80cm x 40cm x 20cm! I posted a photo on Facebook, and before long the National Media got hold of the story, which was then published in the August 5^{th} editions of both the Daily Mail and the Sun newspapers. The story was even discussed on Channel 5’s “The Wright Stuff”.

Huge online warehouses face a real problem when deciding what size cardboard boxes to use. At time of writing, Amazon use seventeen different sizes. Warehouse dispatch staff place the item they wish to send on a special machine; the machine measures the length, width and height and then decides which of the 17 boxes the item should be sent out in. Presumably my 60cm ruler was just too long to fit in a smaller box, resulting in its being sent out in a huge one large enough to contain several hundred such rulers!

As pointed out in the BBC series “Hugh’s War on Waste”, using a box which is larger than it needs to be wastes energy at every stage in the process:

- making the box in the first place.
- sending it out in a van which could carry many more boxes of a smaller size.
- collection of the box to take it off to be recycled (assuming that it does get recycled).

While this may have been was the smallest box eBay had available that would hold my ruler, there are many objects which are long and thin, such as rolled-up posters, back scratchers, bottle brushes etc so should eBay, Amazon and the likes should introduce a long, thin cardboard tube to carry these items with much less wastage? Perhaps House Of Maths should team up with your school to run a workshop on the problem: what other long thin items can we come up with, and what would be the most sensible new size of cardboard box / tube to send them out in?

To finish off this month’s blog, here are some pictures of mathematical shapes which I made using my 60cm ruler. Find out how to make some of these shapes on this House Of Maths YouTube video: https://www.youtube.com/watch?v=MEzStkWfzHQ

Clockwise from top right: an augmented icosahedron, a compound of a (red) cube and (green) octahedron, a rhombicuboctahedron, and a rhombicosidodecahedron. So there!

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