Episode 8: Packing Shapes and graphene

This week the topic was the most efficient way to pack shapes in 2D and 3D space. We interviewed Jacek Wychowaniec, who’s a scientist studying applications of materials science to biology. We talked about how he uses many different types of maths in his work, and how he’s been developing substances which can be used to help regrow damaged nerves.

Interesting links:

• Allotropes of carbon on Wikipedia
• Packing Problems on Wikipedia
• Packing 3D shapes at Nrich
• What is graphene? at Gigaom
• Manchester Graphene institute website
• Is graphene a miracle material at BBC News

Puzzle: If you pack circles onto a surface using a square arrangement (each circle is sitting in one section of a square grid and they all touch), what percentage of the surface is covered by squares? How much of the surface is covered if you pack the circles on a grid of hexagons?

Solution:

If circles are arranged in a square grid, they cover 78.5% of the area. If this is changed to a hexagonal arrangement, where each row of circles is offset from the one above and below, this increases to 90.7%. A detailed description of how to calculate this can be found here: http://nrich.maths.org/604&part=solution