# Happy Holidays from ThinkTank Maths 2014

17 December 2014

This year in the world of mathematics the proof of the Kepler Conjecture was finally completed and to celebrate this achievement, ThinkTank Maths has created a personalised Christmas card for you.

Imagine you had to pack several spheres as efficiently as possible. You would probably choose to arrange them in the most obvious way by stacking them in a pyramid shape, where each set of four spheres is arranged in a little tetrahedron. This arrangement is known as the face centred cubic packing and is what most greengrocers usually do to stack oranges. But how can you be sure that this is the most efficient possible arrangement?

The Kepler Conjecture claimed that this was indeed the optimal way to pack spheres and was first stated by Johannes Kepler in 1611. However, the mathematical proof turned out to be extraordinarily difficult and it was only this year that Thomas Hales and Samuel Ferguson of the University of Pittsburgh finally confirmed it.

The proof makes use of geometric structures known as Voronoi diagrams - scroll down further for more.

Imagine scattering a few small objects of differing colours on a piece of paper, and then colouring each point on the paper to be the same colour as the closest object. The resulting pattern, once you have taken the objects away, is called a Voronoi diagram.

Voronoi diagrams turn out to be extremely useful in many branches of mathematics and science - not only for packing problems, as mentioned above, but also domains such as fluid dynamics, machine learning and cell biology.

In the image above your name defines the number and location of the points and the geometric structure of the space, from which a Voronoi diagram is generated. Obviously different names will generate different distributions of points and structures, so try also entering the names of your family and friends to see the other kinds of patterns that can be produced!

Click the link on the picture to generate a printable image, which you could print out for some eye-catching festive wrapping paper or even an eclectic piece of modern art for your wall.

(There are more options below the image for generating different formats - including the option to set the size or get a greyscale version.)

Season’s greetings and a happy new year from everyone at ThinkTank Maths!