The end of the year (as well as a Plus birthday) put us in the mood to reflect on mathematical milestones. Celebrate with us behind door number 3...

When you saw us outside building snow-mathematicians and throwing snowballs we weren't just larking about, honestly! We were actually conducting in-depth research into symmetry and trajectories — and here our results, behind door number 2...

Inspired by the Science in School Advent Calendar, here is the 1st door to open.... I wonder what is inside?

What are continued fractions? How can they tell us what is the most irrational number? What are they good for and what unexpected properties do they possess? Where are they in the Universe and just what does chaos have to do with it? You can now watch John Barrow's lecture about the fascinating things you can uncover by writing numbers in this way.

To get you in the festive spirit Science in School is offering you an advent calendar with a difference — no little doors to open, no pictures of snowmen and no chocolate. Instead, each day for 24 days, they will send you an email with an inspiring teaching idea. Perhaps a science game to play at the end of term, maybe a fun experiment, some fascinating science facts, links to particularly good websites, or a beautiful picture to use in lessons.

The Further Mathematics Support Programme (FMSP) and Rolls–Royce plc are pleased to invite entries for the third national poster competition for undergraduate or PGCE mathematics students.

The dramatic curved surfaces of some of the iconic buildings created in the last decade, such as 30 St Mary's Axe (AKA the Gherkin) in London, are only logistically and economically possible thanks to mathematics. Curved panels of glass or other material are expensive to manufacture and to fit. Surprisingly, the curved surface of the Gherkin has been created almost entirely out of flat panels of glass — the only curved piece is the cap on the very top of the building. And simple geometry is all that is required to understand how.

Worried you missed Pi day? Never fear! Thanks to the kind people of Wolfram we now have a bevy of mathematical dates to celebrate — six in November alone! November 23, or 11/23 for people in the US, is Fibonacci day as 1,1,2,3 is the start of the Fibonacci sequence. And even mathematically-minded Twilight fans have had something to celebrate...

A group of school students-turned-researchers has delivered new data that will help scientists stem the spread of infectious diseases. A study designed by the students reveals social contact patterns among primary schools students. This type of information is crucial in mathematical models of how diseases spread, which can be used to test the effects of interventions like vaccination and school closures. The study was based on specially designed questionnaires which were handed out to primary schools and achieved an unprecedented response rate of nearly 90%.

Quantum mechanics is usually associated with weird and counterintuitve phenomena we can't observe in real life. But it turns out that quantum processes can occur in living organisms, too, and with very concrete consequences. Some species of birds use quantum mechanics to navigate. And as Plus found out at a recent conference, studying these little creatures' quantum compass may help us achieve the holy grail of computer science: building a quantum computer.