It’s March 14th, which in the US is written as 3/14 — and since 3.14 are the first three digits of that most famous of mathematical constants, , today is celebrated internationally as pi day.

How many revolutions will the smaller circle make when rolling around the bigger one?

The number is the ratio of the circumference of a circle to its diameter. To celebrate this lovely number, here’s a little puzzle to ponder. Imagine a circle with radius 1 cm rolling completely along the circumference of a circle with radius 4 cm. How many rotations does the smaller circle make?

The circumference of a circle with radius is , so the circumference of a circle with radius would be . Since

it seems the answer must be four revolutions. But that’s not true! The answer is actually 5! Can you figure out why?

We found out about this curious question from Yutaka Nishiyama, a mathematical friend in Japan. You can read about the answer in his article Circles rolling on circles. Happy puzzling!

The video above is one of our favourite talks from the last 12 months: it's by Sydney Padua, graphic artist, animator and creator of the wonderful
Thrilling adventures of Lovelace and Babbage. Padua's talk, part of the Ada Lovelace Symposium in December 2015, explains how she used historical newspaper reports, letters and mathematical text books, as well as her extraordinary skill and imagination, to create the comic series featuring mathematicians Ada Lovelace and Charles Babbage in a parallel universe where they built a giant calculating machine to fight crime and have adventures. The comics originally appeared online but now are also available in a beautiful book which we are currently savouring. Stay tuned for a review soon. As well as writing the thrilling adventures, Padua also built the first virtual analytical engine (essentially the first ever computer, conceived by Charles Baggage with lots if input from Lovelace) in 3D animation software — a beautiful sight to behold, which elicited gasps of admiration from the mathematicians, computer scientists and historians in the audience.

The Symposium featured many fascinating talks: you can read some highlights in Analysing Ada and watch many of them on the Symposium website. Our favourites include Judith Grabiner's talk on the radical changes in the 19th century that produced new ideas of space, revolutionising art, making relativity possible and helping create modernism, and the talk by June Barrow-Green about the fascinating stories you can find in mathematical archives.

One of our other favourite lectures of the last year was by Nina Snaith on her work on the
fascinating connection between the Riemann Hypothesis, an unsolved
problem about the distribution of prime numbers, and chaotic quantum
systems. (You can find out more in
her LMS
popular lecture.) We saw Snaith's talk at It all adds up, the London Mathematical Society's 2015 Women in Maths conference. (You can read more about the conference here.)

It all adds up was co-organised by one of our favourite mathematical friends, Vicky Neale, herself a great mathematical speaker who can enthral audiences of all ages and backgrounds. To see how, watch her introduce 7 things you need to know about prime numbers.

Having spent the summer of 1993 on a student placement in a gravitational wave lab, I am finding it very hard to stay calm about the rumours that we may have finally detected gravitational waves. Whispers from a few months ago have built to excited headlines this week that LIGO may have detected gravitational waves produced by the merger of two black holes.

We've poked and prodded our contacts in the field but they don't want to comment at this stage – although it seems the rumours are solid and the scientists themselves are getting quite excited. We'll just have to be patient and wait for the LIGO team to analyse their data, which, to be fair, they only finished collecting yesterday. Stay tuned for an announcement over the coming months. And while you're waiting, you can read, watch and listen to some of our favourite physicists talking about black holes and gravitational waves.

How does gravity work? — We explore Newton's gravity, Einstein's gravity and the ripples in space-time called gravitational waves.

What is general relativity? — Physicist David Tong explains the theory and the equation that expresses it. Watch the video or read the article!

Catching waves with Kip Thorne — What happens when one black hole meets another? Kip Thorne shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.

Tomorrow is Christmas day! We know just how hard it is to pass those last 24 hours before the presents appear under the tree, so we have a little game for you to while away the time. Take turns in moving the hands of the clock, and the first person to reach midnight wins. You can play the game using this interactivity on Wild Maths. There you can also get some help to find a winning strategy, and find further questions to explore.

Happy Christmas!

Wild Maths encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

A huge thank you to Emma Morgan for our favourite idea for Christmas cards – Sierpinski Christmas trees!

Creating these lovely cards is just a matter of simple folding and cutting – there's still time to make some for the big day! You can find out how in Emma's video. And you can find out many more creative things you can do with folding and cutting on Wild Maths.

Wild Maths encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

Think of a number, square it and subtract your starting number. Is there something special about the number you are left with?

Play around with this question for a while and then visit Wild Maths for some help or a further challenge.

Wild Maths encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.