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, $\pi$, today is celebrated internationally as pi day.
The number $\pi$ 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 $r$ is $2\pi r$, so the circumference of a circle with radius $4r$ would be $8\pi r$. Since
$8\pi r \div 2\pi r = 4,$
it seems the answer must be four revolutions. But that's not true! The answer is actually 5! Can you figure out why?
![Coin rolling](/content/sites/plus.maths.org/files/articles/2014/Nishiyama/coins1.jpg)
How many revolutions will the smaller circle make when rolling around the bigger one?
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!