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?