 Maths is all around us. It's almost impossible to think of something that's made without the help of mathematics. Buildings, transport, technology, medicine, even clothes and food all rely on numbers, measurements and sums. Even in the middle of a vast ocean you'll find maths at work keeping boats afloat. But how can heavy metal ships stay on the water's surface when a metal bar or even a tiny coin would sink immediately? Over 2,000 years ago in ancient Greece the mathematician Archimedes came up with an explanation so good it eventually became known as the Archimedes Principle. Imagine a bath full to the brim with water. If you drop a ball into it, it floats. Archimedes discovered that any object that rests on water is affected by an upward force opposite to gravity. This force is called buoyancy or upthrust. In addition, the weight of the ball can cause some water to spill over the sides of the bath. The amount of water spilled is called the ball's displacement. So the upthrust affecting the ball is equal to the weight of the water it displaces. So if a boat weighs 1,000 kilograms it will sink until it displaces 1,000 kilograms of water or until its weight and upthrust are balanced. A ship's buoyancy is also about shape and size. It floats because its weight is distributed over a large area that isn't completely solid like a metal bar but is partly hollow so it has space inside that helps it to float as the density of the ship is less than water. We can calculate density by dividing the ship's mass and volume. And as long as the ship's density isn't greater than the water the ship can be huge. Now, really huge! As long as its weight is spread over a big enough area it's just a case of using maths to work out the density of a ship and to predict its buoyancy. Maths also tells us how much cargo a ship can carry safely. Too much and its density will be greater than the water resulting in the ship sinking. There are now supercontainer vessels designed to carry tens of thousands of tons around the world. But no matter how advanced a ship's design or how strong its construction even a small leak can upset the buoyancy filling the ship with water and making it sink causing the need for another way to float. From the smallest boat to the biggest ship on the sea maths helps to keep vessels afloat proving again that maths really is all around us.