# Archimedes

### background

Archimedes was a famous greek mathematician from Syracuse, Sicily. He probably studied in Alexandria egypt for his education. He created many military siege engines and other inventions such as the water screw. He died during the Siege of Syracuse by a roman soldier for speculated reasons.

### law of the lever

Archimedes revised the law of the lever  from it being the ratio of the weight moved to the weight moving it is the inverse ratio of the distances from the centre. To it being according to him magnitudes are in equilibrium at distances reciprocally proportional to their weights.

### the sphere and cylinder

, Archimedes proved that the ratio of the volume of a sphere to the volume of the cylinder that contains it is 2:3. In that same work he also proved that the ratio of the surface area of a sphere to the surface area of the cylinder that contains it, together with its circular ends, is also 2:3.

### Archimedes principle of buoyancy

Archimedes stated that any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. This allowed him to deduce that the volume of an object to be measured by measuring the volume of the liquid it displaces after submerging volume of an object. This was how he tried to find if a golden crown was fake by measuring the difference of water displacement of pure golden crowns and the actual crown. saying it would be different if there was any other metals in the crown.

### archimedes claw

Archimedes supposedly invented some thing very similar to a crane but instead was used during the siege of Syracuse as a naval defense. A metal hook would be lowered down from an extending beam that would lower and latch on to the boat below. Then it would be pulled back up and hopefully tip the boat over.