Archimedes - the inspiration of all the towns in the US named "Eureka" - was not just famous for thinking in the tub. He also did some contract work for the Syracuse Defense Department.
Archimedes became a very popular figure as a result of his involvement in the defense of Syracuse against the Roman siege in the Second Punic War. He is reputed to have held the Romans at bay with war machines of his own design, to have been able to move a full-size ship complete with crew and cargo by pulling a single rope, and to have discovered the principles of density and buoyancy, also known as Archimedes's principle, while taking a bath. The story goes that a new crown in the shape of a laurel wreath had been made for King Hiero, and Archimedes was asked to determine whether it was of solid gold, or whether other metals had been added by a dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down in order to measure its volume. While taking a bath, he noticed that the level of the water rose as he got in. He realised that this effect could be used to determine the volume of the crown, and therefore its density after weighing it. The density of the crown would be lower if cheaper and lighter metals had been added. He then took to the streets naked, being so elated with his discovery that he forgot to dress, crying "Eureka!" ("I have found it!").   He has also been credited with the possible invention of the odometer during the First Punic War. One of his inventions used for military defense of Syracuse against the invading Romans was the claw of Archimedes. [More]
One of his most audacious ideas was a solar "death ray" to set fire to approaching ships. and before you scoff at the notion, see what happened when industrious students at MIT tried to replicate his work.