In Science class, Mr. Dschida's students have been learning about fluid displacement and hydrostatics, the branch of physics that deals with the characteristics of fluids at rest. Their guide through these lessons has been Archimedes of Syracuse, the Ancient Greek mathematician, physicist, engineer, astronomer, and inventor whose work the students have been studying for several weeks.
Archimedes' law of buoyancy states that the buoyant force (or upward pressure) of a body submerged in fluid is equal to the weight of the liquid displaced by the object. It is said that Archimedes figured this out when he was a young man of 22 and already renowned for his scientific work. Archimedes had been requested by his cousin, King Hiero, to determine whether a goldsmith had cheated the king. Hiero had commissioned a golden laurel leaf crown for which he paid the goldsmith handsomely. The king was pleased with the crown but later heard rumors that the smith had replaced some of the precious gold for silver. Furious, the king asked Archimedes to learn the truth without damaging the crown.
Deep in thought about the king's assignment one day, Archimedes went to the baths and noticed that as he lowered himself into the tub water spilled over its sides. The deeper he sank, the more water was displaced. He was so excited about his discovery he ran back home yelling, "Eureka! Eureka!" meaning "I have found it!" in Greek.
Knowing that gold is denser than silver, Archimedes guessed he could measure the amount of water displaced by equal weights of gold and silver and compare it to the amount of water displaced by the crown. He made sure the lumps of gold and silver weighed the same as the crown. He then conducted his experiment and discovered that the crown was not, in fact, made of pure gold but that the goldsmith must have mixed some silver (or lighter metal) into the gold.
Not only did the students learn the origin of the fabled exclamation "Eureka!" in this lesson, they also learned a bit of ancient history, as well as the principles of water displacement and buoyancy, and they applied various mathematical concepts in conducting their own displacement experiment in class. Such is the nature of classical education wherein subjects are interwoven to form a more complete picture of the specific lesson being taught.