Eureka! A Golden Crown, A Sailing Ship, and a Naked Genius

Written by: By Ellen Yabut Edited by: Carine Medellus

Image by: Helen Liu

Have you ever tried to push a beach ball underwater? That one was tough, right? That's because water also pushes it up at the same time! This invisible upward force from a fluid is called buoyancy – the tendency of an object to float.

How did we discover this phenomenon, you may ask? An ancient tale narrates that this principle was discovered by the Greek mathematician, Archimedes, 2,250 years ago while he was taking a bath, pondering upon the purity of the king’s golden crown. The line between fact and fiction, however, blurs our human knowledge, leaving the reality of this tale an enchanting secret. Regardless of this story’s true nature, a king challenged Archimedes to supervise the engineering of a sailing vessel fifty times larger than a standard ancient warship. From then on, the mathematician reflected on a mind-boggling question: will it sink or will it float? 

Sitting in the comforting embrace of the bathwater, Archimedes realizes that the deeper his body sinks into the water, the higher the water level rises—a concept known as displacement. For example,  a mixed crown of silver and gold would need to be bulkier to achieve the same weight as one made entirely of gold. As a result of its bulkiness, it would displace more water than a true gold crown. When the brilliant scholar found the answer to his puzzling question, he jumped out of the water and ran through the streets naked, yelling, "Eureka! Eureka!", which translates to, "I've found it!"

After delving further, he develops the idea that any object–fully or partially submerged in fluid–is acted upon by this upward push called the buoyant force. Therefore, it enables objects to stay afloat on water, air, or other liquid and gaseous phases of matter. 

Think about the time you used to swim in the pool during a hot, summer day. When you dive headfirst, a certain amount of water from the pool is displaced and splashed over the edge. The weight of this displaced water is equal to the buoyant force acting on you. This is also why you feel lighter in water!

Meanwhile, for a floating object, the forces acting on it are balanced and in a state of equilibrium. This means that the upward buoyant force on a floating body is equivalent in size to its downward weight force. If the buoyant force is less than the object’s weight, the object sinks.

Moreover, buoyancy depends on the fluid’s density and on the object’s volume and density of the object. This is why a tiny pebble sinks when we attempt to create ripples in a pond because its mass is packed into a small volume, making it denser than water. On the other hand, a huge ship, even though it's much heavier, floats. Its shape allows it to displace a large volume of water that pushes back with enough force to keep it afloat! 

This scientific explanation is called the Archimedes’ principle which continues to guide several modern-day scientific processes and industrial engineering, such as those of surface naval ships, cargo ships, and hot air balloons!

Going back to our Archimedes’ Eureka moment, the keel of a ship is actually called korone in Greek, sounding ever so similar to corona, meaning crown. Is this coincidence simply a delightful twist of fate? Perhaps, the universe’s playful bet of heads and tails (or tales!)? One thing’s crystal clear: many of the world’s greatest scientific breakthroughs emerged from a lot of thinking, with a little touch of chance!

Glossary:

Sailing vessel - a massive, cargo-loaded ship that would contain not only a thousand people but also a library, a temple, a gymnasium, and a bath house, as per the king’s request

Density - how much mass is packed into a volume of space 

Volume - a space that matter occupies

References

1. TED-Ed. (2015). The real story behind Archimedes’ Eureka! - Armand D’Angour [YouTube Video]. YouTube. https://www.youtube.com/watch?v=0v86Yk14rf8

2. ‌Black Story. (2023, March 19). How Do Ships Float On Water? | Archimedes Principle Explained. YouTube. https://www.youtube.com/watch?v=68NdPf8f4bE

3. ‌Gregersen, E. (2018). Archimedes’ principle. In Encyclopædia Britannica. https://www.britannica.com/science/Archimedes-principle

4. Biello, D. (2006, December 8). Fact or Fiction?: Archimedes Coined the Term “Eureka!” in the Bath. Scientific American. https://www.scientificamerican.com/article/fact-or-fiction-archimede/