Solving a Royal Mystery: Archimedes & the Crown

In summary, the conversation discussed a problem given to Archimedes to determine if a crown made of pure gold contained any silver. The conversation explored the idea of using density as a method to distinguish between gold and silver, but questioned the availability of the density of gold. The conversation also mentioned the different properties that differentiate gold and silver, such as atomic weight and specific gravity. It was suggested that Archimedes may have used his own method to solve the problem.
  • #1
dami
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Homework Statement


Once upon a time the famous archimedes was given a problem to determine if a crown supposedly made of pure gold actually contained some silver. If Archimedes was your lab partner, explain how the two of you could quickly determine if the crown were gold or not without damaging or destroying it.


Homework Equations





The Attempt at a Solution


I thought of getting the density (by measuring the mass, volume of the crown) and comparing it to the density of gold. But what if the density of gold has not be defined (found). Also, if i may ask, what do you call the shape of a crown and how do i find the volume.
 
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  • #2
Well there are only a few properties that differ greatly between gold and silver. For example atomic weight/number and therefore its specific gravity, boiling point...

I'm guessing the solution will be of some relevance to Archimedes... So I feel that you're on the right track by measuring the crowns volume...
 
  • #3
I used archimedes and solved it.
 

1. Who was Archimedes and why is he important in this mystery?

Archimedes was a Greek mathematician, engineer, and inventor who lived in the 3rd century BC. He is important in this mystery because he was known for his incredible problem-solving abilities and his contributions to mathematics and science.

2. What is the Royal Mystery and what role does Archimedes play in it?

The Royal Mystery refers to the story of King Hiero II of Syracuse who suspected that a goldsmith had cheated him by replacing some gold in a crown with silver. Archimedes played a crucial role in this mystery by using his knowledge of density and displacement to solve the problem.

3. How did Archimedes use his knowledge of density and displacement to solve the mystery?

Archimedes used the principle of buoyancy, which states that an object will displace its own weight in water, to determine the density of the crown and compare it to the density of pure gold. By doing so, he was able to prove that the goldsmith had indeed cheated the king.

4. What was Archimedes' famous "Eureka" moment?

According to legend, Archimedes had been struggling to find a way to solve the mystery for days. One day, while taking a bath, he noticed that the water level rose as he got into the tub. This inspired him to apply the principle of buoyancy to the problem, and he famously exclaimed "Eureka!" which means "I have found it!" in Greek.

5. How did Archimedes' solution impact the world of science and mathematics?

Archimedes' solution to the Royal Mystery not only helped King Hiero II, but it also had a significant impact on the world of science and mathematics. His discovery of the principle of buoyancy and his contributions to geometry and calculus have had a lasting influence on modern science and continue to be studied and applied today.

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