The Importance of Perplexity in Learning

• Learning moments often occur in times of confusion and questioning.
• Historical examples show how these moments can lead to great discoveries.

The Story of Archimedes

• Background:

  • Archimedes was born in 287 BC in Syracuse, Sicily.
  • He was a Greek mathematician, physicist, engineer, inventor, and astronomer.

• The King's Problem:

  • The king of Sicily suspected his goldsmith of cheating him regarding a crown made of gold.
  • The king asked Archimedes to determine if the crown contained silver, but without damaging it.
  • The challenge was to measure the crown's density to compare it with pure gold.

• Discovery in the Bath:

  • While in the bath, Archimedes noticed that the water level rose as he entered the tub.
  • He realized that the amount of water displaced correlates to the volume of the immersed object.
  • This sparked his famous exclamation: "Eureka!" (meaning "I found it!").

Archimedes' Principle

• Density Calculation:

  • Density = Mass / Volume.
  • Pure gold is denser than silver; thus a crown mixed with silver would have a lower density.
  • The crown's volume could be measured by the water it displaced when submerged.

• Testing the Crown:

  • Archimedes submerged the crown in water to measure the volume through displacement.
  • He calculated the density of the crown and found that the goldsmith had indeed cheated by mixing silver.

Legacy

• Archimedes' method of using water displacement to measure volume is now known as Archimedes' Principle.
• This principle remains relevant today, demonstrated every time someone takes a bath.