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Biography of ancient Greek mathematician and inventor Archimedes. Also refer to Euclid, geometry, integral calculus, water pump, pi, area, volume, Syracuse, Carthage, Rome, Romans, Marcellus, Ron Kurtus, School for Champions. Copyright © Restrictions

Archimedes: Early Years and Mathematics

by Ron Kurtus (revised 17 May 2005)

Archimedes (287-212 BC) was a great ancient Greek mathematician and scientist. He was educated in Egypt by followers of the famous mathematician, Euclid. Archimedes later devised ways to calculate areas and volumes, defined pi, and formulated integral calculus. But it was his inventions such as a water pump and discoveries such as hydrostatics, that made him famous in his time. Some of his inventions are still used today. There were several wars during his lifetime, and he was killed when the Romans overran his city.

Questions you may have about his early years include:

• What was Archimedes' education like?
• What did he discover in mathematics?
• What were the influences of war in his life ?

This lesson will answer those questions. There is a mini-quiz near the end of the lesson.

Education

Archimedes was born in Syracuse, Sicily in about 287 BC. Although Sicily is near Italy, at that time Syracuse was a Greek city. His father Phidias had some wealth and considered himself an astronomer.

There was much turmoil in the area during those years. In 275 BC, Hiero—a relative of Phidias—led a military takeover of Syracuse.

Sent to Alexandria

When he was in his teens, Archimedes was sent to Alexandria, Egypt to study mathematics with teachers who had learned from Euclid. Not only was this as a way to gain his education, but his father also felt it was better to send his son away from the warfare being waged around Syracuse.

Invented pump

While in Alexandria, he invented a device now known as Archimedes' screw. It was first used to pump water out of ships and was later used in irrigation. This type of water pump is still used in many parts of the world today.

Archimedes Screw easily pumps water to higher level

Returned to Syracuse

Archimedes had completed his studies and returned home from Alexandria and spent the rest of his life in Syracuse. Unfortunately, there was more warfare.

In 265 BC, Hiero is declared king of Syracuse. Then in 264 BC, First Punic War between Carthage and Rome for control of Sicily began. Syracuse was initially allied with Carthage against Rome. A year later, after the Romans threaten Syracuse, Hiero signed peace treaty with Rome.

In the years that followed, Archimedes developed a close, friendly relationship with Hiero, the king of Syracuse, and his son Gelo. The king would often ask Archimedes to solve some difficult problem for him, and he soon considered Archimedes a "national treasure."

Explained levers and pulleys

In 260 BC, when he was 27 years old, Archimedes explained how lever and pulleys worked. Levers are one of the basic tools and were probably used in prehistoric times, but Archimedes' explanation facilitated their use. He later demonstrated to the king how effective levers and pulleys can be employed to move large objects.

Mathematics

Archimedes had became a master at mathematics, especially geometry. He spent most of his time working on solving new problems. Sometimes he became so involved in his work that he forgot to eat.

Communicated with mathematicians

For years after he left Alexandria, Archimedes would often communicate with mathematician friends who remained in Alexandria. He would send his fellow mathematicians statements of his latest theorems, but he would not send the proofs of those theorems. The reason was that some of the mathematicians would claim the results as their own. Without being able to figure out the proof, they could not claim credit.

Math discoveries

Some of the mathematical problems Archimedes solved concerned areas and volumes of geometric figures. He had to devise a better number system and a new way to determine the formulae for the areas and volumes of spheres, cylinders, parabolas, and other plane and solid figures.

Circles and spheres

Archimedes showed that the surface of a sphere is four times that of a great circle, that the volume of a sphere is two-thirds the volume of a circumscribed cylinder, and that the surface of a sphere is two-thirds the surface of a circumscribed cylinder including its bases.

Pi

In his measurements of circles, Archimedes showed that the exact value of pi (π) was between the numbers 3¹⁰/₇₁ and 3¹/₇. He found this by approximating a circle by a regular polygon having 96 sides. This was the most accurate approximation of pi at that time.

Integration

One of the methods he used to find the areas, volumes and surface areas of many bodies was an early form of integration. This was considered his greatest mathematical invention, leading to the field of Calculus.

To determine the area of sections bounded by geometric figures such as parabolas and ellipses, Archimedes broke the sections into an infinite number of rectangles and added the areas together.

Number system

Unhappy with the unwieldy Greek number system, Archimedes proposed a number system capable of expressing numbers up to 8x10¹⁶ in modern notation. He said that this number was large enough to count the number of grains of sand which could be fitted into the universe.

Center of gravity

He then applied his calculations and methods of geometry to physical objects, discovering fundamental theorems concerning the center of gravity of plane figures and solids.

End of war

In 241 BC, the First Punic War between Carthage and Rome ended. Fortunately, Syracuse had made peace with Rome and was not involved in this 20 year battle. Rome had gained control of all of Sicily outside of a small area surrounding Syracuse. Archimedes was 46 at the time.

The next year, Hiero's son Gelo began co-ruling Syracuse with his father. There was then relative peace for about 20 years.

Summary

Archimedes was born in Syracuse, Sicily, but he was educated in Egypt by followers of the famous mathematician, Euclid. Upon his return to Syracuse, he became a favorite of the king, to whom he was a distant relative. Archimedes spent his life solving mathematical problems, including devising ways to calculate areas and volumes, defining pi, and formulating integral calculus. War or the threat of war was present for the first half of his life.

Lessons learned

Lessons learned from the life of Archimedes include:

• A good education is important
• Intelligent and wealthy parents can help your education
• Parents with good social connections are useful
• Observation and creativity can lead to greatness
• War and political forces can ruin people's lives

You too can move the world

Resources

The following are resources on this subject.

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Books

Top-rated books on Archimedes

Miscellaneous

Mini-quiz to check your understanding

1. How useful was the Archimedes screw invention?

2. What personality traits did Archimedes seem to have?

3. Why is the number pi valuable?

If you got all three correct, you are on your way to becoming a Champion in understanding the Biographies of famous people. If you had problems, you had better look over the material again.

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Archimedes:
Early Years and Mathematics >
Later Years and Science