• Archimedes Principle
• Archimedes Biography
• List Of Archimedes Inventions
• Archimedes Quotes

Archimedes was born around 287 BCE in the town of Syracuse in Sicily and he lived there until his death around 212 BCE. Archimedes is famous for his contribution to the world of mathematics, specifically geometry, and is regarded as one of the greatest mathematicians who ever lived. He was the first person to create the equations for determining the area as well as volume of spheres, found the measurement formula of circles along with cones, discovered the actual value of PI and led the way to integral calculus. Archimedes was also a great scientist and inventor, contributing to the world of physics. Because he lived so long ago and many writings both by him and about him have been lost, there is not much information known about Archimedes' actual life. However, there are many legends that persist about Archimedes that have lasted through the ages, like: his significant mathematical advances and his scientific discoveries. This all contributes to some known truths about Archimedes, like these fifteen facts.

15) Invented the Water Screw

ARCHIMEDE produces high-quality automatic and hand-wound watches: Pilot Watches, DeckWatch Marine Watches, vintage watches 1950's, Classic and Retro. Archimedes, (born c. 287 bce, Syracuse, Sicily Italy—died 212/211 bce, Syracuse), the most famous mathematician and inventor in ancient Greece. Archimedes is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder. Explore Smithsonian: How Can Electricity Correct a Telescope in Outer Space? This is a free resource.

One of the important inventions of Archimedes was the water screw, which is still used for irrigation in Egypt and developing countries today. King Hieron II wanted Archimedes to design a magnificent ship for multi use, including: luxury travel, naval warfare and carrying supplies. According to Greek writer Athenaeus of Naucratis, this ship was the largest ship built in antiquity and it was basically an ancient version of a cruise ship that could also partake in battle. The ship could apparently carry 600 people, had garden decorations, a gymnasium and a temple to Aphrodite. The one downside to such a large ship was that it would leak water, which caused all sorts of problems but Archimedes came up with a solution by creating the water screw. This machine had hollow tubes with a spiral that could be turned by a handle at one end and when you placed the lower end of the tube into the hull of the ship and turned the handle, the water was carried up the tube. The same design could raise water out of the ground in order to bring it to fields, making it perfect for irrigation.

14) Made War Machines
Archimedes may be known as a father of mathematics today but in his own lifetime, he was celebrated for his building of war machines. One of the most famous machines was the 'Claw of Archimedes', also known as the ship shaker.It worked through a crane like arm with a large metal grappling hook that would drop onto the attacking ship, according to legend. Then the arm would swing upwards, lifting the ship out of the water and sinking it. He built the crane when his hometown Syracuse was under siege by the Romans and it helped hold them off for three years. He also invented rock throwing catapults and grappling hooks to aid in the defense of Syracuse. There has been some doubt as to whether the 'Claw of Archimedes' actually worked however, an experiment performed for a 2005 TV documentary concluded it could.

Claw of Archimedes

13) Made a Heat Ray

Another famous but debatable war machine built by Archimedes was a heat ray. In the second century CE, writer Lucian said Archimedes destroyed ships with fire. Anthemius of Tralles also discussed these devices, describing them as burning glasses or the Archimedes heat ray. Basically, Archimedes developed a device to use mirrors to reflect the sun to make the passing ships catch fire. There has been debate since the Renaissance about the credibility of the stories of Archimedes' heat ray and the efficiency as well as the reality of it. Some scientists have been able to validate its possibilities, while others have shown that it was not possible. Bronze or copper shields may have been used as the mirrors, applying the principle of parabolic reflector.

In 1973, Greek scientist Ioannis Sakkas tested out the validity of the heat ray at the Skaramages naval base outside Athens. He used seventy mirrors with copper coating that were about 5 feet by 3 feet and the mirrors were pointed at a plywood mockup of a Roman warship that was about 160 feet away. The mockup of the ship had a coating of tar paint, which was commonplace during Archimedes' lifetime and would aid in the combustion. When focused accurately, the ship went up in flames in minutes. Students at MIT in 2005 also tested the accuracy of the heat ray using 127 one foot square mirror tiles. They found that it took ten minutes for flames to occur and only with a cloudless sky and stationary ship. Although it could be feasible, it would be impractical because it would need such precise conditions. The MIT students took their experiment on the show Myth Busters, which concluded the myth was 'busted'. However, they did say that the mirrors could still have been used to blind, dazzle or distract the crew.

12) Created a Miniature Planetarium
Archimedes was not only interested in math and engineering, he also had an interest in astronomy. He supposedly created a miniature planetarium that imitated the motion of the earth, moon, sun and five planets known in his lifetime. According to legend, there were two such planetariums that went back to Rome with General Marcellus after Archimedes' death. Cicero wrote in his dialogue 'De re publica' that Marcellus kept one and donated the other to the Temple of Virtue in Rome. Pappus of Alexandria also wrote about Archimedes' planetariums, saying Archimedes had written a manuscript on the construction of a planetarium. The knowledge of Archimedes' planetarium is entirely based upon writings after his lifetime, so it is not certain he did make it. For a long time scientists did not believe Archimedes could've been able to create such a device due to a lack of knowledge of differential gearing but the discovery of an Antikythera mechanism in 1902 demonstrated that the ancient Greeks had knowledge about these types of devices, so it is entirely possible that Archimedes built one.

Antikythera mechanism discovered in 1902
By unknown, via Wikimedia Commons

Replica of an Antikythera Model
By Mogi, via Wikimedia Commons

11) Invented the Phrase 'Eureka'
One of the most famous stories about Archimedes involves one of his famous principles and his most famous quote. According to legend, king Hieron came to Archimedes when he suspected a crown maker had used some silver in a crown that was supposed to be pure gold. Archimedes was troubled for a while but One day when Archimedes took a bath, he realized that there was a direct correlation to the water overflowing from the tub with his immersed body. He allegedly ran through the streets naked yelling, 'Eureka' after discovering this. This phrase has become commonplace when finally discovering the answer, since Archimedes.

Whether or not he actually discovered this while in the bath, he did create a principle of hydrostatics described in 'On Floating Bodies'. The principle states that a body immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body. With this principle, Archimedes could help the king. He could decide how much gold was actually in the crown by comparing the weights of silver and gold in the water and compare that data with the crown. Using this principle, Archimedes could prove the crown was not pure gold and the crown maker had in fact tried to cheat the King.

The Eureka moment

10) Worked with Pulleys and Levers
Archimedes often worked and studied pulleys along with levers. According to Plutarch, Archimedes designed block and tackle pulley systems so that a sailor would be able to use leverage in order to lift heavy objects. Papus of Alexandria says that Archimedes' work on levers made him say, 'Give me a place to stand on, and I will move the earth'. A famous legend about Archimedes and his work with levers is that he once moved a fully loaded ship by himself, while seated from very far away. Whether he ever actually moved a ship or not, he definitely understood how to use pulleys and levers to aid in lifting heavy objects. He demonstrated this knowledge through his creation of the Claw of Archimedes, which was basically a large crane.

Archimedes and his lever

Pulley

9) Rome Wanted Him Alive
Archimedes was well known for his powers of invention and by the time Rome succeeded in sacking Syracuse, Archimedes was an old man at 75. Legends of his abilities had spread far and Rome wanted him brought back alive because they wanted to use Archimedes' inventive skills to create weapons to aid them in the conquering of the world. There was a special squad of soldiers in charge of capturing him alive but this was the siege that led to his death. Rome never got to benefit directly from Archimedes' expertise at creating weapons of destruction, they could only learn from what was used for so long against them.

The Death of Archimedes

8) Last Words Focused on Circles
Legend has it that Archimedes' last words were 'don't disturb my circles' when a Roman soldier killed him during the Siege of Syracuse in 212 BCE but what actually occurred differs based on what version of the story you hear. The most famous legend of Archimedes' death said he was unaware of the siege and was busy studying. General Marcellus had commanded Archimedes to come to them because Rome wanted him alive and when he did not, Marcellus sent a soldier to his home. Engrossed in his books, Archimedes did not know what was going on when the soldier entered his home. According to Plutarch, he was contemplating a mathematical diagram when the soldier came in. Archimedes did know who the soldier was and became angry when he kicked around the books, this caused the soldier to get mad then he killed Archimedes with his sword.

A similar version says that General Marcellus commanded him to come see him and sent a soldier but Archimedes said no, he had to finish working on the problem. He said 'don’t disturb my circles' when the soldier disturbed his works and those were his last words, apropos for such an influential mathematician as well as important contributor to geometry. Another alternative story of his death was that he was carrying math instruments as he walked to General Marcellus after the siege; the solider accompanying him thought these instruments were valuable and killed him for them.

Archimedes contemplating math

7) Inventor of Calculus
Archimedes was using aspects of calculus more than 1500 years before Isaac Newton and Gottfried Leibniz discovered what it was. For a long time Archimedes' use of integral calculus was lost but when the Archimedes' Palimpsest was discovered in 1906, the Method of Mechanical Theorems was found. This detailed his use of infinitesimals and demonstrates how you can break up a figure into infinite parts. He used a method known as the method of exhaustion and this is how he was able to figure out the value of Pi. Many mathematicians consider Archimedes to be one of the first to use calculus, although Newton and Leibniz' work still plays a more significant role in the actual study as well as use of calculus.

Tangent Line in Calculus
By Tangent-calculus.svg, via Wikimedia Commons

6) Studied in Alexandria
Archimedes lived in Syracuse almost all his life but he went to school in Alexandria, which was the intellectual capital of the world at the time. Archimedes was sent off to school and studied at the school of Euclid, the famous mathematician. Euclid is known as the father of geometry, making him the perfect teacher for Archimedes. Euclid's Elements was the main textbook for geometry and other math from around 300 BCE until the late 19th century. His works have a huge influence on mathematics as we know them and Archimedes learned a great deal from him.

There is some small debate about whose works came first, since not much detail is known about Euclid and when his works were published. A few scholars have tried to say that Archimedes' citation of Euclid's works came from later additions and sources but most scholars agree that Euclid's Elements were published before Archimedes.

Two important contemporaries of Archimedes that Archimedes probably met at school were Conon of Samos and Eratosthenes of Cyrene; they remained friends even after Archimedes went back home to Syracuse. Two of his works, the Methods of Mechanical Theorems and the Cattle Problem, include instructions addressed to Eratosthenes. In some of his writings, he referred to Conon of Samos. The correspondence demonstrates how important Archimedes' education was to him and the beneficial relationship he had with these men.

The Library of Alexandria

Statue of Euclid

Euclid's Elements fragment

Eratosthenes

5) One of the Top 3 Mathematicians

Archimedes is thought to be one of the three most influential and important mathematicians who ever lived; the other two are Isaac Newton as well as Carl Gauss. Sir Isaac Newton may be known by many as the discoverer of gravity but he gave the world of math and science so much more than that. Newton lived from 1642 to 1727 and his discoveries as well as theories were very important to the scientific revolution. His most famous work was the Principia Mathematica, which detailed his laws of motion and universal gravitation. Newton also is contributed to discovering calculus along with Gottfried Leibniz.

Carl Gauss was a German mathematician who lived from 1777 to 1855 and is thought by many to be the most influential mathematician since antiquity. He contributed greatly to a variety of fields, including: algebra, statistics, differential geometry, astronomy and more. Without these three men, living centuries and even millennia apart, the world of mathematics as well as scientific discovery would not be what it is today.

Carl Gauss

4) Was Possibly Royalty
Not much is known about Archimedes' personal life however, many believe he was most likely related to the king and thereby considered to be royalty. Archimedes' possible royal lineage is mostly attributed to Plutarch writing that Archimedes was related to King Hiero II in his 'Parallel Lives' and the fact that many of the legends surrounding Archimedes connect him with the king means there is a strong possibility that he was royalty. Regardless, Archimedes was definitely not a pauper, he had at least some influence with the king and was respected. The king especially appreciated Archimedes' great intellect and ability to invent, like building ships as well as weapons. Archimedes was able to go to school in Alexandria, so he must have had at least some money in his family. All that is really known about his family is that his father was an astronomer named Phidias and historians only know about Archimedes' father because Archimedes wrote the information in the 'Sand Reckoner'. Whether Archimedes was a royal or not in Syracuse, he is definitely royalty in the realm of mathematics and science.

Plutarch

King Hiero II coin

Phidias
By Yair-haklai, via Wikimedia Commons

3) Nine Treatises are Still in Existence
The fact that nine of Archimedes treatises are still in existence today is amazing, considering he lived over two millennia ago. These treatises discuss his discoveries in both mathematics and science. These treatsies are on: the Sphere, the Cylinder, the Measurement of the Circle, the Equilibrium of Planes, the Conoids, the Spheroids, the Spirals, the Quadrature of the Parabola, Arenarius or sand-reckoner, Floating Bodies and the Method of Mechanical Theorems. Within these numerous treatises exist all of his major findings, like: how to measure the volume of a cone, sphere, or circle; how to define Pi; and more.

On the Equilibrium of Planes discusses how a lever works, demonstrating Archimedes' extensive study into the tool. He also used these principles to develop a theory on the center of gravity. Some of these treaties were lost over time and discovered only recently. However, enough of Archimedes' brilliance remained in existence to make him an influential mathematician throughout the centuries. In addition to his own writings and work, many later mathematicians used his findings, keeping him as well as his work alive. It is amazing that so many of the discoveries he made in the mid 200s BCE are still considered valid today.

Archimedes' Quadrature of the Parabola

Spiral Treatise
By Guillaume Jacquenot, via Wikimedia Commons

2) Invented the Odometer
Many people attribute Archimedes with the invention of the odometer, who lived thousands of years before the first car was invented. An odometer technically just measures distance traveled and it can be mechanical, electrical or a combination. With today's technology, it can even include GPS systems. In Archimedes' time, an odometer was a cart with a gear mechanism that dropped a ball into a container as you traveled each mile. Although the first mention of an odometer was Vitruvius's description around 27 or 23 BCE, many still contribute the invention to Archimedes. There is a gap in the history of the odometer between around 200 CE and 15th century Europe even though the odometer is featured in Archimedes writings during antiquity, showing the ancient Romans and Greeks did use it. Most likely, the ancient odometer used technology similar to the Antkythera mechanism. Next time you drive around in your car and look at your odometer, you can think about the ancient Greeks as well as Romans using a similar device to see how far they have traveled from home.

Archimedes' Odometer

1) More Famous for his Inventions in his life than Math
Today Archimedes is famous for his mathematical contributions but in his own life he was more famous for his inventions. Although a few of his contemporaries that were mainly in Alexandria read his work and even quoted him, it took until around 530 CE for an actually compilation to be made by Isidore of Miletes. In the sixth century CE, Eutocius wrote commentaries on Archimedes work and made them available to a wider audience for the first time. Only a few of his actual written work survived through the Middle Ages and these findings remained important to the scientists during the Renaissance. Although there were discoveries of lost works of Archimedes before this, the major discovery of his work was in 1906 in the Archimedes Palimpsest. A Palimpsest is when someone uses old work to write new work by removing the previous text; paper was expensive during the Middle Ages, so many people would take any old piece of writing, get rid of the ink and use it again

A goatskin parchment with prayers written on it from the 13th century was discovered in 1906 and historians discovered that this 174 page book was actually a palimpsest, underneath was a 10th century copy of many unknown treatises by Archimedes. It was a major find, especially as historians only know of three texts of Archimedes' actual treatises in the original Greek. One was lost in 1331, one in 1550 and the third was lost but then found in 1907. The find of the Archimedes Palimpsest gave a greater insight into the numerous contributions by Archimedes in the fields of math and science. Just imagine what other amazing works are in the world, lost or written over, just like Archimedes' work.

Archimedes Principle

A piece of the Archimedes' Treatises on a Palimpsest

Final Words
Archimedes was famous in his own time but much about his actual life was lost to history. One of his friends allegedly wrote a biography but over the centuries it has also been lost. Any information about if he ever married, had a family, what his personality was like or his private life are now lost to time. All that is remembered are legends, stories and his remarkable work in his treatises. His inventions are still used and his mathematical principles are still a vital part of any math class. Additionally, he has influenced many brilliant minds that came after him. Beyond his mathematical legacy, Archimedes also influenced culture and society in another way. Every time someone yells Eureka, they are copying Archimedes or at least the legend about Archimedes. He was famous in his own lifetime, so famous that Rome wanted him alive when they plummeted his hometown. Despite being an old man, who knows what more Archimedes may have discovered over time if it were not for the soldier who killed him.

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Archimedes is one of history's great thinkers. He was astute in philosophy as well as in the arts, active in mathematics and physics, and was recognized as one of the greatest engineers of his time. His legacy lives on in the modern era through historical accountsof his countless inventions and discoveries from 2000 years ago.

Let's take a look at 7 inventions that Archimedes was responsible for.

Archimedes’ screw

One major concern of farmers in pre-industrial society was the need to irrigate their land, a considerable issue in the time before sophisticated pumping systems. Different cultures had different ways of dealing with this. One solution, whose introduction into ancient Greece has been credited to Archimedes, was the water screw or screw pump, which is more commonly known today as the Archimedes Screw.

This screw-shaped device was rotated by a windmill or through manual labor. As the entire unit rotated, water was lifted inside the spiral tube to a higher elevation.

The design of this device was so useful that it has even carried over into other industries, where it has been used to move light materials like grain in and out of farming silos.

Archimedes' principle

Archimedes is credited as the person who discovered the principle of buoyancy, which is also known as Archimedes' Principle. This states that a body completely or partially submerged in a fluid at rest is acted upon by an upward, or buoyant, force, and that the magnitude of this force is equal to the weight of the fluid displaced by the body.

Archimedes Biography

The story goes that Archimedes discovered this principle after being tasked by the king to figure out whether a crown made for him was pure gold, or whether it contained other metals. Archimedes realized that if he took a lump of gold weighing the same as the gold crown, the two objects should displace the same amount of water, regardless of shape.

If the goldsmith who made the crown replaced any of the gold with a cheaper metal, then the crown would displaced more water.

According to the story, Archimedes used this idea to prove that the goldsmith had cheated the king out of a rightful amount of gold in the crown.

Stories differ on how Archimedes was actually able to discover that the crown wasn't pure gold.

The Iron Claw

Archimedes is particularly famous for designing war machines for his home state of Syracuse, during the Punic Wars. One famous device was called the Iron Claw, which is also known as the Claw of Archimedes.

This machine was thought to have been installed on the seaward-facing walls of the city of Syracuse, to protect the city against amphibious assault. The device is only known about only through snippets of historical accounts, but it was believed to have been some type of crane, with a grappling hook on one end, which was able to lift attacking ships partly out of the water, and then either cause the ship to capsize or suddenly drop it. It may also have been dropped onto enemy ships, to cause them to swing around and destroy themselves..

The odometer

Archimedes has also been credited as coming up with the first idea for an odometer, or at least a mechanical method of keeping track of distance traveled.

The Roman engineer Marcus Vitruvius Pollio (80/70 BC-15 BC), wrote an account of this idea, which he credited to Archimedes. The odometer operated on the idea that every time a wheel goes around, it travels its own circumference. The odometer may have used a large wheel of a known circumference, along with a series of gears.

The theory is that a gear on the drive shaft had only one tooth and a gear holding a box of pebbles had additional teeth. Every time the chariot wheel goes completely around, the pebble-gear moves one notch. After the wheel had gone enough revolutions to equal one mile, the pebble-gear would have moved so that a hole leading from the pebble box lined up with a hole underneath the gear and a pebble dropped into a bucket. Counting the pebbles could tell you how many miles had been travelled. Each dropped marble represents one mile traveled.

The pulley system

Archimedes didn't invent the pulley, but he did develop different systems of compound pulleys, improving on the existing technology that was around at his time. He clearly demonstrated that a wheel supported by a rope could be used as a method of transferring energy, providing the operator with a mechanical advantage in the process.

List Of Archimedes Inventions

Archimedes developed an efficient a block and tackle system, allowing sailors to use leverage to lift heavy objects.

The law of the lever

Archimedes is also credited with finding new uses for the lever. The great inventor supposedly once said, 'Give me a place to stand on, and a lever long enough, and I will move the earth.' To which he was challenged to prove it.

Archimedes Quotes

In one story, he was tasked with launching Syracuse's largest ship. Archimedes is said to have accepted the task and utlized a massive lever mechanism along with a series of pulleys to launch the newly-constructed ship.

Although, Archimedes was not the first to conceive of a lever mechanism, he accurately described the underlying physics and explained the ratios of force, load, and how the fulcrum point interacted with a lever's capability.

Geometry of shapes

The Roman historian Plutarch wrote that Archimedes did not hold his own mechanical inventions in high regard. Rather, he was much prouder of his proofs and theorums in the realm of physics and mathematics. The great engineer is credited with proving that the area of a circle is equal to π multiplied by the square of the radius of the circle. He also proved that the area enclosed by a parabola and a straight line is 4/3 times the area of a corresponding inscribed triangle.

As you can probably tell from this brief list though, the inventor had a significant hand in the elucidation of early physics, mathematics, mechanical design, and even art. He was arguably the greatest polymath to ever live and rightfully deserves his place in the history books.