Archimedes of Syracuse

Archimedes of Syracuse



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Archimedes of Syracuse - History

Archimedes is known as one of the three greatest mathematicians of all time, along with Newton and Gauss. He was known by many as "the wise one." Others referred to him as "the master." However, he was most well known as "the great geometer."

Archimedes probably got his interest of mathematics from his father, Phidias, who was an astronomer. He was so interested in solving problems, that it more or less became his hobby. It was said that he was consumed with solving problems, that he often times forgot to eat. His real hunger was to learn as much as he could about mathematics. This led him to be a student in Euclid's school, to further his mathematical knowledge.

His fascination with solving problems, anywhere or anytime, made for some interesting stories. It was said that he would draw in dust, dirt, or whatever was available. He was also known for his drawing of geometric problems on his stomach with olive oil.

Archimedes' fame came from his relationship with Hiero, the king of Syracuse. He spent most of his time trying to solve problems for the king. His most well known solution was in regards to the golden crown. King Hiero was worried that the metalist who was making him a golden crown was replacing some of the gold with another metal. King Hiero called upon Archimedes to find a way to see if the crown was made of pure gold or a combination of metals. Archimedes came upon the solution on how to prove this as he was taking a bath. Upon entering a full tub of water, he noticed that the weight of his body displaced a certain amount of water. Knowing that this same principle could be used on the crown, he forgot himself with excitement. He jumped out of the tub and ran naked through the town, yelling "Eureka, Eureka."

Archimedes once made the statement, "Give me a long enough lever and a place to stand, and I will move the earth." After this statement, King Hiero asked him to prove it. This challenge was in regards to a huge ship in the harbor that couldn't be launched by all the men of Syracuse. Archimedes launched the ship with the help of a large lever, proving his statement.

Some of his other inventions were the watering screw, and the miniature planetarium. However, his theoretical work was his main calling. The work with levers and pulleys helped make things easier. The discovery of the displacement of water in the bath tub led into hydrostatics. He also did work in integral calculus and work on pi.

King Hiero came to Archimedes to get help in developing weapons to fight the Roman general Marcellus, who attacked Syracuse by both land and sea. To stop the attacking soldiers. Archimedes invented the catapult. This hurled 500 pound boulders at the advancing soldiers. To stop the invasion by sea, he invented large claws that picked up Marcellus' ships, lifted them out of the water, and smashed them against the rocks. The ships that weren't close enough to capture with claws were destroyed by another invention. Mirrors were used to magnify the sun's rays to catch the enemy ships' sails on fire, destroying much of their fleet.

All of these inventions scared the Romans and made it difficult to capture Syracuse.

  1. Archimedes was unaware of the taking of the city, as he was intent on working on a problem by drawing figures in the dust. As the soldier came to capture him, he stepped in the dust where Archimedes had been working. Archimedes said, "Don't disturb my circles." This made the soldier so mad that he drew his sword and slew him.
  2. A soldier found Archimedes and told him to follow him to Marcellus. Archimedes declined to follow him until he finished his problem This enraged the soldier, so he drew his sword and killed him.
  3. While Archimedes was working, a soldier came to take him away to Marcellus. He started dragging him away from his work. Archimedes proceeded to tell the Roman "Stand away from my diagram." As the soldier pulled him away, Archimedes turned and noticed that he was a Roman. He cried, Someone give me one of my engines." This scared the Roman so much that he drew his sword and killed him.
  4. When the soldier came to kill Archimedes, he asked the soldier to wait and allow him to finish the problem he was working on. The soldier, unmoved by the request, was angered to draw his sword and kill Archimedes.
  5. Archimedes was carrying mathematical instruments, dials, spheres, and angles to Marcellus. A soldier saw him and thought he was carrying gold in a vessel. He killed him for the gold.

One thing that all the stories tell is that Archimedes was killed at the hands of one of Marcellus's soldiers. When buried, Archimedes had a tombstone with the figure of a sphere inscribed in a cylinder. They had the 2:3 ratio of volume between them, which he was famous for.


Archimedes of Syracuse - History

Archimedes was, without a doubt, one of the world&rsquos most distinguished scientists and the greatest scientist of the classical age. He was an eminent physicist, mathematician, engineer, inventor, astronomer and scholar. He belonged to his time, as well as, ahead of his time.

Archimedes was born at Syracuse, in Sicily, the seaport city, in c. 287 BC. At that time, Syracuse was a colony in Magna Graecia, which was self-governed. Not much is known about his father, except that he was an astronomer and went by the name of Phidias. In Plutarch&rsquos Parallel Lines, Plutarch makes a reference to Archimedes being related to the ruler of Syracuse, King Hiero II. He says that Archimedes achieved so much fame because of this close relation, with the King and his son, Gelon. Archimedes used to help Hiero solve complex problems and would utterly amaze everyone, with his prowess.

He spent all his life in Syracuse, except for a brief period during his youth when he went to study in Alexandria, Egypt at the school established by the famous Greek mathematician, Euclid.

Archimedes has several mathematical discoveries and other inventions to his name. He pre-empted modern calculus and analysis through the application of concepts, such as the method of exhaustion and infinitesimals. Through these concepts, he also worked towards deriving, as well as, proving a range of geometrical theorems, such as the surface area and volume of a sphere, area of a circle and the area under a parabola. Also, he is credited with the accurate approximation of pi, the creation of a system using exponentiation for expressing large numbers and investigation of the spiral, which bears his name. He is also known for designing cutting-edge machines including compound pulleys, defensive war machines, to help Hiero protect Syracuse from invasion and screw pump.

Even though Archimedes is regarded as one of the highly distinguished scientists in classical antiquity, not much is known about his writings on the same. The mathematicians from Alexandria read and quoted Archimedes and it was not until c. 530 BC that the first detailed compilation was made by Isidore of Miletus in Byzantine Constantinople. The commentaries on Archimedes&rsquo work was compiled and written by Eutocius in the 6th century AD.

Archimedes&rsquo works and inventions have been an influential and inspirational source for scientists during the period of Renaissance.

Archimedes died during the 2nd Punic War in c. 212 BC when the Roman forces captured Syracuse, following a 2-year siege. He was killed by a Roman soldier, Furious, despite orders from General Marcus Claudius Marcellus not to harm Archimedes. The soldier had ordered for the presence of Archimedes, but his command was not obeyed by the scientist as was he was busy contemplating a mathematical diagram. There is another lesser-known account of his death given by Plutarch, according to which, Archimedes died while trying to surrender to the Roman soldier. The soldier killed him thinking that the mathematical instruments he was carrying was something of great value.

&lsquoDo not disturb my circles&rsquo are the last words credited to the great scientist. This was a reference to the mathematical circles that he was drawing, when disturbed by the Roman soldiers. Much like his last words, his tomb depicts his famous diagram of a sphere in a cylinder of the exact same diameter and height. He has proved that the surface area and volume of a sphere are 2/3rds of a cylinder, which included its base.

137 years after Archimedes&rsquo death Cicero, the Roman orator found his tomb in a dilapidated condition near the Agrigentine date in Syracuse. Cicero was serving as questor in Sicily, at that time, and had heard about all the works and discoveries of Archimedes, but the locals had failed to provide him, with the exact location of the tomb. Upon discovery of the tomb, he cleaned it and saw that his tomb consisted of carved verses.

In the early 1960s, there was another tomb discovered in Syracuse&rsquos Hotel Panorama, which was claimed to be of Archimedes&rsquo. Although, there is no evidence to prove that the tomb was of Archimedes&rsquo and its location today is unknown.

Archimedes&rsquo Discoveries and Inventions

A number of discoveries and inventions are attributed to Archimedes&rsquo name. Some of his breakthroughs are stated below:

Archimedes&rsquo Principle & the Riddle of King Hiero II&rsquos Crown

Archimedes&rsquo most famous work is the invention of how to measure the volume of an irregularly shaped object. There is a history behind this invention. The King of Syracuse, King Hiero II, had summoned Archimedes to ascertain, whether his votive crown was made of pure gold or the goldsmith had cheated him by substituting some silver in it. The catch here was that Archimedes had to solve the problem, without causing any harm or damage to the crown. This meant that he could not melt the crown to calculate its density. One day, while taking a bath, he noticed that the water level in the bathtub rose and overflowed as he immersed himself in it. That is the moment, when he realized that he can use this same effect to measure the density of the crown. He was so excited that he immediately got out of the bathtub and ran into the streets of Greece naked, yelling &lsquoEureka! Eureka!&rsquo, meaning &lsquoI have found it&rsquo. Archimedes found the solution to the King&rsquos problems and knew that he had to find the density of the crown and match it, with the density of pure gold as Density = Mass/Volume. He conducted the test successfully and it was found that the goldsmith had indeed cheated the King by mixing silver in the crown.

This discovery is famously known as Archimedes&rsquo Principle or the Law of Buoyancy and is described in detail in his treatise, On Floating Bodies. According to the principle, when a body is immersed in a fluid, it experiences a buoyant force, which is equal to the fluid it displaces. The International Bath Day, which is celebrated on the 14th of June, originally stems from this very bathtub discovery of Archimedes. He realized that the volume of an object can be accurately determined by submerging it in water and since then bath day traditionally promotes the value of bath time discoveries.

On this day, observed by children and adults alike, it is recommended to make bath time interesting by learning about sinking, floating, volume and similar basic concepts of physics.

Achievements in Engineering - Archimedes&rsquo Screw

Archimedes&rsquo inventions and work in engineering mainly sprung from satiating the needs of Syracuse. Athenaceus of Naucratis, the Greek writer, describes an incident of how Archimedes was commissioned to design a ship by King Hiero II, called the Syracusia. The ship was meant to serve three purposes, simultaneously - for carrying supplies, as a means of luxury travel and as a naval warship. The Syracusia, with a carrying capacity of 600 people, along with a gymnasium, garden decorations and a temple for the goddess Aphrodite, became the largest ship to be built in classical antiquity.

As a ship of such a huge size will leak a lot of water through the hull, Archimedes&rsquos screw was developed to expel the bilge water. This device by Archimedes featured a cylinder, with a revolving screw-shaped blade on the inside. The machine had to be turned by the hand and could also be utilized for transferring water into irrigation canals from low-lying water bodies.

Vitruvius had described Archimedes&rsquo screw in the Roman times as an enhanced version of the screw pump used to water the Hanging Gardens of Babylon. Interestingly, the Archimedes&rsquo screw is still used today for pumping granulated solids, as well as, liquids like grain and coal. In 1839, the SS Archimedes, a sea-going steamship, with a screw propeller, was launched and named in the honor of Archimedes and his excellent discovery of the screw.

The Claw of Archimedes & the Defense of Syracuse

In order to protect the city of Syracuse from attack, Archimedes&rsquo claw was invented. The claw of Archimedes was widely known as the ship-shaker and was designed like, the arm of a crane. The claw balanced a large suspended metal hook. When the weapon would be dropped onto attacking ships, its arm would swing upwards and lift the ship out of water and may even sink it.

A number of modern experiments have been conducted to find out the feasibility of Archimedes&rsquo claw. In 2015, Superweapons of the Ancient World, a televised documentary, constructed a version of the weapon and arrived to the conclusion that the device actually works.

Lucian, the 2nd century AD author, wrote that Archimedes had destroyed ships attacking Syracuse, with fire. It is said that he may have used a number of mirrors to burn the enemy ships, which collectively acted as parabolic reflector. A few hundred years later, burning-glasses was mentioned as Archimedes&rsquo weapon by Anthemius of Tralles.

Archimedes&rsquo heat ray was a device that focused sunlight on the approaching enemy ships, resulting in them catching fire. Heliostat or solar furnace is a similar device as that of the heat ray that have been constructed in the recent times.

Since the Renaissance, Archimedes&rsquo weapon has been a major subject for debate. Doubts and questions have been raised regarding its credibility. While contemporary researches have made an attempt to recreate the device by using only the means that would have been available to Archimedes, Rene Descartes has outrightly rejected it as false. It has been propounded that an assortment of highly glossy copper or bronze shields as mirrors may have been utilized to pivot the sunlight onto a ship.

In 1973, Ioannis Sakkas, a Greek scientist, carried out a series of tests on the heat ray by Archimedes at Skaramagas, a naval base situated outside Athens. 70 mirrors measuring 5 by 3 feet were used for the experiment and each of them was covered, with a copper coating. All the mirrors were pointed towards a replica of a Roman warship made of plywood, which was at a distance of 50m (160 feet). With the accurate focus of the mirrors, the ship caught fire, within a few seconds. The combustion may have been hastened due to the presence of tar paint coating on the mock-up ship. Ships, with a coating of tar, were common, during the classical era.

Another experiment for checking the credibility of the heat ray was carried out by the students of the Massachusetts Institute of Technology in October 2005. The experiment was carried out using a 30cm (127 one-foot) square mirror tiles. The tiles were pointed towards a prototype ship situated at a distance of 30m (100 feet). Here, the ship did not burst into flames, but a patch on the ship caught fire. Also, the ship only caught fire after it had been still for about 10 minutes and the sky was clear. This experiment concluded that the device was workable, but only under the above-mentioned conditions. The same experiment was repeated by the students of MIT for MythBusters, a television show. Here, they used a fishing boat made of wood in San Francisco. Yet again, there was some amount of charring and flame, but the ship was not set ablaze. For the wood to burst into flames, it has to reach a certain autoignition temperature, which is approximately 570° F (300° C).

When the result of the experiment in San Francisco was aired by MythBusters in January 2006, it was placed under the failed category. This is because of the combustion requirements of the perfect weather conditions and the length of time. It was further pointed out that the heat ray would have only worked had the Roman fleet attacked during the morning, when the optimal requirements of light and clear sky were fulfilled as Syracuse was situated facing the sea towards the east. Additionally, MythBusters added that under such circumstances, it would have been far easier and convenient to have used bolts or flaming arrows from a catapult to set fire to ships that were at a shorter distance.

The heat ray story was again scrutinized in a notable edition, &lsquoPresident's Challenge&rsquo, by MythBusters in December 2010. There were numerous experiments that were carried out, which included an extensive test being carried out by 500 school-going children holding mirrors focused at a prototype Roman ship situated at a distance of 120m (400 feet). All the experiments failed as the sail did not reach the required temperature of 410 °F (210 °C). Therefore, the heat ray was again claimed to be &lsquobusted&rsquo or failed.

The television show concluded that the plausible effects of the mirrors could have been dazzling, distracting or blinding of the ship&rsquos crew.


Contents

Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia. The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years before his death in 212 BC. [17] In the Sand-Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known. [25] A biography of Archimedes was written by his friend Heracleides, but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children, or if he ever visited Alexandria, Egypt, during his youth. [26] From his surviving written works, it is clear that he maintained collegiate relations with scholars based there, including his friend Conon of Samos and the head librarian Eratosthenes of Cyrene. [a]

The standard versions of the life of Archimedes were written long after his death by Greek and Roman historians. The earliest reference to Archimedes occurs in The Histories by Polybius (c. 200 - 118 BC), written about seventy years after his death. It sheds little light on Archimedes as a person, and focuses on the war machines that he is said to have built in order to defend the city from the Romans. [27] Polybius remarks how, during the Second Punic War, Syracuse switched allegiances from Rome to Carthage, resulting in a military campaign to take the city under the command of Marcus Claudius Marcellus and Appius Claudius Pulcher, which lasted from 213 to 212 BC. He notes that the Romans underestimated Syracuse's defenses, and mentions several machines designed by Archimedes, including improved catapults, crane-like machines that could swung around in an arc, and stone-throwers. Although the Romans ultimately captured the city, they suffered considerable losses due to the inventiveness of Archimedes. [28]

Cicero (106-43 BC) mentions Archimedes in some of his works. While serving as a quaestor in Sicily, Cicero found what was presumed to be Archimedes' tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. Cicero had the tomb cleaned up and was able to see the carving and read some of the verses that had been added as an inscription. The tomb carried a sculpture illustrating Archimedes' favorite mathematical proof, that the volume and surface area of the sphere are two-thirds that of the cylinder including its bases. [29] [30] He also mentions that Marcellus brought to Rome two planetariums built by Archimedes. [31] The Roman historian Livy (59 BC-17 AD) retells Polybius' story regarding the capture of Syracuse and Archimedes' role in it. [27]

Plutarch (45-119 AD) wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse. [32] He also provides at least two accounts on how Archimedes died after the city was taken. According to the most popular account, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet Marcellus, but he declined, saying that he had to finish working on the problem. The soldier was enraged by this and killed Archimedes with his sword. Another story has Archimedes carrying mathematical instruments before being killed because a soldier thought they were valuable items. Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset (he called Archimedes "a geometrical Briareus") and had ordered that he should not be harmed. [33] [34]

The last words attributed to Archimedes are "Do not disturb my circles" (Latin, "Noli turbare circulos meos" Katharevousa Greek, "μὴ μου τοὺς κύκλους τάραττε"), a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. There is no reliable evidence that Archimedes uttered these words and they do not appear in the account given by Plutarch. A similar quote is found in the work of Valerius Maximus (fl. 30 AD), who wrote in Memorable Doings and Sayings ". sed protecto manibus puluere 'noli' inquit, 'obsecro, istum disturbare'" (". but protecting the dust with his hands, said 'I beg of you, do not disturb this ' "). [27]

Archimedes' principle

The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape. According to Vitruvius, a votive crown for a temple had been made for King Hiero II of Syracuse, who had supplied the pure gold to be used Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith. [35] Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density.

In Vitruvius' account, Archimedes noticed while taking a bath that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible, [36] so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" (Greek: "εὕρηκα , heúrēka!, lit. 'I have found [it]!'). [35] The test on the crown was conducted successfully, proving that silver had indeed been mixed in. [37]

The story of the golden crown does not appear anywhere in the known works of Archimedes. The practicality of the method it describes has been called into question due to the extreme accuracy that would be required while measuring the water displacement. [38] Archimedes may have instead sought a solution that applied the principle known in hydrostatics as Archimedes' principle, which he describes in his treatise On Floating Bodies. This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. [39] Using this principle, it would have been possible to compare the density of the crown to that of pure gold by balancing the crown on a scale with a pure gold reference sample of the same weight, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly. [40] Galileo Galilei, who in 1586 invented a hydrostatic balance for weighing metals in air and water inspired by the work of Archimedes, considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself." [41] [42]

Influence

In a 12th-century text titled Mappae clavicula there are instructions on how to perform the weighings in the water in order to calculate the percentage of silver used, and to solve the problem. [43] [44] The Latin poem Carmen de ponderibus et mensuris of the 4th or 5th century describes the use of a hydrostatic balance to solve the problem of the crown, and attributes the method to Archimedes. [43]

Archimedes' screw

A large part of Archimedes' work in engineering probably arose from fulfilling the needs of his home city of Syracuse. The Greek writer Athenaeus of Naucratis described how King Hiero II commissioned Archimedes to design a huge ship, the Syracusia, which could be used for luxury travel, carrying supplies, and as a naval warship. The Syracusia is said to have been the largest ship built in classical antiquity. [45] According to Athenaeus, it was capable of carrying 600 people and included garden decorations, a gymnasium and a temple dedicated to the goddess Aphrodite among its facilities. Since a ship of this size would leak a considerable amount of water through the hull, the Archimedes' screw was purportedly developed in order to remove the bilge water. Archimedes' machine was a device with a revolving screw-shaped blade inside a cylinder. It was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. The Archimedes' screw is still in use today for pumping liquids and granulated solids such as coal and grain. The Archimedes' screw described in Roman times by Vitruvius may have been an improvement on a screw pump that was used to irrigate the Hanging Gardens of Babylon. [46] [47] The world's first seagoing steamship with a screw propeller was the SS Archimedes, which was launched in 1839 and named in honor of Archimedes and his work on the screw. [48]

Claw of Archimedes

The Claw of Archimedes is a weapon that he is said to have designed in order to defend the city of Syracuse. Also known as "the ship shaker", the claw consisted of a crane-like arm from which a large metal grappling hook was suspended. When the claw was dropped onto an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it. There have been modern experiments to test the feasibility of the claw, and in 2005 a television documentary entitled Superweapons of the Ancient World built a version of the claw and concluded that it was a workable device. [49] [50]

Heat ray

Archimedes may have used mirrors acting collectively as a parabolic reflector to burn ships attacking Syracuse. The 2nd century AD author Lucian wrote that during the siege of Syracuse (c. 214–212 BC), Archimedes destroyed enemy ships with fire. Centuries later, Anthemius of Tralles mentions burning-glasses as Archimedes' weapon. [51] The device, sometimes called the "Archimedes heat ray", was used to focus sunlight onto approaching ships, causing them to catch fire. In the modern era, similar devices have been constructed and may be referred to as a heliostat or solar furnace. [52]

This purported weapon has been the subject of ongoing debate about its credibility since the Renaissance. René Descartes rejected it as false, while modern researchers have attempted to recreate the effect using only the means that would have been available to Archimedes. [53] It has been suggested that a large array of highly polished bronze or copper shields acting as mirrors could have been employed to focus sunlight onto a ship.

Modern tests

A test of the Archimedes heat ray was carried out in 1973 by the Greek scientist Ioannis Sakkas. The experiment took place at the Skaramagas naval base outside Athens. On this occasion 70 mirrors were used, each with a copper coating and a size of around 5 by 3 feet (1.52 m × 0.91 m). The mirrors were pointed at a plywood mock-up of a Roman warship at a distance of around 160 feet (49 m). When the mirrors were focused accurately, the ship burst into flames within a few seconds. The plywood ship had a coating of tar paint, which may have aided combustion. [54] A coating of tar would have been commonplace on ships in the classical era. [b]

In October 2005 a group of students from the Massachusetts Institute of Technology carried out an experiment with 127 one-foot (30 cm) square mirror tiles, focused on a mock-up wooden ship at a range of around 100 feet (30 m). Flames broke out on a patch of the ship, but only after the sky had been cloudless and the ship had remained stationary for around ten minutes. It was concluded that the device was a feasible weapon under these conditions. The MIT group repeated the experiment for the television show MythBusters, using a wooden fishing boat in San Francisco as the target. Again some charring occurred, along with a small amount of flame. In order to catch fire, wood needs to reach its autoignition temperature, which is around 300 °C (572 °F). [55] [56]

When MythBusters broadcast the result of the San Francisco experiment in January 2006, the claim was placed in the category of "busted" (i.e. failed) because of the length of time and the ideal weather conditions required for combustion to occur. It was also pointed out that since Syracuse faces the sea towards the east, the Roman fleet would have had to attack during the morning for optimal gathering of light by the mirrors. MythBusters also pointed out that conventional weaponry, such as flaming arrows or bolts from a catapult, would have been a far easier way of setting a ship on fire at short distances. [57]

In December 2010, MythBusters again looked at the heat ray story in a special edition entitled "President's Challenge". Several experiments were carried out, including a large scale test with 500 schoolchildren aiming mirrors at a mock-up of a Roman sailing ship 400 feet (120 m) away. In all of the experiments, the sail failed to reach the 210 °C (410 °F) required to catch fire, and the verdict was again "busted". The show concluded that a more likely effect of the mirrors would have been blinding, dazzling, or distracting the crew of the ship. [58]

Lever

While Archimedes did not invent the lever, he gave an explanation of the principle involved in his work On the Equilibrium of Planes. [59] Earlier descriptions of the lever are found in the Peripatetic school of the followers of Aristotle, and are sometimes attributed to Archytas. [60] [61] According to Pappus of Alexandria, Archimedes' work on levers caused him to remark: "Give me a place to stand on, and I will move the Earth" (Greek: δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω ). [62] Plutarch describes how Archimedes designed block-and-tackle pulley systems, allowing sailors to use the principle of leverage to lift objects that would otherwise have been too heavy to move. [63] Archimedes has also been credited with improving the power and accuracy of the catapult, and with inventing the odometer during the First Punic War. The odometer was described as a cart with a gear mechanism that dropped a ball into a container after each mile traveled. [64]

Astronomical instruments

Archimedes discusses astronomical measurements of the Earth, Sun, and Moon, as well as Aristarchus' heliocentric model of the universe, in the Sand-Reckoner. Despite a lack of trigonometry and a table of chords, Archimedes describes the procedure and instrument used to make observations (a straight rod with pegs or grooves), [65] [66] applies correction factors to these measurements, and finally gives the result in the form of upper and lower bounds to account for observational error. [25] Ptolemy, quoting Hipparchus, also references Archimedes's solstice observations in the Almagest. This would make Archimedes the first known Greek to have recorded multiple solstice dates and times in successive years. [26]

Cicero (106–43 BC) mentions Archimedes briefly in his dialogue, De re publica, which portrays a fictional conversation taking place in 129 BC. After the capture of Syracuse c. 212 BC, General Marcus Claudius Marcellus is said to have taken back to Rome two mechanisms, constructed by Archimedes and used as aids in astronomy, which showed the motion of the Sun, Moon and five planets. Cicero mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus. The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated the other to the Temple of Virtue in Rome. Marcellus' mechanism was demonstrated, according to Cicero, by Gaius Sulpicius Gallus to Lucius Furius Philus, who described it thus: [67] [68]

Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione.

When Gallus moved the globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth, when the Sun was in line.

This is a description of a planetarium or orrery. Pappus of Alexandria stated that Archimedes had written a manuscript (now lost) on the construction of these mechanisms entitled On Sphere-Making. [31] [69] Modern research in this area has been focused on the Antikythera mechanism, another device built c. 100 BC that was probably designed for the same purpose. [70] Constructing mechanisms of this kind would have required a sophisticated knowledge of differential gearing. [71] This was once thought to have been beyond the range of the technology available in ancient times, but the discovery of the Antikythera mechanism in 1902 has confirmed that devices of this kind were known to the ancient Greeks. [72] [73]

While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics. Plutarch wrote that Archimedes "placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life", [33] though some scholars believe this may be a mischaracterization. [74] [75] [76]

Method of exhaustion

Archimedes was able to use indivisibles (an early form of infinitesimals) in a way that is similar to modern integral calculus. [14] Through proof by contradiction (reductio ad absurdum), he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the method of exhaustion, and he employed it to approximate the areas of figures and the value of π.

Archimedean property

He also proved that the area of a circle was equal to π multiplied by the square of the radius of the circle ( π r 2 < extstyle pi r^<2>> ). In On the Sphere and Cylinder, Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude. Today this is known as the Archimedean property of real numbers. [78]


Improved Artillery

As well as these two fantastical weapons, Archimedes was responsible for enhancing and improving the city’s artillery defences. The Romans were famed military engineers but even they were amazed by the number of rocks and arrows fired at them by the defenders.

Roman accounts state that the largest of these siege engines were capable of launching rocks as large as 318kg (700 pounds) in weight. Marcellus also reported another device that made it appear as if the city wall itself was firing out arrows and stones at the attackers. It is believed these were scorpions, a small version of ballistae that could fire through a narrow hole in the wall.


Archimedes’ Syracusia Ship & Noah’s Ark

Athenaeus (c. late 100’s into 200’s AD) was a very learned Greek writer and rhetorician. His Deipnosophistae (Philosophers at Dinner) is a fascinating ancient survival containing the conversations of a group of Greek literate people invited to a banquet. They talk of culinary things and other historical and literary stories about outstanding people and events still living or who had lived centuries before their first century AD Greek banquet.One such topic was a ship called the Syracusia built c. 240 BC and designed by the famed Archimedes for King Hieron of Syracuse (died c. 215 BC). Archimedes (died c. 212 BC) was very famous in his time and, hands down, the greatest “Renaissance” man who ever lived.

CLICK HERE for article on the Archimedes’ Antikythera Mechanism

Athenaeus states he got all the information about this legendary ship from the writings of Moschion aka Machon: “Moschion writes as follows.” Deipnosophistae 5.3. Nothing by Moschion has survived the tramp of history. But it is, nevertheless considered to be an accurate description through Athenaeus of this most amazing ship in the ancient world. Almost.

Archimedes (left) had boasted to King Heiron that he could move anything, could solve any mechanical problems by principles he had discovered.

The King challenged him to build and to launch into the water the biggest and the best ship ever. After all, Archimedes had stated about the principle and power of the lever: “Give me a place to stand, and I shall move the earth.” (Pappus of Alexandria, 290-350 AD, Synagoge, Book VIII).

The great Greek mathematician and inventor was bathing either in his own bath or in the public baths when he discovered the Principle of Buoyancy (weight of displaced water=weight of object in air=weight of object in water).

According to ancient writers, he climbed out of his bath and ran, buck naked, through the streets of Syracuse yelling “EUREKA! EUREKA!!” “I HAVE FOUND IT! I HAVE FOUND IT!”

A statue of Archimedes in a bathtub demonstrates his aha moment about the principle of the buoyant force. Located at Madatech, Israel’s National Museum of Science, Technology and Space in Haifa. Credit: Andrii Zhezhera/Shutterstock

All of the “quotes” parts in this article will be from Athenaeus’ book Deipnosophistae 5.3.

Slaves and other very able men actually built the Syracusia, but it was “superintended by the mathematician Archimedes….timber was brought from Aetna, enough in quantity for the building of sixty quadriremes.” A quadrireme was c.115 feet long and 30 feet wide. The Syracusia was about c. 361 feet long. The largest merchant ships at that time were c. 150 ft long. Notice in the following the description of efforts to get pitch for insulation and to prevent the hull from “biofouling,” to prevent the attachment of water fouling organisms rather than to remove them. They assembled:

“…hemp from Iberia for the cables, hemp and pitch from the river Rhone and all needful from many places…got together shipwrights and all other kinds of artisans…One half, then, of the entire ship he finished in six months…as each part of the ship was completed it was overlaid with tiling made of lead….This part of the ship, then, was ordered to be launched in the sea, that it might receive the finishing touches there. But after considerable discussion in regard to the method of pulling it into the water, Archimedes the mechanician alone was able to launch it with the help of a few persons. For by the construction of a windlass he was able to launch a ship of so great proportions in the water. Archimedes was the first to invent the construction of the windlass. The remaining parts of the ship were completed in another period of six months.” Archimedes’ windlass is still used today (below):

Windlass—“a type of winch used especially on ships to hoist anchors and haul on mooring lines and, especially formerly, to lower buckets into and hoist them up from wells.” Archimedes used his principle to launch the Syracusia from land into the sea.

The Syracusisa was three decks high. ”Couch” was one of the length measures used (3 people on a standard Greco-Roman couch) in ancient times as one sees in the text. Now begins the description of what sounds like a modern first-class cruise ship:

“Now the ship was constructed to hold twenty banks of rowers, with three gangways. the lowest gangway which it contained led to cargo…the second deck was designed for the use of those (men and women passengers) who wished to enter the cabins after this came the third and last, which was for men posted under arms. Belonging to the second gangway were cabins for men ranged on each side of the ship, large enough for four couches (12 people), and numbering thirty. The officers’ cabin could hold fifteen couches (45 people) and contained three apartments of the size of three couches (9 people) that toward the stern was the cooks’ galley. All these rooms had a tessellated floor (mosaics) made of a variety of stones, in the pattern of which was wonderfully wrought the entire story of the Iliad.

Floor mosaic of “The first bath of Achilles” in the House of Theseus (100’s AD) in Paphos, Cyprus

The astonishing floor mosaics with scenes from Homer’s Iliad were in all the rooms reserved for passengers on the second floor deck of the Syracusia. Those mosaics are one of the first mentions in literature of an entire floor mosaic. It took 300 skilled artists one whole year to execute them.

Athenaeus continues: “On the level of the (3rd story) there were a gymnasium and promenades built on a scale proportionate to the size of the ship in these were garden-beds of every sort, luxuriant with plants and watered by lead tiles hidden from sight then there were bowers of white ivy and grape-vines, the roots of which got their nourishment in casks filled with earth, and receiving the same irrigation as the garden-beds.”

In 2009, Ambius was commissioned to create the world’s first “garden at sea” (below) aboard the world’s largest ship, Royal Caribbean’s Oasis of the Seas. But we know from the above text the 2009 Ambius creation of “a Garden on the Sea” was NOT the world’s first ship with a “Garden at Sea.”

“….Built next to these was a shrine to Aphrodite large enough to contain three couches , with a floor (mosaic) made of agate and other stones, the most beautiful kinds found in the island it had walls and ceiling of Cyprus-wood, and doors of ivory and fragrant cedar it was also most lavishly furnished with paintings and statues and drinking-vessels of every shape.

Adjoining the Aphrodite room was a library large enough for five couches (c.15 people), the walls and doors of which were made of boxwood it contained a collection of books, and on the ceiling was a concave dial made in imitation of the sun-dial on Achradina (a section in Syracuse).”

Syracusia’s Library was perhaps akin to this library on the modern cruise ship SeaDream

“….There was also a bathroom, of three-couch size, with three bronze tubs and a wash-stand of variegated Tauromenian marble, having a capacity of fifty gallons. (Our modern tubs hold c. 70 gallons of water.)…There were ten stalls for horses on each side of the ship and next them was the storage-place for the horses’ food, and the belongings of the riders and their slaves….There was also a water-tank at the bow, which was kept covered and had a capacity of twenty thousand gallons it was constructed of planks, caulked with pitch and covered with tarpaulins. By its side was built a fish-tank enclosed with lead and planks this was filled with sea-water, and many live fish were kept in it.….Outside the interior, a row of colossi, nine feet high, ran round the ship these supported the upper weight and the triglyph, all standing at proper intervals apart. And the whole ship was adorned with appropriate paintings.

There were also eight turrets on it (see below), of a size proportional to the weight of the ship….two cranes were made fast, and over them portholes were built, through which stones could be hurled at an enemy sailing underneath. Upon each of the turrets were mounted four sturdy men in full armor and two archers. The whole interior of the turrets was full of Saracen (handbows) and missiles.”Athenaeus: “A wall with battlements and decks athwart the ship was built on supports on this stood a stone-hurler, which could shoot by its own power a stone weighing one hundred and eighty pounds or a javelin eighteen feet long. This engine was constructed by Archimedes. Either one of these missiles could be hurled six hundred feet….There were four anchors of wood, eight of iron….The bilge-water, even when it became very deep, could easily be pumped out by one man with the aid of the screw, an invention of Archimedes.”

The Archimedes Screw (below), as it is called, is a machine for raising water or removing water from the hold of a large ship. Perhaps this previous sentence from Athenaeus’ book is when Archimedes first invented and used that screw?

This almost improbable ship for its time in ancient history could carry c. 1,940 passengers in addition to the 20 horses in addition to 200 soldiers and catapults in addition to the hardly believable amount of cargo it was carrying to Alexandria, Egypt in its hold: “On board were loaded:

  • 90,000 bushels of grain
  • 10,000 jars (amphorae) Sicilian salt-fish
  • 600 tons of wool
  • and other front amounting to 600 tons.”

The Syracusia sailed from Syracuse to Alexandria, Egypt where it was presented as a gift to the Ptolemaic Pharaoh and named the Alexandria.What must the royalty and wealthy who sailed on the Syracusia to Egypt have thought? Imagine they were as stunned by that ship as they were stunned by Egypt’s pyramids and Sphinx who were constructed several thousand years before Archimedes’ ship was even conceived.

Thousands of years previous to the Syracusia another 3-story ship was built—Noah’s Ark:

  • c. 450-500 ft. long
  • c. 75 ft. wide
  • c. 45 ft high
  • Cargo capacity c. 24,000 tons

Watch the Noah’s Ark video at the end of this article and come to your own conclusion as to which was the most amazing ship ever built in Antiquity—Syracusia or the Ark.—Sandra Sweeny Silver


History Of Archimedes

Archimedes was born in Syracuse, and he was educated in Alexandria. He studied under the famous mathematician called Euclid. Archimedes is best known for the term eureka because he screamed eureka when he found the secret behind the relationship between pressure and mass. Eureka in Greek language means I found it.

A famous story suggests that the King Hieron of Syracuse had a deep suspicion that the crown he had ordered for himself from a goldsmith was not made out of pure gold. He then asked Archimedes to find out a way where he can measure the true value of the crown. Archimedes thought about it for a long time, but he did not find any solution. One day when he stepped into the bath he saw the water overflowing as he stepped in. He suddenly got the idea that by measuring the water that falls over when it is immersed in water, one can measure the weight of the object. So, he screamed eureka and started running on the streets of Syracuse naked. This was the most famous incident in Greece during Archimedes time.

Archimedes made several other inventions after he found out how to measure mass of a substance. He discovered how to measure surface and volume, and also how to decide what pi is. He also defined what the lever is, and how it works. In Egypt, he invented the hydraulic screw which brought the water from a lower to a higher level. After the Romans conquered Sicily, he brought several inventions like the catapult, and also a device that used mirrors to focus the sunlight and make fire.

Archimedes was killed in 212 BC during the sack of Syracuse by a Roman soldier. It is believed that he was 75 years old at that time.

Archimedes died in Syracuse in the 212 B.C. He was 75 years old at that time. Archimedes was killed by a Roman soldier during the siege of Syracuse. He is considered as one of the greatest scientists in the world who had discovered some of the greatest things which are still beneficial to mankind. Archimedes is best known for his mathematical contributions, for inventing the famous Archimedes screw, the magnifying glass and also the catapult the concepts of which is still used in modern warfare. More..


Guide of Syracuse, Italy

Syracuse was founded by Greek colonies in 734 B.C. The city grew at a rapid rate, giving life to a series of internal conflicts and creating the ideal atmosphere for tyranny.

In 485 B.C. Hieron, the first tyrant of Syracuse came to power. Through his policy of conquests and victories, the importance of Siracusa grew, making the city strong and famous as a ruling power. In spite of these conquests, however, the Syracusan people rebelled against tyranny and drove out his successor, the tyrant Gerone, and then set up a democracy (466 B.C.).

After fighting and beating the Athens fleet (413 B.C.), Siracusa then had to defend itself against the expansionist ambitions of another city, the powerful Carthage. The city placed itself under the protection of the tyrant Dionysius in order to survive and he then began a plan to fortify the city, which was completed by his successors.

Under the reign of Hieron II (269-215 B.C.) Syracuse enjoyed a period of peace and splendor, that was the last before the city lost its independence and liberty after it was conquered by the Roman Empire. Siracusa fell under Roman rule in 212 B.C., in spite of the strong contribution made to their battles by the war inventions created by the famous Archimedes. This was the beginning of the city&rsquos decline.

When the Roman Empire fell in 476 A.D., the city was at the mercy of other populations: in 493 was sacked by the Goths and then in 535 A.D. it was conquered by Belisarius and annexed to the Byzantine Empire.

In 878 the Arabs took over a large part of Eastern Sicily including Syracuse, and the city stayed in their hands for about 2 centuries.

The Byzantines took over from the Arabs for a brief period (1038) but they were soon replaced by the Normans (1081), who managed to hold onto power for more than a century.

In 1209 the Swabians ruled by Frederick II took over the city. After the Swabians it was the turn of the Spanish who occupied Syracuse in the 14th century and built several fortresses and defense walls around the city.

A tremendous earthquake shook the East of Sicily in 1693, including Syracuse and the other cities in the Val di Noto area. The city was completely rebuilt in the early decades of the eighteenth century and thus became one of the best examples of the Sicilian Baroque style together with the nearby Noto.

Between 1800 and 1900, Syracuse enjoyed a period of economic, urban and cultural expansion, greatly helped by the fact that it was annexed to the Kingdom of Italy (1870).


Archimedes’ Contribution to Mathematics

On his own, Archimedes continued to study geometry and science and the principles of mechanics and made such major contributions to these disciplines as an understanding of specific gravity, hydrostatics, and buoyancy along with ingenious everyday applications of the use of the lever and the pulley.

He created formulations for such mathematical accomplishments as a formula to measure the area of a circle. This was done using a system he created called using infinitesimals. This is quite similar to modern day integral calculus.

Archimedes also created a formula that enabled him to determine the volume of a solid or the volume of an item of irregular shape. Additionally, he was able to discover the precise value of pi and create a formula for determining the volume of a sphere. His formulas are still in use today.


When Was Archimedes Born ?

Archimedes was born in Syracuse in 290 B.C., and he lived up to 212 B.C. He was 75 years old when he died. In fact, he was murdered by a Roman soldier. Syracuse is today&rsquos Sicily and it was taken over by the Romans from the Greeks.

Archimedes was a renowned mathematician and he helped both the Greeks and the Romans with equal fervent.He studied under a very famous mathematician called Euclid. However, Archimedes ended up being more popular than Euclid because of his principles and inventions. Some of his inventions are used even today under the most modern circumstances, and also in technology. His equations are used for arriving at several conclusions that are considered as important calculations. The Archimedes principle forms the basis of several laws of physics.

He was the one who discovered that there was a relationship between surface and volume in a sphere. He invented a way to measure cylindrical object, and he invented the pi. He defined pi by giving it a value. He invented the hydraulic pump, which brought water from a lower level to a higher level, and he invented the Archimedes screw which was mainly used in boats those days. He gave the world the catapult which is used for modern warfare. The principle of the catapult is used in making several advanced weapons. He also invented the fire glass, which is known as the magnifying glass today. The fire glass channeled the rays of the sun in such a way that it could light a fire.

Archimedes is one of the most popular inventors known to people in the modern world. Everyone has studied the Archimedes principle in their school. He invented so many practical things. The Archimedes screw most probably is the greatest invention that is mentioned frequently. The screw is a common item of use even today. More..


Watch the video: Αρχιμήδης ο Συρακούσιος: Ο ευφυής εφευρέτης και σπουδαίος μαθηματικός της αρχαιότητας