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Math War

Mathematics and War

Mathematics and war have been linked directly since Babylonian times around 1800 BC and will continue develop each other in the distant future.

In 1939, the British crystallographer and science historian John Desmond Bernal wrote: "Science and war have always most closely connected, in fact, except a certain part of the nineteenth century can be exempted that the majority of the important technical and scientific advances owe their origin directly to the military or naval requirements. "

This project aims to look at the role of mathematics and mathematicians in history of warfare, which specifically Archimedes and the siege of Syracuse, forts and ballistics.

The siege of Syracuse was fought from 214 BC to 212 BC between the rebel Syracuse city, and a Roman army commanded by Marcus Claudius Marcellus, sent to put down rebellion in the city. Marcellus fell off the walls of Syracuse with sixty quinqueremes (battleships Five men oar banks), while his co-commander, Appius Claudius Pulcher, the interior walls attacked with ground troops.

"The Wicker Romans' screens, missiles and other siege equipment was prepared in advance, and they felt confident that the men at their disposal they could within five days after their preparations to bring to a point that would give them the advantage over the enemy. But here they do not consider the talents of Archimedes or to provide that in some cases the genius of a man much more effective than superiority in numbers. "

The Greek mathematician Archimedes was military adviser to King Hiero for many years and were well prepared for Syracuse each attack. Archimedes had constructed an ingenious defense including advanced catapults, scorpions and Trebuchet, Polybius describes some of these defenses

"Archimedes had constructed artillery which could cover a variety of ranges, so that the attacking ships while still at a distance, he scored numerous hits with his catapults and stone throwers he was able to cause them serious injury and their approach to bother. Then, as the distance decreased and these weapons began to be implemented over the heads of the enemy, he resorted to smaller and smaller machines, and so demoralized the Romans that their advance was brought to a halt. "

Archimedes invented the "Archimedes Claw 'and the "Archimedes 'Death Ray'.

The "Archimedes claw 'is essentially a large crane on the outer walls of the city, equipped with a grappling hook that could lift some attacking ships from the water, and then the ship capsizing or sudden drop. Plutarch describes the devastating effects of the 'claw'

"Other [ships] seized on the bow with iron claws or beaks like those of cranes, drawn in the air by means of counterweights until they upright on their sterns, and then allowed to deposit soil, or else were turned by means of anchor winches located within the city and crashed into the steep cliffs and rocks stuck under of the walls, with great loss of life on the crews. Often, there is the frightening spectacle of a ship seen lifted clean out of the water in the air and turned over as it hung there, until every man had shaken out of the trunk and thrown in the other direction, then down the empty on the walls would be interrupted. "

Lucian wrote that During the siege of Syracuse, Archimedes repelled an attack by Roman forces with a burning glass. Archimedes' built a kind hexagonal mirror, and with an interval proportional the size of the mirror, he set similar small mirrors with four edges, moved by links and by a kind of hinge, glass and made it the center of the sun beams … So after that, when the beams were shown in this, a terrible lighting of fire came on the ships, and he reduced them to ashes. So does his tricks [Archimedes] Marcellus overcome. "

Archimedes wonderful inventions were so effective that "a council of war on the decision to give the attack, as all efforts were stunned, and to limit activities to a blockade by sea and land. "

But in 212 BC, while residents participating in a festival to their goddess Artemis, the Romans managed to have the walls and the attack began.

The city of Syracuse and fell "was delivered to the troops to plunder what they wanted. "

It was during this time that Archimedes was slain while "the implementation of Marcellus mathematical instruments, dials, spheres, and angles, which the size of the sun can be measured to the sight, some soldiers saw him and thought he carried gold in a vessel, slew him, "much to the distress of Marcellus that" happy with extraordinary skill of the man, that he gave his life would be spared, making almost as much glory in saving like Archimedes in Syracuse crushing. "

The fact that the attacking army commander is distraught at the death of the man who masterminded the destruction of his forces shows the incredible impact that this great mathematician and his ingenious inventions had.

Fortifications are military constructions and buildings designed for defense in warfare. The Renaissance period was the golden age of fortification. During these 400 years, fortification attained the stature of art and science. Fortification's most notable achievement was the construction of many impressive castles found throughout the world.

During the 15th century, a revolution in weapons development, in the form of the canon made it necessary for forts and fortresses are made stronger and harder to be violated. The original medieval castle walls were high and built to scale the castle walls to prevent, by means of ladders. But with the new developments in the artillery, the high walls were easy targets and simply crushed under the precision and the strength of the gun. This required a change in the Design of the fortifications. In the early 1500's, a simple square with bastions was the first, most basic design. However, the small slopes and sharp angular features of This model produced cramped interiors and thus limited the troops and guns that could garrison. The bastion square design was soon replaced by polygonal shape of forts. This polygonal walls offered more sides were clear and easy to defend. Also allowed for expansion to reach more interior space — this is done by increasing the number of bastions and length of the enclosing walls. Although most theories were based on a fort bastioned geometric motifs, nature often changes in the original design. Many forts were meeting area with mountains, rivers and swamps and were therefore built as irregular polygons.

By the end of the 16th century, the fortification system relatively well developed and new elements were added to the design bastion. Defenses lies near the castle walls, but behind the enclosing ditch were developed, known as outside work. A ravelin, a detached triangular Outwork equidistant between the bastions, was almost like an island in the moat of the castle wall. It was designed ravelin crossfire to produce on the ground for neighboring bastions. If an attacker Ravelin caught, he would find himself isolated in the middle of the ditch, and in the middle of the vicious flanking fire. The defensive fortification structured in this way facilitates the transport of guns and ammunition from one place to another defensive during the period of siege. The final form of the new defensive structures like a star, and for this reason they were known as star forts.

Gunnery was a topic for practical mathematics in the 16th century. Printed books and new mathematical tools dealt with the measurement of the shot, the elevation of guns and mortars, and the calculation of the range of the fire. The prediction of coverage in relation to the height of a gun was considered the pinnacle of artillery as a mathematical science.

Tartaglia, who experimented with virtually every type of gun exist in Europe, had a large part of the data on guns and so was able to first develop ballistic firing tables and these tables are in the role gun training and the development of an Irish artillery precise as a military tool.

The next major contribution came from ballistics to Galileo, who showed that the acceleration of gravity is the same for all objects and the air resistance is the factor that changed their descent speeds. He could see that parabolic ballistic trajectories be. He theory that the speed of a projectile was related to the drag acting upon the projectile.

Sir Isaac Newton made major contributions to ballistics and the study of the resistance. In the Principia, he led and completed the formulas of mechanics ballistics. He concluded that the retarding force (drag) who works in a projectile by the air is proportional to the density of the air, the cross section of the projectile and around the square of the speed.

In conclusion, given that mathematics and mathematicians an important role in the art of warfare, and the two disciplines direct impact on the development and style of one another. Even math and war continue to cooperate civilization to promote and protect the free world has to offer, given the developments in computer and other types of machines built for military purposes by mathematicians. Indeed, power, influence and wealth of available forces and remains great potential for mathematical progress.