## Un algorithme de rencontre original

Their writing material consisted of a stylus and a tablet of soft clay which, when completed, was allowed to harden into a permanent document. They used a vertical wedge to represent a unit and a sidewys wedge to represent ten units. With arrangements of these two symbols they could represnt numbers of any size. Numbers between 1 and 59 were the symbols for 1 and 10 tightly grouped together. When these "digits" were to multiply powers of 60, they were separated by more space. If the Sumerians wanted to represent our number 10,, they would put three closely spaced vertical wedges followed by a space and then one vertical wedge followed by a space and finally two sideways wedges and four vertical wedges closely spaced to each other.

This papyrus was copied by an unknown scribe around B. It was brought to Russia during the middle of the 19th century. Of course the equations are not in modern form. The problem that generates the most interest is the calculation of the volume of a truncated pyramid a square based pyramid with the top portion removed.

The Egyptians seemed to know the formula for this even though this is a difficult formula to derive. It evidently was a copy of a copy. It was copied by a scribe, Ahmes around B. This document was possibly copied from another document dating to around B. The Rhind Papyrus is located in the British Museum. This document is one of the primary sources of early Egyptian mathematics. Modern geological research has proved this theory to be correct.

The catastrophe was the eruption, and resulting tsunamis, of the Satorini Volcano also known as Thera in the Aegean Sea. This eruption is considered to be one of the largest in the last 10, years and is the probable cause of the end of the Minoan civilization. Legend has it that this Minoan civilization is the lost civilization of Atlantis! It appears that rather than contradict each other, the tale of Aeneas adds to that of Romulus and Remus. Archaeological evidence shows that early settlement of the Palatine Hill dates back to about B.

This agrees very closely to the established legend that Rome was founded on 21 April B. This date has been traditionally celebrated in Rome with the festival of Parilia.

Thales of Miletus — deductive geometry Thales of Miletus — B. Thales seems to be the first known Greek mathematician and philosopher. He is often referred to as one of the Seven Sages of antiquity. A circle is bisected by any diameter. The base angles of an isosceles triangle are equal.

The angles between two intersecting straight lines are equal. Two triangles are congruent if they have two angles and one side equal. An angle in a semicircle is a right angle. Pythagorean arithmetic and geometry Pythagoras of Samos — B. Pythagoras founded a philosophical and religious school in Croton now Crotone, in southern Italy that had many followers.

Pythagoras had started an earlier school in Samos which he abandoned. Pythagoras was the leader of a Society Brotherhood which included an inner circle of followers known as mathematikoi. The mathematikoi lived permanently with the Society, had no personal possessions and were vegetarians. They were taught by Pythagoras himself and obeyed strict rules set down by Pythagoras.

All knowledge and discoveries were attributed to Pythagoras. The rule that probably had the most impact on the history of mathematics was that all members of the brotherhood should observe strict loyalty to Pythagoras and the brotherhood and maintain secrecy. All of what we know of Pythagoras and his followers come from commentators who lived a hundred years of more later, since it appears that all knowledge and information was passed on orally.

What has become evident is that Pythagoras and his followers were considered to be, among other things, pure mathematicians. Much of the early Greek arithmetic and geometry can be traced back to the Pythagoreans. Persians took Babylon In B. A remarkable aspect of the capture of Babylon is the fact that Cyrus allowed the Jews who were exiled in Babylonia to return home.

This empire lasted for over two centuries until it was divided by the successors of Alexander the Great. Parmenides' spherical earth Parmenides of Elia ca. Parmenides was Greek philosopher who was a follower of Pythagoras. He was an early believer of a cosmology that consisted of a spherical earth and a finite, motionless, spherical universe.

Death of Zeno Zeno of Elea ca. Zeno was an Eleatic philosopher and was a favorite disciple of Parmenides. Philosophers of his time considered his philosophy to be quite negative. Zeno wrote a book that reportedly contained forty paradoxes concerning the continuum. Four of the paradoxes were to have a significant impact on the development of mathematics. An interesting discussion of these can be found at http: Hippocrates of Chios was an excellent geometer who taught in Athens.

He worked on the problems of squaring the circle and duplicating the cube. While working on the problem of squaring the circle, he was able to find the areas of lunes. An interesting account of his quadrature squaring of the lune can be found in Journey Through Genius: The Great Theorems of Mathematics by William Dunham Hippocrates was the first to write an Elements of Geometry and although his work is no longer extant it has been reported by later Greek writers to have contained much of what Euclid included in his first two books of the Elements, which appeared about years later.

Hippocrates of Cos is known to us as the Father of Western Medicine and he is credited with originating the Hippocratic Oath that all doctors take upon completing their studies. The modern oath is quite close to the original. Pericles was born to a family of wealth and position. Among his accomplishments was to bring the ordinary citizen into the Athenian democracy. He was a gifted orator as was documented by the historian Thycidides. Pericles was credited with creating the mighty Athenian empire.

The fear of the power of this empire by Sparta lead to the Peloponnesian War and while Athens was besieged by the enemy outside the walls, a terrible plague raged within. All these troubles caused Pericles to lose his popular support and he was deposed from office; however, a few weeks later the people repented and he was reinstated with greater powers than before. He finally died from the after effects of the plague. His strategy was to bring all citizens from the surrounding area into Athens and let the Spartans have control of the outlying area.

He planned on having Athens supplied with essential food and necessities by the navy. However, he did not count on the overcrowding in the city causing a disastrous plague. His major contribution to mathematics was the quadratrix also called the trisectrix which he reportedly used for trisecting an angle and squaring the circle. The curve may be used for dividing an angle into any number of equal parts.

It appears that this was the first curve in in mathematics that was not either a straight line or part of a circle. This was a war between Athens and the Athenian empire versus Sparta, Thebes, Corinth, and other members of the Peloponnesian Confederacy.

It was the first war in history to be recorded by an eyewitness historian, Thycidides. According to Thycidides the cause of the war was Sparta's fear of the growth of the power of Athens. Death of Socrates Socrates B. Socrates set the standard for all Western philosophy. Like the mathematician Pythagoras, Socrates left no literary legacy of his own. All we know of Socrates comes from others writing about his life and work.

In his early years Socrates showed a great deal of interest in science, but he abandoned science to investigate the development of moral character.

Socrates served, with distinction, as a soldier in the Peloponnesian War and after the war he worked as a stonemason. After his father's death Socrates used the money he inherited to devoting all his time to inventing the practice of philosophical dialog.

In doing so he became a controversial political figure and he was charged with corrupting the youth of the city and interfering with the religion of the city.

For this he was sentenced to death. Socrates drank hemlock and died in the company of his friends and disciples. Eudoxus' method of exhaustion Eudoxus of Cnidos ? BCE Eudoxus was the first to employ the method of exhaustion in geometric proofs, a method that later geometers would return to again and again.

The basic idea is structured like an indirect proof. For example, to show that region A has the same area as region B one could proceed as follows: Birth of Eudemus Eudemus of Rhodes B.

A course in the history of mathematics cannot overlook Eudemus of Rhodes for he seems to have been the first major historian of mathematics.

Eudemus was not considered to be a producer of original mathematics; however, he did write an original mathematical work called On the Angle. This work is lost so we are unable to judge its importance but most historians consider it to be less important than his contributions to the recording of the history of mathematics.

There were three works on the history of mathematics by Eudemus; namely, History of Arithmetic , History of Geometry , and History of Astronomy. The History of Geometry is considered the most important of the three mathematical histories of Eudemus.

Even though the work is not extant, it was available to many later writers who cited it heavily. Alexandria founded The city of Alexandria was the dream of Alexander the Great.

He wanted to create a cosmopolitan city that would be a center of commerce, culture and knowledge. Alexander died before he could see the end result. However, under the rule of the Ptolemys, Alexandria flourished and became the city of Alexander's dreams. The Museum and Library drew scholars from all over the known world.

Almost every major mathematician of the period spent time in Alexandria. Those who didn't spend time there likely corresponded with the scholars who were there.

Death of Alexander Alexander the Great - B. Alexander's parents wanted the best for their son, so they employed some of the finest scholars around to educate him. When Alexander was thirteen, he was tutored by the great Greek philosopher, Aristotle.

From him he learned the ways of the Greeks which influenced his life from that point on. Alexander had great character and values and these were two of the things that made Alexander the Great a prominent individual in history. Another being that he was a great military leader that allowed him to conquer a very vast amount of territory in a relatively short amount of time.

Alexander died of mysterious causes and with no successor named on his death bed, his empire went out to generals and officers who would then become governors of sections of his empire.

It was not long after that that Alexander the Great's fractured empire crumbled. It was one of Alexander's desires that a great cosmopolitan city be built, and thus Alexandria came into existence. He was responsible for much of the greatness of Alexandria, even though much of the work was completed by his son, Ptolemy II.

It was Ptolemy I who began the construction of the Pharos Lighthouse in Alexandria, which was completed after his death. He also was responsible for the erection of the great Mouseion, Alexandria's famous ancient university. It was also Ptolemy I who created the famous Library of Alexandria, and filled it with the books that would attract great scholars to Egypt. In addition, it was Ptolemy I who was responsible for having the Hebrew Bible translated into the Greek language.

Ptolemy I not only supported and encouraged the intellectual infrastructure of Alexandria, he was also a scholar himself, for he wrote a history of Alexander the Great. Euclid's Elements Euclid of Alexandria ca.

Little is known of Euclid of Alexandria's life except that he taught at Alexandria. He is probably the most famous mathematician of antiquity because of his being the author of the 13 books of The Elements.

To this day there are still mathematicians who quote from The Elements. This must make Euclid by far the leading mathematics teacher of all time.

The Elements are most often thought of in terms of geometry; however, Euclid presented material on most of the known mathematics of his time. It was approximately feet high and it guided sailors for about years. It has been classified as one of the Seven Wonders of the Ancient World. It was destroyed by an earthquake in the 14th century C.

Aristarchus' heliocentric astronomy Aristarchus of Samos ca. Aristarchus was a mathematician and astronomer and is best known as the first to propose a sun-centered heliocentric universe.

Nicolaus Copernicus, in the mid 15th century, revived and acknowledged Aristarchus's heliocentric concept. Aristarchus also gave his calculations for the sizes and distances of the sun and moon. Sieve of Eratosthenes Eratosthenes of Cyrene B. In about B.

Although Eratosthenes was very knowledgeable in many areas, he was not considered to be the top scholar in any one field. One of the areas that Eratosthenes worked in was number theory, in particular the study of prime numbers. With this sieve it is possible to sift the prime numbers out of the set of positive integers with minimal computations. Eratosthenes is credited with having made a surprisingly accurate measurement of the circumference of the Earth.

An interesting point to ponder is that when Columbus decided to sail West to reach India he supposedly thought that the circumference of the Earth was about 17, miles—about 7, miles short of the actual value. Would he have ventured out in his three little boats if he had a more accurate value for the circumference of the Earth? Conics of Apollonius Apollonius of Perga B. He is most remembered for his book Conics about the conic sections, curves that are created by slicing through a double cone with a plane , in which he introduced the terms parabola, ellipse and hyperbola.

The Greek studies of conics are all the more remarkable when one realizes that they did not have the advantages of a coordinate system nor the tools of algebra that we use today. Death of Archimedes Archimedes of Syracuse B. Archimedes is considered to be one of the all-time great mathematicians and inventors. Even though he resided in Syracuse, Sicily, he is considered to be an Alexandrian scholar.

He corresponded with many of the scholars in Alexandria. There are many references to Archimedes in the writings of the time. This was remarkable since his reputation was not gained after the fact, which was most common for that time period.

Much of his reputation came about from his inventions. At the end of his life Syracuse was under siege by the Romans under the leadership of Marcellus. Archimedes had invented many machines which were used as engines of war that frustrated the attacking Romans. Although Archimedes gained great fame from his mechanical inventions, he believed that pure mathematics was the only worthy pursuit. In fact, he believed that a result was not truly established until a geometric proof was supplied.

Archimedes would devise a solution to a problem and then transform it into a geometrical solution. Archimedes was killed by a Roman soldier when the Romans finally succeeded in gaining access to the city of Syracuse after many years of frustration.

Plutarch a Greek historian gave three different accounts of the death of Archimedes. All seem to indicate that he was busy with mathematical pursuits. Great Wall of China begun The Great Wall was originally built as a defensive fortification by the three states: Yan, Zhao and Qin. The Great Wall actually began as independent walls for different states when it was first built. Emperor Qin Shihuang succeeded in his effort to have the walls joined together to fend off the invasions from the Huns in the north after the unification of China.

The wall is approximately miles long and some sections are in ruins and some parts have totally disappeared. However, it is still observable by astronauts in space.

Trigonometry of Hipparchus Hipparchus of Rhodes B. Message du président Rapport d'activité Téléchargez ici le numéro complet. Retrouvez tous les anciens numéros. Retrouvez ici les dernières mises à jour de sécurité du ministère des Affaires étrangères. Rendez-vous aussi dans notre rubrique Sécurité des envoyés. La semaine mondiale de prière pour la Paix en Palestine et Israël aura lieu du 16 au 23 septembre. Elle comprend la Journée internationale de prière pour la paix, le 21 septembre.

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