A mathematician is someone who uses an extensive knowledge of mathematics in his or her work to solve mathematical problems. Mathematics is concerned with numbers, quantity, space and change. One of the earliest known mathematicians was Thales of Miletus, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number", it was the Pythagoreans who coined the term "mathematics", with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria, she succeeded her father as Librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells.
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences; as these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many scholars working under Muslim rule in medieval times is that they were polymaths. Examples include the work on optics and astronomy of Ibn al-Haytham; the Renaissance brought an increased emphasis on science to Europe.
During this period of transition from a feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli. As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking.” In 1810, Humboldt convinced the King of Prussia to build a university in Berlin based on Friedrich Schleiermacher’s liberal ideas. Thus and laboratories started to evolve. British universities of this period adopted some approaches familiar to the Italian and German universities, but as they enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
The Universities of Oxford and Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt’s idea of a university than German universities, which were subject to state authority. Overall, science became the focus of universities in the 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge; the German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of “freedom of scientific research and study.” Mathematicians cover a breadth of topics within mathematics in their undergraduate education, proceed to specialize in topics of their own choice at the graduate level.
In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics. Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, localized constructs, applied mathematicians work in the study and formulation of mathematical models. Mathematicians and applied mathematicians are considered to be two of the STEM careers; the discipline of applied mathematics concerns
Jews or Jewish people are an ethnoreligious group and a nation, originating from the Israelites and Hebrews of historical Israel and Judah. Jewish ethnicity and religion are interrelated, as Judaism is the traditional faith of the Jewish people, while its observance varies from strict observance to complete nonobservance. Jews originated as an ethnic and religious group in the Middle East during the second millennium BCE, in the part of the Levant known as the Land of Israel; the Merneptah Stele appears to confirm the existence of a people of Israel somewhere in Canaan as far back as the 13th century BCE. The Israelites, as an outgrowth of the Canaanite population, consolidated their hold with the emergence of the kingdoms of Israel and Judah; some consider that these Canaanite sedentary Israelites melded with incoming nomadic groups known as'Hebrews'. Though few sources mention the exilic periods in detail, the experience of diaspora life, from the Ancient Egyptian rule over the Levant, to Assyrian captivity and exile, to Babylonian captivity and exile, to Seleucid Imperial rule, to the Roman occupation and exile, the historical relations between Jews and their homeland thereafter, became a major feature of Jewish history and memory.
Prior to World War II, the worldwide Jewish population reached a peak of 16.7 million, representing around 0.7% of the world population at that time. 6 million Jews were systematically murdered during the Holocaust. Since the population has risen again, as of 2016 was estimated at 14.4 million by the Berman Jewish DataBank, less than 0.2% of the total world population. The modern State of Israel is the only country, it defines itself as a Jewish and democratic state in the Basic Laws, Human Dignity and Liberty in particular, based on the Declaration of Independence. Israel's Law of Return grants the right of citizenship to Jews who have expressed their desire to settle in Israel. Despite their small percentage of the world's population, Jews have influenced and contributed to human progress in many fields, both and in modern times, including philosophy, literature, business, fine arts and architecture, music and cinema, science and technology, as well as religion. Jews have played a significant role in the development of Western Civilization.
The English word "Jew" continues Iewe. These terms derive from Old French giu, earlier juieu, which through elision had dropped the letter "d" from the Medieval Latin Iudaeus, like the New Testament Greek term Ioudaios, meant both "Jew" and "Judean" / "of Judea"; the Greek term was a loan from Aramaic Y'hūdāi, corresponding to Hebrew יְהוּדִי Yehudi the term for a member of the tribe of Judah or the people of the kingdom of Judah. According to the Hebrew Bible, the name of both the tribe and kingdom derive from Judah, the fourth son of Jacob. Genesis 29:35 and 49:8 connect the name "Judah" with the verb yada, meaning "praise", but scholars agree that the name of both the patriarch and the kingdom instead have a geographic origin—possibly referring to the gorges and ravines of the region; the Hebrew word for "Jew" is יְהוּדִי Yehudi, with the plural יְהוּדִים Yehudim. Endonyms in other Jewish languages include the Yiddish ייִד Yid; the etymological equivalent is in use in other languages, e.g. يَهُودِيّ yahūdī, al-yahūd, in Arabic, "Jude" in German, "judeu" in Portuguese, "Juif" /"Juive" in French, "jøde" in Danish and Norwegian, "judío/a" in Spanish, "jood" in Dutch, "żyd" in Polish etc. but derivations of the word "Hebrew" are in use to describe a Jew, e.g. in Italian, in Persian and Russian.
The German word "Jude" is pronounced, the corresponding adjective "jüdisch" is the origin of the word "Yiddish". According to The American Heritage Dictionary of the English Language, fourth edition, It is recognized that the attributive use of the noun Jew, in phrases such as Jew lawyer or Jew ethics, is both vulgar and offensive. In such contexts Jewish is the only acceptable possibility; some people, have become so wary of this construction that they have extended the stigma to any use of Jew as a noun, a practice that carries risks of its own. In a sentence such as There are now several Jews on the council, unobjectionable, the substitution of a circumlocution like Jewish people or persons of Jewish background may in itself cause offense for seeming to imply that Jew has a negative connotation when used as a noun. Judaism shares some of the characteristics of a nation, an ethnicity, a religion, a culture, making the definition of, a Jew vary depending on whether a religious or national approach to identity is used.
In modern secular usage Jews include three groups: people who were born to a Jewish family regardless of whether or not they follow the religion, those who have some Jewish ancestral background or lineage, people without any Jewish ancestral background or lineage who have formally converted to Judaism and therefore are followers of the religion. Historical definitions of Jewish identity have traditionally been based on halakhic definitions of matrilineal descent, halakhic conversions; these definitions of, a Jew date back to the codification of the Oral
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, moons and galaxies – in either observational or theoretical astronomy. Examples of topics or fields astronomers study include planetary science, solar astronomy, the origin or evolution of stars, or the formation of galaxies. Related but distinct subjects like physical cosmology. Astronomers fall under either of two main types: observational and theoretical. Observational astronomers analyze the data. In contrast, theoretical astronomers create and investigate models of things that cannot be observed; because it takes millions to billions of years for a system of stars or a galaxy to complete a life cycle, astronomers must observe snapshots of different systems at unique points in their evolution to determine how they form and die. They use these data to create models or simulations to theorize how different celestial objects work.
Further subcategories under these two main branches of astronomy include planetary astronomy, galactic astronomy, or physical cosmology. Astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using physical laws. Today, that distinction has disappeared and the terms "astronomer" and "astrophysicist" are interchangeable. Professional astronomers are educated individuals who have a Ph. D. in physics or astronomy and are employed by research institutions or universities. They spend the majority of their time working on research, although they quite have other duties such as teaching, building instruments, or aiding in the operation of an observatory; the number of professional astronomers in the United States is quite small. The American Astronomical Society, the major organization of professional astronomers in North America, has 7,000 members; this number includes scientists from other fields such as physics and engineering, whose research interests are related to astronomy.
The International Astronomical Union comprises 10,145 members from 70 different countries who are involved in astronomical research at the Ph. D. beyond. Contrary to the classical image of an old astronomer peering through a telescope through the dark hours of the night, it is far more common to use a charge-coupled device camera to record a long, deep exposure, allowing a more sensitive image to be created because the light is added over time. Before CCDs, photographic plates were a common method of observation. Modern astronomers spend little time at telescopes just a few weeks per year. Analysis of observed phenomena, along with making predictions as to the causes of what they observe, takes the majority of observational astronomers' time. Astronomers who serve as faculty spend much of their time teaching undergraduate and graduate classes. Most universities have outreach programs including public telescope time and sometimes planetariums as a public service to encourage interest in the field.
Those who become astronomers have a broad background in maths and computing in high school. Taking courses that teach how to research and present papers are invaluable. In college/university most astronomers get a Ph. D. in astronomy or physics. While there is a low number of professional astronomers, the field is popular among amateurs. Most cities have amateur astronomy clubs that meet on a regular basis and host star parties; the Astronomical Society of the Pacific is the largest general astronomical society in the world, comprising both professional and amateur astronomers as well as educators from 70 different nations. Like any hobby, most people who think of themselves as amateur astronomers may devote a few hours a month to stargazing and reading the latest developments in research. However, amateurs span the range from so-called "armchair astronomers" to the ambitious, who own science-grade telescopes and instruments with which they are able to make their own discoveries and assist professional astronomers in research.
List of astronomers List of women astronomers List of Muslim astronomers List of French astronomers List of Hungarian astronomers List of Russian astronomers and astrophysicists List of Slovenian astronomers Dallal, Ahmad. "Science and Technology". In Esposito, John; the Oxford History of Islam. Oxford University Press, New York. ISBN 0-300-15911-0. Kennedy, E. S.. "A Survey of Islamic Astronomical Tables. 46. Philadelphia: American Philosophical Society. Toomer, Gerald. "Al-Khwārizmī, Abu Jaʿfar Muḥammad ibn Mūsā". In Gillispie, Charles Coulston. Dictionary of Scientific Biography. 7. New York: Charles Scribner's Sons. ISBN 0-684-16962-2. American Astronomical Society European Astronomical Society International Astronomical Union Astronomical Society of the Pacific Space's astronomy news
Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in Italy. Early-Pythagorean communities lived throughout Magna Graecia. Espousing a rigorous life of the intellect and strict rules on diet and behavior comprised a cult of following Pythagorean's Code. For example, the Code's diet prohibits the consumption or touching any sort of bean or legume. Pythagoras’ death and disputes about his teachings led to the development of two philosophical traditions within Pythagoreanism; the practitioners of akousmatikoi were superseded in the 4th century BC as a significant mendicant school of philosophy by the Cynics. The Pythagorean mathēmatikoi philosophers were in the 4th century BC absorbed into the Platonic school. Following the political instability in the Magna Graecia, some Pythagorean philosophers fled to mainland Greece while others regrouped in Rhegium. By about 400 BC the majority of Pythagorean philosophers had left Italy.
Pythagorean ideas exercised a marked influence on Plato and through him, on all of Western philosophy. Many of the surviving sources on Pythagoras originate with Aristotle and the philosophers of the Peripatetic school; as a philosophic tradition, Pythagoreanism was revived in the 1st century BC, giving rise to Neopythagoreanism. The worship of Pythagoras continued in Italy and as a religious community Pythagoreans appear to have survived as part of, or influenced, the Bacchic cults and Orphism. Pythagoras was in ancient times well known for the mathematical achievement of the Pythagorean theorem. Pythagoras had discovered that "in a right-angled triangle the square of the hypotenuse is equal to the squares of the other two sides". In ancient times Pythagoras was noted for his discovery that music had mathematical foundations. Antique sources that credit Pythagoras as the philosopher who first discovered music intervals credit him as the inventor of the monochord, a straight rod on which a string and a movable bridge could be used to demonstrate the relationship of musical intervals.
Much of the surviving sources on Pythagoras originate with Aristotle and the philosophers of the Peripatetic school, which founded histographical academic traditions such as biography and the history of science. The surviving 5th century BC sources on Pythagoras and early Pythagoreanism are void of supernatural elements. While surviving 4th century BC sources on Pythagoreas' teachings introduced legend and fable. Philosophers who discussed Pythagoreanism, such as Anaximander, Andron of Ephesus and Neanthes had access to historical written sources as well as the oral tradition about Pythagoreanism, which by the 4th century BC was in decline. Neopythagorean philosophers, who authored many of the surviving sources on Pythagoreanism, continued the tradition of legend and fantasy; the earliest surviving ancient source on Pythagoras and his followers is a satire by Xenophanes, on the Pythagorean beliefs on the transmigration of souls. Xenophanes wrote of Pythagoras that: Once they say that he was passing by when a puppy was being whipped, And he took pity and said: "Stop!
Do not beat it! For it is the soul of a friend That I recognized when I heard it giving tongue." In a surviving fragment from Heraclitus and his followers are described as follows: Pythagoras, the son of Mnesarchus, practised inquiry beyond all other men and selecting of these writings made for himself a wisdom or made a wisdom of his own: a polymathy, an imposture. Two other surviving fragments of ancient sources on Pythagoras are by Ion of Empedocles. Both were born after Pythagoras' death. By that time he was known as a sage and his fame had spread throughout Greece. According to Ion, Pythagoras was:... distinguished for his many virtue and modesty in death has a life, pleasing to his soul, if Pythagoras the wise achieved knowledge and understanding beyond that of all men. Empedocles described Pythagoras as "a man of surpassing knowledge, master of all kinds of wise works, who had acquired the upmost wealth of understanding." In the 4th century BC the Sophist Alcidamas wrote that Pythagoras was honored by Italians.
Today scholars distinguish two periods of Pythagoreanism: early-Pythagoreanism, from the 6th till the 5th century BC, late-Pythagoreanism, from the 4th till the 3rd century BC. The Spartan colony of Taranto in Italy became the home for many practitioners of Pythagoreanism and for Neopythagorean philosophers. Pythagoras had lived in Crotone and Metaponto, both were Achaean colonies. Early-Pythagorean sects lived throughout Magna Graecia, they espoused to a rigorous life of the intellect and strict rules on diet and behavior. Their burial rites were tied to their belief in the immortality of the soul. Early-Pythagorean sects were closed societies and new Pythagoreans were chosen based on merit and discipline. Ancient sources record that early-Pythagoreans underwent a five year initiation period of listening to the teachings in silence. Initiates could through a test become members of the inner circle. However, Pythagoreans could leave the community if they wished. Iamblichus listed 235 Pythagoreans by name, among them 17 women who he described as the "most famous" women practitioners of Pythagoreanism.
It was customary that family members became Pythagoreans, as Pythagoreanism developed into a philosophic traditions that entailed rules for everyday life and Pythagoreans were bound by secrets. The home of a Pythagorean was known as the site of mysteries. Pythagoras had been born on the island of Samos at around 570 BC and left his homeland at around 530 BC in opposition
Geese are waterfowl of the family Anatidae. This group comprises the genera Branta. Chen, a genus comprising'white geese', is sometimes used to refer to a group of species that are more placed within Anser; some other birds related to the shelducks, have "goose" as part of their names. More distantly related members of the family Anatidae are swans, most of which are larger than true geese, ducks, which are smaller; the word "goose" is a direct descendent of Proto-Indo-European root, ghans-. In Germanic languages, the root gave Old English gōs with the plural gēs and gandres, Frisian goes and guoske, New High German Gans, Gänse, Ganter, Old Norse gās; this term gave Lithuanian: žąsìs, Irish: gé, Latin: anser, Ancient Greek: χήν, Dutch: gans, Albanian: gatë, Sanskrit hamsa and hamsi, Finnish: hanhi, Avestan zāō, Polish: gęś, Romanian: gâscă / gânsac, Ukrainian: гуска / гусак, Russian: гусыня / гусь, Czech: husa, Persian: غاز. The term goose applies to the female in particular. Young birds before fledging are called goslings.
The collective noun for a group of geese on the ground is a gaggle. The three living genera of true geese are: Anser, grey geese, including the greylag goose, domestic geese. Two genera of geese are only tentatively placed in the Anserinae. Either these or, more the goose-like Coscoroba swan is the closest living relative of the true geese. Fossils of true geese are hard to assign to genus; the aptly named Anser atavus from some 12 million years ago had more plesiomorphies in common with swans. In addition, some goose-like birds are known from subfossil remains found on the Hawaiian Islands. Geese are monogamous. Paired geese are feed more, two factors that result in more young; some Southern Hemisphere birds are called "geese", most of which belong to the shelduck subfamily Tadorninae. These are: Orinoco goose, Neochen jubata Egyptian goose, Alopochen aegyptiaca The South American sheldgeese, genus Chloephaga The prehistoric Malagasy sheldgoose, Centrornis majoriOthers: The spur-winged goose, Plectropterus gambensis, is most related to the shelducks, but distinct enough to warrant its own subfamily, the Plectropterinae.
The blue-winged goose, Cyanochen cyanopterus, the Cape Barren goose, Cereopsis novaehollandiae, have disputed affinities. They belong to separate ancient lineages that may ally either to the Tadorninae, Anserinae, or closer to the dabbling ducks; the three species of small waterfowl in the genus Nettapus are named "pygmy geese". They seem to represent another ancient lineage, with possible affinities to the Cape Barren goose or the spur-winged goose. A genus of prehistorically extinct seaducks, Chendytes, is sometimes called "diving-geese" due to their large size; the unusual magpie goose is in the Anseranatidae. The northern gannet, a seabird, is known as the "Solan goose", although it is a bird unrelated to the true geese, or any other Anseriformes for that matter. Well-known sayings about geese include: To "have a gander" is to examine something in detail. "What's sauce for the goose is sauce for the gander" or "What's good for the goose is good for the gander" means that what is an appropriate treatment for one person is appropriate for someone else.
Saying that someone's "goose is cooked" means that they have suffered, or are about to suffer, a terrible setback or misfortune. The common phrase "silly goose", used when referring to someone, acting silly. "Killing the goose that lays the golden eggs," derived from an old fable, is a saying referring to any greed-motivated, unprofitable action that destroys or otherwise renders a favourable situation useless. "A wild goose chase" is a futile waste of time and effort. There is a legendary old woman called Mother Goose; the oldest collection of Medieval Icelandic laws is known as "Grágás". Various etymologies were offered for that name: The fact that the laws were written with a goose quill. Carboneras, Carles. "Family Anatidae". In del Hoyo, Josep. Handbook of Birds of the World. Volume 1: Ostrich to Ducks. Barcelona: Lynx Edicions. Pp. 536–629. ISBN 84-87334-10-5. Terres, John K.. The Audubon Society Encyclopedia of North American Birds. New York: Wings Books. ISBN 0-517-03288-0. Anatidae media on the Internet Bird Collection
North Rhine-Westphalia is a state of Germany. North Rhine-Westphalia is located in western Germany covering an area of 34,084 square kilometres. With a population of 17.9 million, it is the most populous state in Germany. It is the most densely populated German state apart from the city-states of Berlin and Hamburg, the fourth-largest by area. Düsseldorf is the state capital and Cologne is the largest city. North Rhine-Westphalia features four of Germany's 10 largest cities: Düsseldorf, Cologne and Essen, the Rhine-Ruhr metropolitan area, the largest in Germany and the third-largest on the European continent. North Rhine-Westphalia was established in 1946 after World War II from the Prussian provinces of Westphalia and the northern part of Rhine Province, the Free State of Lippe by the British military administration in Allied-occupied Germany. North Rhine-Westphalia became a state of the Federal Republic of Germany in 1949, the city of Bonn served as the federal capital until the reunification of Germany in 1990 and as the seat of government until 1999.
The first written account of the area was by its conqueror, Julius Caesar, the territories west of the Rhine were occupied by the Eburones and east of the Rhine he reported the Ubii and the Sugambri to their north. The Ubii and some other Germanic tribes such as the Cugerni were settled on the west side of the Rhine in the Roman province of Germania Inferior. Julius Caesar conquered the tribes on the left bank, Augustus established numerous fortified posts on the Rhine, but the Romans never succeeded in gaining a firm footing on the right bank, where the Sugambri neighboured several other tribes including the Tencteri and Usipetes. North of the Sigambri and the Rhine region were the Bructeri; as the power of the Roman empire declined, many of these tribes came to be seen collectively as Ripuarian Franks and they pushed forward along both banks of the Rhine, by the end of the fifth century had conquered all the lands, under Roman influence. By the eighth century, the Frankish dominion was established in western Germany and northern Gaul, but at the same time, to the north, Westphalia was being taken over by Saxons pushing south.
The Merovingian and Carolingian Franks built an empire which controlled first their Ripuarian kin, the Saxons. On the division of the Carolingian Empire at the Treaty of Verdun, the part of the province to the east of the river fell to East Francia, while that to the west remained with the kingdom of Lotharingia. By the time of Otto I, both banks of the Rhine had become part of the Holy Roman Empire, the Rhenish territory was divided between the duchies of Upper Lorraine on the Moselle and Lower Lorraine on the Meuse; the Ottonian dynasty had both Frankish ancestry. As the central power of the Holy Roman Emperor weakened, the Rhineland split into numerous small, separate vicissitudes and special chronicles; the old Lotharingian divisions became obsolete, although the name survives for example in Lorraine in France, throughout the Middle Ages and into modern times, the nobility of these areas sought to preserve the idea of a preeminent duke within Lotharingia, something claimed by the Dukes of Limburg, the Dukes of Brabant.
Such struggles as the War of the Limburg Succession therefore continued to create military and political links between what is now Rhineland-Westphalia and neighbouring Belgium and the Netherlands. In spite of its dismembered condition and the sufferings it underwent at the hands of its French neighbours in various periods of warfare, the Rhenish territory prospered and stood in the foremost rank of German culture and progress. Aachen was the place of coronation of the German emperors, the ecclesiastical principalities of the Rhine bulked in German history. Prussia first set foot on the Rhine in 1609 by the occupation of the Duchy of Cleves and about a century Upper Guelders and Moers became Prussian. At the peace of Basel in 1795, the whole of the left bank of the Rhine was resigned to France, in 1806, the Rhenish princes all joined the Confederation of the Rhine. After the Congress of Vienna, Prussia was awarded the entire Rhineland, which included the Grand Duchy of Berg, the ecclesiastic electorates of Trier and Cologne, the free cities of Aachen and Cologne, nearly a hundred small lordships and abbeys.
The Prussian Rhine province was formed in 1822 and Prussia had the tact to leave them in undisturbed possession of the liberal institutions to which they had become accustomed under the republican rule of the French. In 1920, the districts of Eupen and Malmedy were transferred to Belgium. Around AD 1, numerous incursions occurred through Westphalia and even some permanent Roman or Romanized settlements; the Battle of Teutoburg Forest took place near Osnabrück and some of the Germanic tribes who fought at this battle came from the area of Westphalia. Charlemagne is thought to have spent considerable time in nearby parts, his Saxon Wars partly took place in what is thought of as Westphalia today. Popular legends link his adversary Widukind to places near Detmold, Lemgo, Osnabrück, other places in Westphalia. Widukind was buried in Enger, a subject of a legend. Along with Eastphalia and Engern, Westphalia was a district of the Duchy of Saxony. In 1180, Westphalia was elevated to the rank of a duchy by Emperor Barbarossa.
The Duchy of Westphalia comprised only a small area
In astronomy, the geocentric model is a superseded description of the Universe with Earth at the center. Under the geocentric model, the Sun, Moon and planets all orbited Earth; the geocentric model served as the predominant description of the cosmos in many ancient civilizations, such as those of Aristotle and Ptolemy. Two observations supported the idea. First, from anywhere on Earth, the Sun appears to revolve around Earth once per day. While the Moon and the planets have their own motions, they appear to revolve around Earth about once per day; the stars appeared to be fixed on a celestial sphere rotating once each day about an axis through the geographic poles of Earth. Second, Earth seems to be unmoving from the perspective of an earthbound observer. Ancient Greek, ancient Roman, medieval philosophers combined the geocentric model with a spherical Earth, in contrast to the older flat Earth model implied in some mythology; the ancient Jewish Babylonian uranography pictured a flat Earth with a dome-shaped, rigid canopy called the firmament placed over it.
However, the ancient Greeks believed that the motions of the planets were circular and not elliptical, a view, not challenged in Western culture until the 17th century, when Johannes Kepler postulated that orbits were heliocentric and elliptical. In 1687, Newton showed; the astronomical predictions of Ptolemy's geocentric model were used to prepare astrological and astronomical charts for over 1500 years. The geocentric model held sway into the early modern age, but from the late 16th century onward, it was superseded by the heliocentric model of Copernicus and Kepler. There was much resistance to the transition between these two theories; some Christian theologians were reluctant to reject a theory. Others felt a unknown theory could not subvert an accepted consensus for geocentrism; the geocentric model entered Greek philosophy at an early point. In the 6th century BC, Anaximander proposed a cosmology with Earth shaped like a section of a pillar, held aloft at the center of everything; the Sun and planets were holes in invisible wheels surrounding Earth.
About the same time, Pythagoras thought that the Earth was a sphere, but not at the center. These views were combined, so most educated Greeks from the 4th century BC on thought that the Earth was a sphere at the center of the universe. In the 4th century BC, two influential Greek philosophers and his student Aristotle, wrote works based on the geocentric model. According to Plato, the Earth was a sphere; the stars and planets were carried around the Earth on spheres or circles, arranged in the order: Moon, Venus, Mars, Saturn, fixed stars, with the fixed stars located on the celestial sphere. In his "Myth of Er", a section of the Republic, Plato describes the cosmos as the Spindle of Necessity, attended by the Sirens and turned by the three Fates. Eudoxus of Cnidus, who worked with Plato, developed a less mythical, more mathematical explanation of the planets' motion based on Plato's dictum stating that all phenomena in the heavens can be explained with uniform circular motion. Aristotle elaborated on Eudoxus' system.
In the developed Aristotelian system, the spherical Earth is at the center of the universe, all other heavenly bodies are attached to 47–55 transparent, rotating spheres surrounding the Earth, all concentric with it. These spheres, known as crystalline spheres, all moved at different uniform speeds to create the revolution of bodies around the Earth, they were composed of an incorruptible substance called aether. Aristotle believed that the Moon was in the innermost sphere and therefore touches the realm of Earth, causing the dark spots and the ability to go through lunar phases, he further described his system by explaining the natural tendencies of the terrestrial elements: Earth, fire, air, as well as celestial aether. His system held that Earth was the heaviest element, with the strongest movement towards the center, thus water formed a layer surrounding the sphere of Earth; the tendency of air and fire, on the other hand, was to move upwards, away from the center, with fire being lighter than air.
Beyond the layer of fire, were the solid spheres of aether in which the celestial bodies were embedded. They, were entirely composed of aether. Adherence to the geocentric model stemmed from several important observations. First of all, if the Earth did move one ought to be able to observe the shifting of the fixed stars due to stellar parallax. In short, if the Earth was moving, the shapes of the constellations should change over the course of a year. If they did not appear to move, the stars are either much farther away than the Sun and the planets than conceived, making their motion undetectable, or in reality they are not moving at all; because the stars were much further away than Greek astronomers postulated, stellar parallax was not detected until the 19th century. Therefore, the Greeks chose the simpler of the two explanations. Another observ