1.
Eratosthenes (crater)
–
Eratosthenes crater is a relatively deep lunar impact crater that lies on the boundary between the Mare Imbrium and Sinus Aestuum mare regions. It forms the terminus of the Montes Apenninus mountain range. The crater has a circular rim, terraced inner wall, central mountain peaks, an irregular floor. It lacks a ray system of its own, but is overlain by rays from the prominent crater Copernicus to the south-west and it is named after ancient Greek astronomer Eratosthenes of Cyrene, who estimated the circumference of the Earth, and the distance from the Earth to the Sun. The Eratosthenian period in the geological timescale is named after this crater. The crater is believed to have formed about 3.2 billion years ago. At low Sun-angles, this crater is prominent due to the shadow cast by the rim, when the Sun is directly overhead, however, Eratosthenes visually blends into the surroundings, and it becomes more difficult for an observer to locate it. The rays from Copernicus lie across this area, and their higher albedo serves as a form of camouflage, in 1851 Shropshire Astronomer Henry Blunt constructed a model of the moons surface showing Eratosthenes. The model is based on observations made by Blunt with a telescope from his home in Shrewsbury and was displayed in the same year at the Great Exhibition, London. In 1910–1920th, William H. Pickering noted dark patches in the crater that varied in a regular manner over each lunar day and he put forward the speculative idea that these patches appeared to migrate across the surface, suggestive of herds of small life forms. The idea received a degree of attention due to Pickerings reputation. By convention these features are identified on maps by placing the letter on the side of the crater midpoint that is closest to Eratosthenes
Eratosthenes (crater)
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Eratosthenes (lower right of center) and surroundings from Apollo 17.
NASA image.
Eratosthenes (crater)
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Lunar Reconnaissance Orbiter image
Eratosthenes (crater)
–
Eratosthenes crater. Photo taken from Earth. Author: Georgi Georgiev, Stara Zagora, Bulgaria.
Eratosthenes (crater)
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American projects
2.
Cyrene, Libya
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Cyrene was an ancient Greek and Roman city near present-day Shahhat, Libya. It was the oldest and most important of the five Greek cities in the region and it gave eastern Libya the classical name Cyrenaica that it has retained to modern times. Cyrene lies in a valley in the Jebel Akhdar uplands. The city was named after a spring, Kyre, which the Greeks consecrated to Apollo and it was also the seat of the Cyrenaics, a famous school of philosophy in the 3rd century BC, founded by Aristippus, a disciple of Socrates. It was then nicknamed the Athens of Africa, Grinus, son of Aesanius a descendant of Theras, and king of the island of Thera, had visited the Oracle and offered a hecatomb to the Oracle on sundry matters. The Oracle had offered the advice to found a new city in Libya, many years had passed and the advice was not taken, and Thera had succumbed to a horrific drought and all of the crops and trees had perished. Not knowing how to get to Libya they sent a messenger to Crete to find someone to lead them on their journey and they found a dealer in purple dyes named Corobius. He had once traveled to an island across from Libya called Platea, Grinus and Corobius sailed to Platea, when they reached their destination they left Corobius with months of supplies and Grinus went back to Thera to collect men to settle the newly made colony. After two years of settling the colony they had success and went back to the Oracle to get advice. The Oracle had repeated her advice to move directly to the country of Libya instead of across from Libya, so they moved to a place called Aziris. They settled there for six years, and were successful until the Libyans visited the settlement of Aziris to convince the people to move further inland. They were swayed by the Libyans to move and settled into what is now Cyrene, traditional details concerning the founding of the city are contained in Herodotus Histories IV. Cyrene promptly became the town of ancient Libya and established commercial relations with all the Greek cities. Soon after 460 BC it became a republic, in 413 BC, during the Peloponnesian War, Cyrene supplied Spartan forces with two triremes and pilots. After the death of Alexander the Great of Macedon, the Cyrenian republic became subject to the Ptolemaic dynasty, ophelas, the general who occupied the city in Ptolemy Is name, ruled the city almost independently until his death, when Ptolemys son-in-law Magas received governorship of the territory. In 276 BC Magas crowned himself king and declared de facto independence, the invasion was unsuccessful and in 250 BC, after Magas death, the city was reabsorbed into Ptolemaic Egypt. Cyrenaica became part of the Ptolemaic empire controlled from Alexandria, in 74 BC the territory was formally transformed into a Roman province. The inhabitants of Cyrene at the time of Sulla were divided into four classes, citizens, farmers, resident aliens, the ruler of the town, Ptolemy Apion, bequeathed it to the Romans, but it kept its self-government
Cyrene, Libya
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The ruins of Cyrene
Cyrene, Libya
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Apollo Kitharoidos from Cyrene. Roman statue from the 2nd century AD now in the
British Museum.
Cyrene, Libya
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Detail of the Cyrene bronze head in the British Museum (300 BC).
3.
Alexandria
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Alexandria is the second largest city and a major economic centre in Egypt, extending about 32 km along the coast of the Mediterranean Sea in the north central part of the country. Its low elevation on the Nile delta makes it vulnerable to rising sea levels. Alexandria is Egypts largest seaport, serving approximately 80% of Egypts imports and exports and it is an important industrial center because of its natural gas and oil pipelines from Suez. Alexandria is also an important tourist destination, Alexandria was founded around a small Ancient Egyptian town c.331 BC by Alexander the Great. Alexandria was the second most powerful city of the ancient world after Rome, Alexandria is believed to have been founded by Alexander the Great in April 331 BC as Ἀλεξάνδρεια. Alexanders chief architect for the project was Dinocrates, Alexandria was intended to supersede Naucratis as a Hellenistic center in Egypt, and to be the link between Greece and the rich Nile valley. The city and its museum attracted many of the greatest scholars, including Greeks, Jews, the city was later plundered and lost its significance. Just east of Alexandria, there was in ancient times marshland, as early as the 7th century BC, there existed important port cities of Canopus and Heracleion. The latter was rediscovered under water. An Egyptian city, Rhakotis, already existed on the shore also and it continued to exist as the Egyptian quarter of the city. A few months after the foundation, Alexander left Egypt and never returned to his city, after Alexanders departure, his viceroy, Cleomenes, continued the expansion. Although Cleomenes was mainly in charge of overseeing Alexandrias continuous development, the Heptastadion, inheriting the trade of ruined Tyre and becoming the center of the new commerce between Europe and the Arabian and Indian East, the city grew in less than a generation to be larger than Carthage. In a century, Alexandria had become the largest city in the world and and it became Egypts main Greek city, with Greek people from diverse backgrounds. Alexandria was not only a center of Hellenism, but was home to the largest urban Jewish community in the world. The Septuagint, a Greek version of the Tanakh, was produced there, in AD115, large parts of Alexandria were destroyed during the Kitos War, which gave Hadrian and his architect, Decriannus, an opportunity to rebuild it. On 21 July 365, Alexandria was devastated by a tsunami, the Islamic prophet, Muhammads first interaction with the people of Egypt occurred in 628, during the Expedition of Zaid ibn Haritha. He sent Hatib bin Abi Baltaeh with a letter to the king of Egypt and Alexandria called Muqawqis In the letter Muhammad said, I invite you to accept Islam, Allah the sublime, shall reward you doubly. But if you refuse to do so, you bear the burden of the transgression of all the Copts
Alexandria
–
Alexandria Ἀλεξάνδρεια
Alexandria
Alexandria
–
Residential neighborhood in Alexandria
Alexandria
–
Fishing in Alexandria
4.
Greek language
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Greek is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean. It has the longest documented history of any living language, spanning 34 centuries of written records and its writing system has been the Greek alphabet for the major part of its history, other systems, such as Linear B and the Cypriot syllabary, were used previously. The alphabet arose from the Phoenician script and was in turn the basis of the Latin, Cyrillic, Armenian, Coptic, Gothic and many other writing systems. Together with the Latin texts and traditions of the Roman world, during antiquity, Greek was a widely spoken lingua franca in the Mediterranean world and many places beyond. It would eventually become the official parlance of the Byzantine Empire, the language is spoken by at least 13.2 million people today in Greece, Cyprus, Italy, Albania, Turkey, and the Greek diaspora. Greek roots are used to coin new words for other languages, Greek. Greek has been spoken in the Balkan peninsula since around the 3rd millennium BC, the earliest written evidence is a Linear B clay tablet found in Messenia that dates to between 1450 and 1350 BC, making Greek the worlds oldest recorded living language. Among the Indo-European languages, its date of earliest written attestation is matched only by the now extinct Anatolian languages, the Greek language is conventionally divided into the following periods, Proto-Greek, the unrecorded but assumed last ancestor of all known varieties of Greek. The unity of Proto-Greek would have ended as Hellenic migrants entered the Greek peninsula sometime in the Neolithic era or the Bronze Age, Mycenaean Greek, the language of the Mycenaean civilisation. It is recorded in the Linear B script on tablets dating from the 15th century BC onwards, Ancient Greek, in its various dialects, the language of the Archaic and Classical periods of the ancient Greek civilisation. It was widely known throughout the Roman Empire, after the Roman conquest of Greece, an unofficial bilingualism of Greek and Latin was established in the city of Rome and Koine Greek became a first or second language in the Roman Empire. The origin of Christianity can also be traced through Koine Greek, Medieval Greek, also known as Byzantine Greek, the continuation of Koine Greek in Byzantine Greece, up to the demise of the Byzantine Empire in the 15th century. Much of the written Greek that was used as the language of the Byzantine Empire was an eclectic middle-ground variety based on the tradition of written Koine. Modern Greek, Stemming from Medieval Greek, Modern Greek usages can be traced in the Byzantine period and it is the language used by the modern Greeks, and, apart from Standard Modern Greek, there are several dialects of it. In the modern era, the Greek language entered a state of diglossia, the historical unity and continuing identity between the various stages of the Greek language is often emphasised. Greek speakers today still tend to regard literary works of ancient Greek as part of their own rather than a foreign language and it is also often stated that the historical changes have been relatively slight compared with some other languages. According to one estimation, Homeric Greek is probably closer to demotic than 12-century Middle English is to modern spoken English, Greek is spoken by about 13 million people, mainly in Greece, Albania and Cyprus, but also worldwide by the large Greek diaspora. Greek is the language of Greece, where it is spoken by almost the entire population
Greek language
–
Idealized portrayal of
Homer
Greek language
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regions where Greek is the official language
Greek language
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Greek language road sign, A27 Motorway, Greece
5.
Greek mathematics
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Greek mathematics, as the term is used in this article, is the mathematics written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by culture, Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. The word mathematics itself derives from the ancient Greek μάθημα, meaning subject of instruction, the study of mathematics for its own sake and the use of generalized mathematical theories and proofs is the key difference between Greek mathematics and those of preceding civilizations. The origin of Greek mathematics is not well documented, the earliest advanced civilizations in Greece and in Europe were the Minoan and later Mycenaean civilization, both of which flourished during the 2nd millennium BC. While these civilizations possessed writing and were capable of advanced engineering, including four-story palaces with drainage and beehive tombs, though no direct evidence is available, it is generally thought that the neighboring Babylonian and Egyptian civilizations had an influence on the younger Greek tradition. Historians traditionally place the beginning of Greek mathematics proper to the age of Thales of Miletus. Little is known about the life and work of Thales, so little indeed that his date of birth and death are estimated from the eclipse of 585 BC, despite this, it is generally agreed that Thales is the first of the seven wise men of Greece. The two earliest mathematical theorems, Thales theorem and Intercept theorem are attributed to Thales. The former, which states that an angle inscribed in a semicircle is a right angle and it is for this reason that Thales is often hailed as the father of the deductive organization of mathematics and as the first true mathematician. Thales is also thought to be the earliest known man in history to whom specific mathematical discoveries have been attributed, another important figure in the development of Greek mathematics is Pythagoras of Samos. Like Thales, Pythagoras also traveled to Egypt and Babylon, then under the rule of Nebuchadnezzar, Pythagoras established an order called the Pythagoreans, which held knowledge and property in common and hence all of the discoveries by individual Pythagoreans were attributed to the order. And since in antiquity it was customary to give all credit to the master, aristotle for one refused to attribute anything specifically to Pythagoras as an individual and only discussed the work of the Pythagoreans as a group. One of the most important characteristics of the Pythagorean order was that it maintained that the pursuit of philosophical and mathematical studies was a basis for the conduct of life. Indeed, the philosophy and mathematics are said to have been coined by Pythagoras. From this love of knowledge came many achievements and it has been customarily said that the Pythagoreans discovered most of the material in the first two books of Euclids Elements. The reason it is not clear exactly what either Thales or Pythagoras actually did is that almost no documentation has survived. The only evidence comes from traditions recorded in such as Proclus’ commentary on Euclid written centuries later. Some of these works, such as Aristotle’s commentary on the Pythagoreans, are themselves only known from a few surviving fragments
Greek mathematics
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Statue of Euclid in the
Oxford University Museum of Natural History
Greek mathematics
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An illustration of
Euclid 's proof of the
Pythagorean Theorem
Greek mathematics
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The
Antikythera mechanism, an ancient mechanical calculator.
6.
Geographer
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A geographer is a scholar whose area of study is geography, the study of Earths natural environment and human society. Although geographers are historically known as people who make maps, map making is actually the field of study of cartography, geographers do not study only the details of the natural environment or human society, but they also study the reciprocal relationship between these two. For example, they study how the natural environment contributes to the human society, in particular, physical geographers study the natural environment while human geographers study human society. There is a painting by Johannes Vermeer titled The Geographer. These paintings are thought to represent the growing influence and rise in prominence of scientific enquiry in Europe at the time of their painting. Human geography, including Urban geography, cultural geography, economic geography, political geography, historical geography, marketing geography, health geography, and social geography
Geographer
–
Johannes Vermeer,
The Geographer 1668-69 oil on canvas; 53×47 cm. max roy Frankfurt, Germany
Geographer
–
History of geography
7.
Poet
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POET LLC is a U. S. biofuel company that specializes in the creation of bioethanol. The privately held corporation, which was originally called Broin Companies, is headquartered in Sioux Falls, in 2007, the Renewable Fuels Association named POET the largest U. S. ethanol producer, creating 1.1 billion US gallons of fuel per year. Currently, POET produces 1.7 billion gallons of ethanol per year, POET operates 27 ethanol plants spread across Indiana, Iowa, Michigan, Missouri, Ohio, Minnesota, and South Dakota. In 2007, the received a US$80 million grant from the U. S. Department of Energy for the creation of a cellulosic ethanol production facility in Emmetsburg. A grand opening was held for the facility on September 3rd,2014 and it is expected to produce 25 million gallons of ethanol per year from corncobs, leaves and husks provided by farmers in and around the area. POET has also collaborated with companies, including Deere & Co. and Vermeer Company. Among its products in the process are distillers grains branded Dakota Gold, Inviz, the company traces its history to the family farm in Wanamingo, Minnesota where the Broins began producing ethanol in 1983. In 1986 it became commercial launching its flagship plant in Scotland, in 2007, it was renamed POET. Then company president Jeff Broin said the new name is not an acronym, bush in Wentworth, South Dakota in April 2002 and by Barack Obama in Macon, Missouri in April 2010. POET has constructed an $8 million pilot plant to produce cellulosic ethanol made from corn cobs, a commercial scale project, based on the pilot plant, was undertaken as a joint venture with Royal DSM under the name POET-DSM Advanced Biofuels, LLC. A federal loan guarantee was obtained in July,2011 for a plant to be built in Emmetsburg. This loan guarantee was later declined when the joint venture with Royal DSM was announced. Originally scheduled to open in 2013, the facility opened a year late in September,2014
Poet
8.
Astronomer
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An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside of the scope of Earth. They look at stars, planets, moons, comets and galaxies, as well as other celestial objects — either in observational astronomy. Examples of topics or fields astronomers work on include, planetary science, solar astronomy, there are also related but distinct subjects like physical cosmology which studies the Universe as a whole. Astronomers usually fit into two types, Observational astronomers make direct observations of planets, stars and galaxies, and analyze the data, theoretical astronomers create and investigate models of things that cannot be observed. They use this data to create models or simulations to theorize how different celestial bodies work, there are further subcategories inside these two main branches of astronomy such as planetary astronomy, galactic astronomy or physical cosmology. Today, that distinction has disappeared and the terms astronomer. Professional astronomers are highly educated individuals who typically 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 quite often have other duties such as teaching, building instruments. The number of astronomers in the United States is actually quite small. The American Astronomical Society, which is the organization of professional astronomers in North America, has approximately 7,000 members. This number includes scientists from other such as physics, geology. The International Astronomical Union comprises almost 10,145 members from 70 different countries who are involved in research at the Ph. D. level. Before CCDs, photographic plates were a method of observation. Modern astronomers spend relatively little time at telescopes usually 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 also have outreach programs including public telescope time and sometimes planetariums as a public service to encourage interest in the field. Those who become astronomers usually have a background in maths, sciences. Taking courses that teach how to research, write and present papers are also invaluable, in college/university most astronomers get a Ph. D. in astronomy or physics. Keeping in mind how few there are it is understood that graduate schools in this field are very competitive
Astronomer
–
The Astronomer by
Johannes Vermeer
Astronomer
–
Galileo is often referred to as the Father of
modern astronomy
Astronomer
–
Guy Consolmagno (Vatikan observatory), analyzing a meteorite, 2014
Astronomer
–
Emily Lakdawalla at the Planetary Conference 2013
9.
Music theory
–
Music theory is the study of the practices and possibilities of music. The term is used in three ways in music, though all three are interrelated. The first is what is otherwise called rudiments, currently taught as the elements of notation, of key signatures, of time signatures, of rhythmic notation, Theory in this sense is treated as the necessary preliminary to the study of harmony, counterpoint, and form. The second is the study of writings about music from ancient times onwards, Music theory is frequently concerned with describing how musicians and composers make music, including tuning systems and composition methods among other topics. However, this medieval discipline became the basis for tuning systems in later centuries, Music theory as a practical discipline encompasses the methods and concepts composers and other musicians use in creating music. The development, preservation, and transmission of music theory in this sense may be found in oral and written music-making traditions, musical instruments, and other artifacts. In ancient and living cultures around the world, the deep and long roots of music theory are clearly visible in instruments, oral traditions, and current music making. Many cultures, at least as far back as ancient Mesopotamia and ancient China, have also considered music theory in more formal ways such as written treatises, in modern academia, music theory is a subfield of musicology, the wider study of musical cultures and history. Etymologically, music theory is an act of contemplation of music, from the Greek θεωρία, a looking at, viewing, contemplation, speculation, theory, also a sight, a person who researches, teaches, or writes articles about music theory is a music theorist. University study, typically to the M. A. or Ph. D level, is required to teach as a music theorist in a US or Canadian university. Methods of analysis include mathematics, graphic analysis, and especially analysis enabled by Western music notation, comparative, descriptive, statistical, and other methods are also used. See for instance Paleolithic flutes, Gǔdí, and Anasazi flute, several surviving Sumerian and Akkadian clay tablets include musical information of a theoretical nature, mainly lists of intervals and tunings. The scholar Sam Mirelman reports that the earliest of these dates from before 1500 BCE. Further, All the Mesopotamian texts are united by the use of a terminology for music that, much of Chinese music history and theory remains unclear. The earliest texts about Chinese music theory are inscribed on the stone and they include more than 2800 words describing theories and practices of music pitches of the time. The bells produce two intertwined pentatonic scales three tones apart with additional pitches completing the chromatic scale, Chinese theory starts from numbers, the main musical numbers being twelve, five and eight. Twelve refers to the number of pitches on which the scales can be constructed, the Lüshi chunqiu from about 239 BCE recalls the legend of Ling Lun. On order of the Yellow Emperor, Ling Lun collected twelve bamboo lengths with thick, blowing on one of these like a pipe, he found its sound agreeable and named it huangzhong, the Yellow Bell
Music theory
–
Ancient Egyptian musicians playing lutes in an ensemble.
Music theory
–
Pythagoras and
Philolaus engaged in theoretical investigations, in a woodcut from
Franchinus Gaffurius, Theorica musicæ (1492)
Music theory
–
A set of bells from China, 5th Century BCE.
Music theory
–
Barbershop quartets, such as this US Navy group, sing 4-part pieces, made up of a melody line (normally the second-highest voice, called the "lead") and 3 harmony parts.
10.
Library of Alexandria
–
The Royal Library of Alexandria or Ancient Library of Alexandria in Alexandria, Egypt, was one of the largest and most significant libraries of the ancient world. It was dedicated to the Muses, the nine goddesses of the arts, the library was part of a larger research institution called the Musaeum of Alexandria, where many of the most famous thinkers of the ancient world studied. The library was created by Ptolemy I Soter, who was a Macedonian general, most of the books were kept as papyrus scrolls. It is unknown precisely how many such scrolls were housed at any given time, arguably, this library is most famous for having been burned down resulting in the loss of many scrolls and books, its destruction has become a symbol for the loss of cultural knowledge. Sources differ on who was responsible for its destruction and when it occurred, the library may in truth have suffered several fires over many years. Possible occasions for the partial or complete destruction of the Library of Alexandria include a set by the army of Julius Caesar in 48 BC. After the main library was destroyed, scholars used a library in a temple known as the Serapeum. The library may have finally been destroyed during the Muslim conquest of Egypt in AD642, the library itself is known to have had an acquisitions department and a cataloguing department. A hall contained shelves for the collections of papyrus scrolls known as bibliothekai, according to popular description, an inscription above the shelves read, The place of the cure of the soul. The library was but one part of the Musaeum of Alexandria, in addition to the library, the Musaeum included rooms for the study of astronomy, anatomy, and even a zoo containing exotic animals. The classical thinkers who studied, wrote, and experimented at the Musaeum include the names of mathematics, astronomy, physics, geometry, engineering, geography, physiology. These included notable thinkers such as Euclid, Archimedes, Eratosthenes, Herophilus, Erasistratus, Hipparchus, Aedesia, Pappus, Theon, Hypatia and it is not possible to determine the collections size in any era with any certainty. A single piece of writing might occupy several scrolls, and this division into self-contained books was an aspect of editorial work. King Ptolemy II Philadelphus is said to have set 500,000 scrolls as an objective for the library. The librarys index, Callimachus Pinakes, was lost with the rest of the library and this library, with the largest holdings of the age, acquired its collection by laborious copying of originals. Galen spoke of how all ships visiting the city were obliged to surrender their books for immediate copying, the owners received a copy while the pharaohs kept the originals in the library within their museum. As a research institution, the library filled its stacks with new works in mathematics, astronomy, physics, natural sciences and its empirical standards applied in one of the first and certainly strongest homes for serious textual criticism. As the same text often existed in different versions, comparative textual criticism was crucial for ensuring their veracity
Library of Alexandria
–
The Great Library of Alexandria, O. Von Corven, 19th century
Library of Alexandria
–
This Latin inscription regarding
Tiberius Claudius Balbilus of Rome (d. c. AD 79) mentions the "ALEXANDRINA BYBLIOTHECE" (line eight).
Library of Alexandria
–
The Burning of the Library at Alexandria in 391 AD, an illustration from 'Hutchinsons History of the Nations', c. 1910
Library of Alexandria
–
5th century scroll which illustrates the destruction of the Serapeum by Theophilus
11.
Geography
–
Geography is a field of science devoted to the study of the lands, the features, the inhabitants, and the phenomena of Earth. The first person to use the word γεωγραφία was Eratosthenes, Geography is an all-encompassing discipline that seeks an understanding of the Earth and its human and natural complexities—not merely where objects are, but how they have changed and come to be. It is often defined in terms of the two branches of geography and physical geography. Geography has been called the world discipline and the bridge between the human and the physical sciences, Geography is a systematic study of the Earth and its features. Traditionally, geography has been associated with cartography and place names, although many geographers are trained in toponymy and cartology, this is not their main preoccupation. Geographers study the space and the temporal database distribution of phenomena, processes, because space and place affect a variety of topics, such as economics, health, climate, plants and animals, geography is highly interdisciplinary. The interdisciplinary nature of the approach depends on an attentiveness to the relationship between physical and human phenomena and its spatial patterns. Names of places. are not geography. know by heart a whole gazetteer full of them would not, in itself and this is a description of the world—that is Geography. In a word Geography is a Science—a thing not of mere names but of argument and reason, of cause, just as all phenomena exist in time and thus have a history, they also exist in space and have a geography. Geography as a discipline can be split broadly into two main fields, human geography and physical geography. The former largely focuses on the environment and how humans create, view, manage. The latter examines the environment, and how organisms, climate, soil, water. The difference between these led to a third field, environmental geography, which combines physical and human geography. Physical geography focuses on geography as an Earth science and it aims to understand the physical problems and the issues of lithosphere, hydrosphere, atmosphere, pedosphere, and global flora and fauna patterns. Physical geography can be divided into broad categories, including, Human geography is a branch of geography that focuses on the study of patterns. It encompasses the human, political, cultural, social, and it requires an understanding of the traditional aspects of physical and human geography, as well as the ways that human societies conceptualize the environment. Integrated geography has emerged as a bridge between the human and the geography, as a result of the increasing specialisation of the two sub-fields. Examples of areas of research in the environmental geography include, emergency management, environmental management, sustainability, geomatics is concerned with the application of computers to the traditional spatial techniques used in cartography and topography
Geography
–
Map of the
Earth
Geography
–
Biogeography
Geography
Geography
12.
History of geodesy
–
Geodesy, also named geodetics, is the scientific discipline that deals with the measurement and representation of the Earth. The history of geodesy began in antiquity and blossomed during the Age of Enlightenment, early ideas about the figure of the Earth held the Earth to be flat, and the heavens a physical dome spanning over it. The early Greeks, in their speculation and theorizing, ranged from the flat disc advocated by Homer to the spherical body postulated by Pythagoras, pythagorass idea was supported later by Aristotle. Pythagoras was a mathematician and to him the most perfect figure was a sphere and he reasoned that the gods would create a perfect figure and therefore the Earth was created to be spherical in shape. Anaximenes, an early Greek philosopher, believed strongly that the Earth was rectangular in shape, since the spherical shape was the most widely supported during the Greek Era, efforts to determine its size followed. Platos figure was a guess and Archimedes a more conservative approximation, in Egypt, a Greek scholar and philosopher, Eratosthenes, is said to have made more explicit measurements. He had heard that on the longest day of the summer solstice, at the same time, he observed the sun was not directly overhead at Alexandria, instead, it cast a shadow with the vertical equal to 1/50th of a circle. Legend has it that he had someone walk from Alexandria to Syene to measure the distance, the circumference of the Earth is 24,902 mi. Over the poles it is more precisely 40,008 km or 24,860 mi, the actual unit of measure used by Eratosthenes was the stadion. No one knows for sure what his stadion equals in modern units, had the experiment been carried out as described, it would not be remarkable if it agreed with actuality. What is remarkable is that the result was only about 0. 4% too high. A parallel later ancient measurement of the size of the Earth was made by another Greek scholar and he is said to have noted that the star Canopus was hidden from view in most parts of Greece but that it just grazed the horizon at Rhodes. Posidonius is supposed to have measured the elevation of Canopus at Alexandria and he assumed the distance from Alexandria to Rhodes to be 5000 stadia, and so he computed the Earths circumference in stadia as 48 times 5000 =240,000. Some scholars see these results as luckily semi-accurate due to cancellation of errors, the abovementioned larger and smaller sizes of the Earth were those used by Claudius Ptolemy at different times,252,000 stadia in his Almagest and 180,000 stadia in his later Geography. The Indian mathematician Aryabhata was a pioneer of mathematical astronomy and he describes the earth as being spherical and that it rotates on its axis, among other things in his work Āryabhaṭīya. Aryabhatiya is divided into four sections, the discovery that the earth rotates on its own axis from west to east is described in Aryabhatiya. Aryabhata gives the radii of the orbits of the planets in terms of the Earth-Sun distance as essentially their periods of rotation around the Sun and he also gave the correct explanation of lunar and solar eclipses and that the Moon shines by reflecting sunlight. The Muslim scholars, who held to the spherical Earth theory, used it to calculate the distance and this determined the Qibla, or Muslim direction of prayer
History of geodesy
–
Archive with
lithography plates for maps of
Bavaria in the Landesamt für Vermessung und Geoinformation in
Munich
History of geodesy
–
Geodesy
History of geodesy
–
Negative lithography stone and positive print of a historic map of Munich
13.
Axial tilt
–
In astronomy, axial tilt, also known as obliquity, is the angle between an objects rotational axis and its orbital axis, or, equivalently, the angle between its equatorial plane and orbital plane. At an obliquity of zero, the two axes point in the direction, i. e. the rotational axis is perpendicular to the orbital plane. Over the course of an orbit, the obliquity usually does not change considerably, and this causes one pole to be directed more toward the Sun on one side of the orbit, and the other pole on the other side — the cause of the seasons on the Earth. Earths obliquity oscillates between 22.1 and 24.5 degrees on a 41, 000-year cycle, the mean obliquity is currently 23°26′13. 4″. There are two methods of specifying tilt. The IAU also uses the rule to define a positive pole for the purpose of determining orientation. Using this convention, Venus is tilted 177° and it is denoted by the Greek letter ε. Earth currently has a tilt of about 23. 4°. This value remains about the relative to a stationary orbital plane throughout the cycles of axial precession. But the ecliptic due to planetary perturbations, and the obliquity of the ecliptic is not a fixed quantity. At present, it is decreasing at a rate of about 47″ per century, Earths obliquity may have been reasonably accurately measured as early as 1100 BC in India and China. The ancient Greeks had good measurements of the obliquity since about 350 BC, about 830 AD, the Caliph Al-Mamun of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years. It was widely believed, during the Middle Ages, that both precession and Earths obliquity oscillated around a value, with a period of 672 years. Earths axis remains tilted in the direction with reference to the background stars throughout a year. This means that one pole will be directed away from the Sun at one side of the orbit and this is the cause of Earths seasons. Summer occurs in the Northern hemisphere when the pole is directed toward the Sun. Variations in Earths axial tilt can influence the seasons and is likely a factor in climate change. The exact angular value of the obliquity is found by observation of the motions of Earth, from 1984, the Jet Propulsion Laboratorys DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac
Axial tilt
Axial tilt
14.
Astronomical unit
–
The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that varies as Earth orbits the Sun, from a maximum to a minimum. Originally conceived as the average of Earths aphelion and perihelion, it is now defined as exactly 149597870700 metres, the astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars. However, it is also a component in the definition of another unit of astronomical length. A variety of symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A for the astronomical unit, in 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In 2012, the IAU, noting that various symbols are presently in use for the astronomical unit, in the 2014 revision of the SI Brochure, the BIPM used the unit symbol au. In ISO 80000-3, the symbol of the unit is ua. Earths orbit around the Sun is an ellipse, the semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. The centre of the sun lies on this line segment. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, knowing Earths shift and a stars shift enabled the stars distance to be calculated. But all measurements are subject to some degree of error or uncertainty, improvements in precision have always been a key to improving astronomical understanding. Improving measurements were continually checked and cross-checked by means of our understanding of the laws of celestial mechanics, the expected positions and distances of objects at an established time are calculated from these laws, and assembled into a collection of data called an ephemeris. NASAs Jet Propulsion Laboratory provides one of several ephemeris computation services, in 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition. Equivalently, by definition, one AU is the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass. As with all measurements, these rely on measuring the time taken for photons to be reflected from an object. However, for precision the calculations require adjustment for such as the motions of the probe. In addition, the measurement of the time itself must be translated to a scale that accounts for relativistic time dilation
Astronomical unit
–
Transits of Venus across the face of the Sun were, for a long time, the best method of measuring the astronomical unit, despite the difficulties (here, the so-called "
black drop effect ") and the rarity of observations.
Astronomical unit
–
The red line indicates the Earth-Sun distance, which is on average about 1 astronomical unit.
15.
Leap day
–
February 29, also known as leap day or leap year day, is a date added to most years that are divisible by 4, such as 2008,2012,2016,2020, and 2024. A leap day is added in various solar calendars, including the Gregorian calendar standard in most of the world, lunisolar calendars instead add a leap or intercalary month. In the Gregorian calendar, years that are divisible by 100, thus,1700,1800, and 1900 did not contain a leap day, neither will 2100,2200, and 2300. Conversely,1600 and 2000 did and 2400 will, Years containing a leap day are called leap years. Years not containing a leap day are called common years, February 29 is the 60th day of the Gregorian calendar, in such a year, with 306 days remaining until the end of the year. In the Chinese calendar, this day will only occur in years of the monkey, dragon, a leap day is observed because a complete revolution around the Sun takes approximately 6 hours longer than 365 days. A leap day compensates for this lag, realigning the calendar with the Earths position in the Solar System, otherwise, although most modern calendar years have 365 days, a complete revolution around the Sun takes approximately 365 days and 6 hours. An extra 24 hours thus accumulates every four years, requiring that a calendar day be added to align the calendar with the Suns apparent position. A solar year is slightly shorter than 365 days and 6 hours. The currently accepted figure is 365 days,5 hours,48 minutes,45 seconds. Adding a calendar day every four years, therefore, results in an excess of around 44 minutes for those four years, to compensate for this, three days are removed every 400 years. The Gregorian calendar reform implements this adjustment by making an exception to the rule that there is a leap year every four years. Instead, a year divisible by 100 is not a year unless that year is also divisible by 400. This means that the years 1600,2000, and 2400 are leap years, while the years 1700,1800,1900,2100,2200,2300, the Gregorian calendar repeats itself every 400 years, which is exactly 20,871 weeks including 97 leap days. Over this period, February 29 falls on Sunday, Tuesday, and Thursday 13 times each,14 times each on Friday and Saturday, the calendar of the Roman king Numa Pompilius had only 355 days which meant that it would quickly become unsynchronized with the solar year. An earlier Roman solution to this problem was to lengthen the calendar periodically by adding days to February. February consisted of two parts, each with an odd number of days, the first part ended with the Terminalia on the 23rd, which was considered the end of the religious year, and the five remaining days formed the second part. To keep the calendar year roughly aligned with the solar year, the second part of February was incorporated in the intercalary month as its last five days, with no change either in their dates or the festivals observed on them
Leap day
–
Adding a leap day (after 23 February) shifts the commemorations in the 1962
Roman Missal.
16.
Ancient world maps
–
The earliest known world maps date to classical antiquity, the oldest examples of the 6th to 5th centuries BCE still based on the flat Earth paradigm. World maps assuming a spherical Earth first appear in the Hellenistic period, a Babylonian world map, known as the Imago Mundi, is commonly dated to the 6th century BCE. The accompanying text mentions seven outer regions beyond the encircling ocean, the descriptions of five of them have survived, the third island is where the winged bird ends not his flight, i. e. cannot reach. On the fourth island the light is brighter than that of sunset or stars, it lay in the northwest, the fifth island, due north, lay in complete darkness, a land where one sees nothing, and the sun is not visible. The sixth island, where a horned bull dwells and attacks the newcomer the seventh island lay in the east and is where the morning dawns. Anaximander is credited with having created one of the first maps of the world and this was all surrounded by the ocean. Hecataeus of Miletus is credited with a work entitled Ges Periodos, one on Europe, is essentially a periplus of the Mediterranean, describing each region in turn, reaching as far north as Scythia. The other book, on Asia, is arranged similarly to the Periplus of the Erythraean Sea of which a version of the 1st century CE survives. The work only survives in some 374 fragments, by far the majority being quoted in the geographical lexicon Ethnika compiled by Stephanus of Byzantium, Eratosthenes drew an improved world map, incorporating information from the campaigns of Alexander the Great and his successors. Asia became wider, reflecting the new understanding of the size of the continent. Eratosthenes was also the first geographer to incorporate parallels and meridians within his cartographic depictions and his work about the ocean and the adjacent areas was a general geographical discussion, showing how all the forces had an effect on each other and applied also to human life. He measured the Earths circumference by reference to the position of the star Canopus and his measure of 240,000 stadia translates to 24,000 miles, close to the actual circumference of 24,901 miles. He was informed in his approach by Eratosthenes, who a century used the elevation of the Sun at different latitudes. Both mens figures for the Earths circumference were uncannily accurate, aided in each case by mutually compensating errors in measurement, Strabo is mostly famous for his 17-volume work Geographica, which presented a descriptive history of people and places from different regions of the world known to his era. The Geographica first appeared in Western Europe in Rome as a Latin translation issued around 1469, Geographica provides a valuable source of information on the ancient world, especially when this information is corroborated by other sources. Within the books of Geographica is a map of Europe, whole world maps according to Strabo are reconstructions from his written text. Marinus of Tyres world maps were the first in the Roman Empire to show China, around 120 CE, Marinus wrote that the habitable world was bounded on the west by the Fortunate Islands. The text of his geographical treatise however is lost and he also invented the equirectangular projection, which is still used in map creation today
Ancient world maps
–
Imago Mundi Babylonian map, the oldest known world map, 6th century BCE
Babylonia.
Ancient world maps
–
1883 reconstruction of
Eratosthenes ' map
Ancient world maps
–
A 1628 reconstruction of
Posidonius ideas about the positions of continents (many details couldn't have been known by Posidonius)
Ancient world maps
–
An 1898 reconstruction of
Pomponius Melas view of the World.
17.
Circle of latitude
–
A circle of latitude on the Earth is an abstract east–west circle connecting all locations around the earth at a given latitude. Circles of latitude are called parallels because they are parallel to each other – that is. A locations position along a circle of latitude is given by its longitude and their length can be calculated by a common sine or cosine function. The 60th circle of latitude is half as long as the equator, a circle of latitude is perpendicular to all meridians. The latitude of the circle is approximately the angle between the equator and the circle, with the vertex at the Earths centre. The equator is at 0°, and the North and South poles are at 90° north, the Equator is the longest circle of latitude and is the only circle of latitude which also is a great circle. There is no limit to how precisely latitude can be measured, on a map, the circles of latitude may or may not be parallel, and their spacing may vary, depending on which projection is used to map the surface of the Earth onto a plane. On an equirectangular projection, centered on the equator, the circles of latitude are horizontal, parallel, on other cylindrical and pseudocylindrical projections, the circles of latitude are horizontal and parallel, but may be spaced unevenly to give the map useful characteristics. On most non-cylindrical and non-pseudocylindrical projections, the circles of latitude are neither straight nor parallel, North American nations and states have also mostly been created by straight lines, which are often parts of circles of latitudes. For instance, the border of Colorado is at 41°N while the southern border is at 37°N. Roughly half the length of border between the United States and Canada follows 49°N, there are five major circles of latitude, listed below from north to south. The position of the Equator is fixed but the latitudes of the other circles depend on the tilt of this axis relative to the plane of the Earths orbit, the equator is the circle that is equidistant from the North Pole and South Pole. It divides the Earth into the Northern Hemisphere and the Southern Hemisphere, of the parallels or circles of latitude, it is the longest, and the only great circle. All the other parallels are smaller and centered only on the earths axis, the Arctic Circle is the southernmost latitude in the Northern Hemisphere at which the sun can remain continuously above or below the horizon for 24 hours. Similarly, the Antarctic Circle marks the northernmost latitude in the Southern Hemisphere at which the sun can remain continuously above or below the horizon for 24 hours. The Tropic of Cancer and Tropic of Capricorn mark the northernmost and southernmost latitudes at which the sun may be directly overhead. The latitude of the circles is equal to the Earths axial tilt. In 2000 the mean value of the tilt was about 23° 26′ 21″, the main long-term cycle causes the axial tilt to fluctuate between about 22. 1° and 24. 5° with a period of 41,000 years
Circle of latitude
18.
Chronology
–
Chronology is the science of arranging events in their order of occurrence in time. Consider, for example, the use of a timeline or sequence of events and it is also the determination of the actual temporal sequence of past events. It is also part of the discipline of history, including history, the earth sciences. Chronology is the science of locating historical events in time and it relies upon chronometry, which is also known as timekeeping, and historiography, which examines the writing of history and the use of historical methods. Radiocarbon dating estimates the age of living things by measuring the proportion of carbon-14 isotope in their carbon content. Dendrochronology is used in turn as a reference for radiocarbon dating curves. The familiar terms calendar and era concern two complementary concepts of chronology. Dionysius Exiguus was the founder of that era, which is nowadays the most widespread dating system on earth, an epoch is the date when an era begins. Ab Urbe condita is Latin for from the founding of the City and it was used to identify the Roman year by a few Roman historians. Modern historians use it more frequently than the Romans themselves did. Before the advent of the critical edition of historical Roman works, AUC was indiscriminately added to them by earlier editors. It was used systematically for the first time only about the year 400, pope Boniface IV, in about the year 600, seems to have been the first who made a connection between these this era and Anno Domini. Dionysius Exiguus’ Anno Domini era was extended by Bede to the complete Christian era, while of critical importance to the historian, methods of determining chronology are used in most disciplines of science, especially astronomy, geology, paleontology and archaeology. In the absence of written history, with its chronicles and king lists and this method of dating is known as seriation. Known wares discovered at strata in sometimes quite distant sites, the product of trade, laboratory techniques developed particularly after mid-20th century helped constantly revise and refine the chronologies developed for specific cultural areas. Unrelated dating methods help reinforce a chronology, an axiom of corroborative evidence, ideally, archaeological materials used for dating a site should complement each other and provide a means of cross-checking. Conclusions drawn from just one unsupported technique are usually regarded as unreliable, the fundamental problem of chronology is to synchronize events. By synchronizing an event it becomes possible to relate it to the current time, among historians, a typical need to is to synchronize the reigns of kings and leaders in order to relate the history of one country or region to that of another
Chronology
–
Joseph Scaliger 's De emendatione temporum (1583) began the modern science of chronology
Chronology
–
Key concepts
19.
Troy
–
The present-day location is known as Hisarlik. It was the setting of the Trojan War described in the Greek Epic Cycle, in particular in the Iliad, a new capital called Ilium was founded on the site in the reign of the Roman Emperor Augustus. It flourished until the establishment of Constantinople and declined gradually in the Byzantine era and these excavations revealed several cities built in succession. Troy VII has been identified with the city that the Hittites called Wilusa, the origin of the Greek Ἴλιον. Today, the hill at Hisarlık has given its name to a village near the ruins. It lies within the province of Çanakkale, some 30 km south-west of the provincial capital, the map here shows the adapted Scamander estuary with Ilium a little way inland across the Homeric plain. Troy was added to the UNESCO World Heritage list in 1998, Ancient Greek historians variously placed the Trojan War in the 12th, 13th, or 14th centuries BC, Eratosthenes to 1184 BC, Herodotus to 1250 BC, Duris of Samos to 1334 BC. Modern archaeologists associate Homeric Troy with archaeological Troy VII, in the Iliad, the Achaeans set up their camp near the mouth of the River Scamander, where they had beached their ships. The city of Troy itself stood on a hill, across the plain of Scamander, recent geological findings have permitted the identification of the ancient Trojan coastline, and the results largely confirm the accuracy of the Homeric geography of Troy. In November 2001, the geologist John C, kraft from the University of Delaware and the classicist John V. Luce from Trinity College, Dublin, presented the results of investigations, begun in 1977, into the geology of the region. Besides the Iliad, there are references to Troy in the major work attributed to Homer. The Homeric legend of Troy was elaborated by the Roman poet Virgil in his Aeneid, the Greeks and Romans took for a fact the historicity of the Trojan War and the identity of Homeric Troy with the site in Anatolia. Alexander the Great, for example, visited the site in 334 BC and there made sacrifices at tombs associated with the Homeric heroes Achilles and Patroclus. After the 1995 find of a Luwian biconvex seal at Troy VII, with the rise of critical history, Troy and the Trojan War were, for a long time, consigned to the realms of legend. However, the location of ancient Troy had from classical times remained the subject of interest. The Troad peninsula was anticipated to be the location, leChavaliers location, published in his Voyage de la Troade, was the most commonly accepted theory for almost a century. In 1822, the Scottish journalist Charles Maclaren was the first to identify with confidence the position of the city as it is now known, the hill, near the city of Çanakkale, was known as Hisarlık. In 1868, Heinrich Schliemann visited Calvert and secured permission to excavate Hisarlık, in 1871–73 and 1878–79, he excavated the hill and discovered the ruins of a series of ancient cities dating from the Bronze Age to the Roman period
Troy
–
The walls of the
acropolis belong to Troy VII, which is identified as the site of the
Trojan War (c. 1200 BC).
Troy
–
Silver
tetradrachm from Troy with head of
Athena, c. 165–150 BC
Troy
–
The
odeon dates to the
Roman Troy IX and was renovated by
Hadrian in 124 AD.
Troy
–
The view from
Hisarlık across the plain of Ilium to the
Aegean Sea.
20.
Iliupersis
–
The Iliupersis, also known as The Sack of Troy, is a lost epic of ancient Greek literature. It was one of the Epic Cycle, that is, the Trojan cycle, the story of the Iliou persis comes chronologically after that of the Little Iliad, and is followed by the Nostoi. The Iliou persis was sometimes attributed by ancient writers to Arctinus of Miletus, the poem comprised two books of verse in dactylic hexameter. The Iliou persis was probably composed in the seventh century BCE, ancient sources date Arctinus to the eighth century, but evidence concerning another of his poems, the Aethiopis, suggests that he lived considerably later than that. Only ten lines of the text of the Iliou persis survive. For its storyline we are almost entirely dependent on a summary of the Cyclic epics contained in the Chrestomathy written by an unknown Proclus, a few other references give indications of the poems storyline. A further impression of the content may be gained from book 2 of Virgils Aeneid. Note that different sources record some details differently, for example the manner of Aeneas departure from Troy, the version told here specifically follows what is known of the early epic poem, rather than any other source. The poem opens with the Trojans discussing what to do with the horse which the Greeks have left behind. Cassandra and Laocoön proclaim that there is a force of Greeks inside. The latter opinion prevails, and the Trojans celebrate their apparent victory, the god Poseidon, meanwhile, sends an ill omen of two snakes which kill Laocoön and his sons, seeing this, Aeneas and his men leave Troy in anticipation of what is to come. When night comes, the Greek warriors inside the horse emerge, and open the city gates to let in the Greek army, the Trojans are massacred, and the Greeks set fire to the city. The gods consider whether they should stone Ajax in retribution, later, when the Greeks are sailing home, Athena kills him at sea. Odysseus kills Hectors baby son Astyanax and Neoptolemus takes Hectors wife Andromache captive, the Greeks make a human sacrifice of Priams daughter Polyxena at Achilless tomb, to placate his angry spirit
Iliupersis
–
The Fall of Troy, by Johann Georg Trautmann (1713–1769). From the collections of the
Grand Dukes of Baden, Karlsruhe.
Iliupersis
–
Achilles tending the wounded
Patroclus (
Attic red-figure kylix, c. 500 BC)
21.
Number theory
–
Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called The Queen of Mathematics because of its place in the discipline. Number theorists study prime numbers as well as the properties of objects out of integers or defined as generalizations of the integers. Integers can be considered either in themselves or as solutions to equations, questions in number theory are often best understood through the study of analytical objects that encode properties of the integers, primes or other number-theoretic objects in some fashion. One may also study real numbers in relation to rational numbers, the older term for number theory is arithmetic. By the early century, it had been superseded by number theory. The use of the arithmetic for number theory regained some ground in the second half of the 20th century. In particular, arithmetical is preferred as an adjective to number-theoretic. The first historical find of a nature is a fragment of a table. The triples are too many and too large to have been obtained by brute force, the heading over the first column reads, The takiltum of the diagonal which has been subtracted such that the width. The tables layout suggests that it was constructed by means of what amounts, in language, to the identity 2 +1 =2. If some other method was used, the triples were first constructed and then reordered by c / a, presumably for use as a table. It is not known what these applications may have been, or whether there could have any, Babylonian astronomy, for example. It has been suggested instead that the table was a source of examples for school problems. While Babylonian number theory—or what survives of Babylonian mathematics that can be called thus—consists of this single, striking fragment, late Neoplatonic sources state that Pythagoras learned mathematics from the Babylonians. Much earlier sources state that Thales and Pythagoras traveled and studied in Egypt, Euclid IX 21—34 is very probably Pythagorean, it is very simple material, but it is all that is needed to prove that 2 is irrational. Pythagorean mystics gave great importance to the odd and the even, the discovery that 2 is irrational is credited to the early Pythagoreans. This forced a distinction between numbers, on the one hand, and lengths and proportions, on the other hand, the Pythagorean tradition spoke also of so-called polygonal or figurate numbers
Number theory
–
A
Lehmer sieve, which is a primitive
digital computer once used for finding
primes and solving simple
Diophantine equations.
Number theory
–
The Plimpton 322 tablet
Number theory
–
Title page of the 1621 edition of Diophantus' Arithmetica, translated into
Latin by
Claude Gaspard Bachet de Méziriac.
Number theory
–
Leonhard Euler
22.
Prime number
–
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a number is called a composite number. For example,5 is prime because 1 and 5 are its only positive integer factors, the property of being prime is called primality. A simple but slow method of verifying the primality of a number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and n, algorithms much more efficient than trial division have been devised to test the primality of large numbers. Particularly fast methods are available for numbers of forms, such as Mersenne numbers. As of January 2016, the largest known prime number has 22,338,618 decimal digits, there are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no simple formula that separates prime numbers from composite numbers. However, the distribution of primes, that is to say, many questions regarding prime numbers remain open, such as Goldbachs conjecture, and the twin prime conjecture. Such questions spurred the development of branches of number theory. Prime numbers give rise to various generalizations in other domains, mainly algebra, such as prime elements. A natural number is called a number if it has exactly two positive divisors,1 and the number itself. Natural numbers greater than 1 that are not prime are called composite, among the numbers 1 to 6, the numbers 2,3, and 5 are the prime numbers, while 1,4, and 6 are not prime. 1 is excluded as a number, for reasons explained below. 2 is a number, since the only natural numbers dividing it are 1 and 2. Next,3 is prime, too,1 and 3 do divide 3 without remainder, however,4 is composite, since 2 is another number dividing 4 without remainder,4 =2 ·2. 5 is again prime, none of the numbers 2,3, next,6 is divisible by 2 or 3, since 6 =2 ·3. The image at the right illustrates that 12 is not prime,12 =3 ·4, no even number greater than 2 is prime because by definition, any such number n has at least three distinct divisors, namely 1,2, and n
Prime number
–
The number 12 is not a prime, as 12 items can be placed into 3 equal-size columns of 4 each (among other ways). 11 items cannot be all placed into several equal-size columns of more than 1 item each without some extra items leftover (a remainder). Therefore, the number 11 is a prime.
23.
Suda
–
The Suda or Souda is a large 10th-century Byzantine encyclopedia of the ancient Mediterranean world, formerly attributed to an author called Suidas. It is a lexicon, written in Greek, with 30,000 entries, many drawing from ancient sources that have since been lost. The Suda is somewhere between a grammatical dictionary and an encyclopedia in the modern sense and it explains the source, derivation, and meaning of words according to the philology of its period, using such earlier authorities as Harpocration and Helladios. The articles on history are especially valuable. These entries supply details and quotations from authors whose works are otherwise lost and they use older scholia to the classics, and for later writers, Polybius, Josephus, the Chronicon Paschale, George Syncellus, George Hamartolus, and so on. This lexicon represents a convenient work of reference for people who played a part in political, ecclesiastical, the chief source for this is the encyclopedia of Constantine VII Porphyrogenitus, and for Roman history the excerpts of John of Antioch. Krumbacher counts two main sources of the work, Constantine VII for ancient history, and Hamartolus for the Byzantine age, the system is not difficult to learn and remember, but some editors—for example, Immanuel Bekker – rearranged the Suda alphabetically. Little is known of the compilation of work, except that it must have been written before it was quoted from extensively by Eustathius who lived from about 1115 AD to about 1195 or 1196. It would thus appear that the Suda was compiled sometime after 975, passages referring to Michael Psellus are considered later interpolations. It includes numerous quotations from ancient writers, the scholiasts on Aristophanes, Homer, other principal sources include a lexicon by Eudemus, perhaps derived from the work On Rhetorical Language by Eudemus of Argos. The work deals with biblical as well as subjects, from which it is inferred that the writer was a Christian. A prefatory note gives a list of dictionaries from which the portion was compiled. Although the work is uncritical and probably much interpolated, and the value of its articles is very unequal and its quotations from ancient authors make it a useful check on their manuscript traditions. A modern translation, the Suda On Line, was completed on 21 July 2014, the Suda has a near-contemporaneous Islamic parallel, the Kitab al-Fehrest of Ibn al-Nadim. Compare also the Latin Speculum Maius, authored in the 13th century by Vincent of Beauvais and this article incorporates text from a publication now in the public domain, Chisholm, Hugh, ed. Sūïdas. This article incorporates text from a now in the public domain, Herbermann, Charles. Ancient Greek Scholarship, a guide to finding, reading, and understanding scholia, commentaries, lexica, Oxford, New York, Oxford University Press,2006. Tachypaedia Byzantina, The Suda On Line as Collaborative Encyclopedia, Digital Humanities Quarterly 3.1, an on-line edition of the Ada Adler edition with ongoing translations and commentary by registered editors
Suda
–
First page of an early printed edition of the Suda
24.
Cyrene (city)
–
Cyrene was an ancient Greek and Roman city near present-day Shahhat, Libya. It was the oldest and most important of the five Greek cities in the region and it gave eastern Libya the classical name Cyrenaica that it has retained to modern times. Cyrene lies in a valley in the Jebel Akhdar uplands. The city was named after a spring, Kyre, which the Greeks consecrated to Apollo and it was also the seat of the Cyrenaics, a famous school of philosophy in the 3rd century BC, founded by Aristippus, a disciple of Socrates. It was then nicknamed the Athens of Africa, Grinus, son of Aesanius a descendant of Theras, and king of the island of Thera, had visited the Oracle and offered a hecatomb to the Oracle on sundry matters. The Oracle had offered the advice to found a new city in Libya, many years had passed and the advice was not taken, and Thera had succumbed to a horrific drought and all of the crops and trees had perished. Not knowing how to get to Libya they sent a messenger to Crete to find someone to lead them on their journey and they found a dealer in purple dyes named Corobius. He had once traveled to an island across from Libya called Platea, Grinus and Corobius sailed to Platea, when they reached their destination they left Corobius with months of supplies and Grinus went back to Thera to collect men to settle the newly made colony. After two years of settling the colony they had success and went back to the Oracle to get advice. The Oracle had repeated her advice to move directly to the country of Libya instead of across from Libya, so they moved to a place called Aziris. They settled there for six years, and were successful until the Libyans visited the settlement of Aziris to convince the people to move further inland. They were swayed by the Libyans to move and settled into what is now Cyrene, traditional details concerning the founding of the city are contained in Herodotus Histories IV. Cyrene promptly became the town of ancient Libya and established commercial relations with all the Greek cities. Soon after 460 BC it became a republic, in 413 BC, during the Peloponnesian War, Cyrene supplied Spartan forces with two triremes and pilots. After the death of Alexander the Great of Macedon, the Cyrenian republic became subject to the Ptolemaic dynasty, ophelas, the general who occupied the city in Ptolemy Is name, ruled the city almost independently until his death, when Ptolemys son-in-law Magas received governorship of the territory. In 276 BC Magas crowned himself king and declared de facto independence, the invasion was unsuccessful and in 250 BC, after Magas death, the city was reabsorbed into Ptolemaic Egypt. Cyrenaica became part of the Ptolemaic empire controlled from Alexandria, in 74 BC the territory was formally transformed into a Roman province. The inhabitants of Cyrene at the time of Sulla were divided into four classes, citizens, farmers, resident aliens, the ruler of the town, Ptolemy Apion, bequeathed it to the Romans, but it kept its self-government
Cyrene (city)
–
The ruins of Cyrene
Cyrene (city)
–
Apollo Kitharoidos from Cyrene. Roman statue from the 2nd century AD now in the
British Museum.
Cyrene (city)
–
Detail of the Cyrene bronze head in the British Museum (300 BC).
25.
Libya
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The three traditional parts of the country are Tripolitania, Fezzan and Cyrenaica. With an area of almost 1.8 million square kilometres, Libya is the fourth largest country in Africa, Libya has the 10th-largest proven oil reserves of any country in the world. The largest city and capital, Tripoli, is located in western Libya, the other large city is Benghazi, which is located in eastern Libya. Libya has been inhabited by Berbers since the late Bronze Age, the Phoenicians established trading posts in western Libya, and ancient Greek colonists established city-states in eastern Libya. Libya was variously ruled by Carthaginians, Persians, Egyptians and Greeks before becoming a part of the Roman Empire, Libya was an early center of Christianity. After the fall of the Western Roman Empire, the area of Libya was mostly occupied by the Vandals until the 7th century, in the 16th century, the Spanish Empire and the Knights of St John occupied Tripoli, until Ottoman rule began in 1551. Libya was involved in the Barbary Wars of the 18th and 19th centuries, Ottoman rule continued until the Italian occupation of Libya resulted in the temporary Italian Libya colony from 1911 to 1943. During the Second World War Libya was an important area of warfare in the North African Campaign, the Italian population then went into decline. Libya became an independent kingdom in 1951, a military coup in 1969 overthrew King Idris I, beginning a period of sweeping social reform. Since then, Libya has experienced a period of instability, the European Union is involved in an operation to disrupt human trafficking networks exploiting refugees fleeing from wars in Africa for Europe. At least two political bodies claim to be the government of Libya, the Council of Deputies is internationally recognized as the legitimate government, but it does not hold territory in the capital, Tripoli, instead meeting in the Cyrenaica city of Tobruk. Parts of Libya are outside of either governments control, with various Islamist, rebel, the United Nations is sponsoring peace talks between the Tobruk and Tripoli-based factions. An agreement to form an interim government was signed on 17 December 2015. Under the terms of the agreement, a nine-member Presidency Council, the leaders of the new government, called the Government of National Accord, arrived in Tripoli on 5 April 2016. Since then the GNC, one of the two governments, has disbanded to support the new GNA. The name Libya was introduced in 1934 for Italian Libya, reviving the name for Northwest Africa. The name was based on use in 1903 by Italian geographer Federico Minutilli. It was intended to supplant terms applied to Ottoman Tripolitania, the region of what is today Libya having been ruled by the Ottoman Empire from 1551 to 1911
Libya
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The temple of
Zeus in the ancient Greek city of
Cyrene.
Libya
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Flag
Libya
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The
Atiq Mosque in
Awjila is the oldest mosque in the
Sahara.
Libya
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The
Siege of Tripoli in 1551 allowed the Ottomans to capture the city from the Knights of St. John.
26.
Pentapolis (North Africa)
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Cyrenaica is the eastern coastal region of Libya. Also known as Pentapolis in antiquity, it formed part of the Roman province of Crete and Cyrenaica, later divided into Libya Pentapolis, during the Islamic period, the area came to be known as Barqa, after the city of Barca. In a wider sense, still in use, Cyrenaica includes all of the part of Libya. Cyrenaica borders on Tripolitania in the northwest and on Fezzan in the southwest, the region that used to be Cyrenaica officially until 1963 has formed several shabiyat, the administrative divisions of Libya, since 1995. The 2011 Libyan Civil War started in Cyrenaica, which came largely under the control of the National Transitional Council for most of the war. Geologically, Cyrenaica rests on a mass of Miocene limestone that tilts up steeply from the Mediterranean Sea and this mass is divided into two blocks. The Jebel Akhdar extends parallel to the coast from the Gulf of Sidra to the Gulf of Bomba, there is no continuous coastal plain, the longest strip running from the recess of Gulf of Sidra past Benghazi to Tolmeita. Thereafter, except for deltaic patches at Susa and Derna, the shore is all precipitous, a steep escarpment separates the coastal plain from a relatively level plateau, known as the Marj Plain, which lies at about 300 meters elevation. Above the Marj Plain lies a plateau at about 700 meters elevation. The Jebel Akhdar and its adjacent coast are part of the Mediterranean woodlands and forests ecoregion, the plant communities of this portion of Cyrenaica include forest, woodland, maquis, garrigue, steppe, and oak savanna. Small areas of maquis are found on north-facing slopes near the sea, juniperus phoenicea, Pistacia lentiscus, Quercus coccifera and Ceratonia siliqua are common tree and large shrub species in the maquis. Areas of red soil are found on the Marj Plain, which has borne abundant crops of wheat, plenty of springs issue on the highlands. Wild olive trees are abundant, and large areas of oak savanna provide pasture to the flocks, historically large areas of range were covered in forest. The forested area of the Jebel Akhdar has been shrinking in recent decades, a 1996 report to the UN Food and Agriculture Organization estimated that the forested area was reduced to 320,000 hectares from 500,000 hectares, mostly cleared to grow crops. The Green Mountain Conservation and Development Authority estimates that the area decreased from 500,000 hectares in 1976 to 180,000 hectares in 2007. The lower Jebel el-Akabah lies to the south and east of the Jebel Akhdar, the two highlands are separated by a depression. This eastern region, known in ancient times as Marmarica, is drier than the Jebel Akhdar. Historically, salt-collecting and sponge fishing were more important than agriculture, Bomba and Tobruk have good harbors
Pentapolis (North Africa)
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Map of Cyrenaica and
Marmarica in the Roman era (
Samuel Butler, 1907)
Pentapolis (North Africa)
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Flag
Pentapolis (North Africa)
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Roman ruins of
Ptolemais, Cyrenaica
Pentapolis (North Africa)
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Emir
Idris as-Senussi (left), and behind him (from left)
Hussein Maziq,
Muhammad Sakizli, and
Mustafa Ben Halim formed the government of Cyrenaica in late 1940s
27.
Apollonia, Cyrenaica
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Apollonia in Cyrenaica was founded by Greek colonists and became a significant commercial centre in the southern Mediterranean. It served as the harbour of Cyrene,20 km to the southwest. D and it became the capital of the Roman province of Libya Superior or Libya Pentapolitana. The city became known as Sozusa, which explains the name of Marsa Susa or Susa. Sozusa was a see and is included in the Catholic Churchs list of titular sees. The existence of buildings in the sea was noted by Beechey, with rough drawings. The results of work were published, complete with maps. Carlo Beltrame and colleagues have made an underwater photographic survey of some of the buildings. The Crete earthquake and tsunami of 21 July 365 AD apparently caused extensive damage to the city, the Apollonia Museum houses many artifacts found on the ancient site. Apollonia is particularly known for its ruins of three churches dating from the Byzantine period, the Palace was last used as the Byzantine Dukes Palace and contains over 100 rooms. The previous use was as a Roman military commanders house, the well-preserved Greek theatre stands facing the sea outside the old city walls. The cavea has 28 seat levels, barca Ptolemais, Cyrenaica This article incorporates text from a publication now in the public domain, Chisholm, Hugh, ed. article name needed. Proceedings of an Expedition to Explore the North African coast, geographical Magazine, v.31, pp. 497–508. Doubleday, New York,222 pp, New English Library, London, flemming, N. C. and Webb, C. O,1986. Tectonic and eustatic coastal changes during the last 10,000 years derived from archaeological data, december, Suppl – Bd62, p.129
Apollonia, Cyrenaica
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Map of underwater ruins at Apollonia made by divers in 1958-1959
Apollonia, Cyrenaica
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Map of Apollonia
Apollonia, Cyrenaica
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Late apsidal building at Apollonia superimposed on earlier structures (grid square C4) drawn by divers in 1958-1959
Apollonia, Cyrenaica
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Theatre in Apollonia
28.
Alexander the Great
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Alexander III of Macedon, commonly known as Alexander the Great, was a king of the Ancient Greek kingdom of Macedon and a member of the Argead dynasty. He was born in Pella in 356 BC and succeeded his father Philip II to the throne at the age of twenty and he was undefeated in battle and is widely considered one of historys most successful military commanders. During his youth, Alexander was tutored by Aristotle until the age of 16, after Philips assassination in 336 BC, he succeeded his father to the throne and inherited a strong kingdom and an experienced army. Alexander was awarded the generalship of Greece and used this authority to launch his fathers Panhellenic project to lead the Greeks in the conquest of Persia, in 334 BC, he invaded the Achaemenid Empire and began a series of campaigns that lasted ten years. Following the conquest of Anatolia, Alexander broke the power of Persia in a series of battles, most notably the battles of Issus. He subsequently overthrew Persian King Darius III and conquered the Achaemenid Empire in its entirety, at that point, his empire stretched from the Adriatic Sea to the Indus River. He sought to reach the ends of the world and the Great Outer Sea and invaded India in 326 BC and he eventually turned back at the demand of his homesick troops. Alexander died in Babylon in 323 BC, the city that he planned to establish as his capital, without executing a series of planned campaigns that would have begun with an invasion of Arabia. In the years following his death, a series of civil wars tore his empire apart, resulting in the establishment of several states ruled by the Diadochi, Alexanders surviving generals, Alexanders legacy includes the cultural diffusion which his conquests engendered, such as Greco-Buddhism. He founded some twenty cities that bore his name, most notably Alexandria in Egypt, Alexander became legendary as a classical hero in the mold of Achilles, and he features prominently in the history and mythic traditions of both Greek and non-Greek cultures. He became the measure against which military leaders compared themselves, and he is often ranked among the most influential people in human history. He was the son of the king of Macedon, Philip II, and his wife, Olympias. Although Philip had seven or eight wives, Olympias was his wife for some time. Several legends surround Alexanders birth and childhood, sometime after the wedding, Philip is said to have seen himself, in a dream, securing his wifes womb with a seal engraved with a lions image. Plutarch offered a variety of interpretations of dreams, that Olympias was pregnant before her marriage, indicated by the sealing of her womb. On the day Alexander was born, Philip was preparing a siege on the city of Potidea on the peninsula of Chalcidice. That same day, Philip received news that his general Parmenion had defeated the combined Illyrian and Paeonian armies, and it was also said that on this day, the Temple of Artemis in Ephesus, one of the Seven Wonders of the World, burnt down. This led Hegesias of Magnesia to say that it had burnt down because Artemis was away, such legends may have emerged when Alexander was king, and possibly at his own instigation, to show that he was superhuman and destined for greatness from conception
Alexander the Great
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"Alexander fighting king
Darius III of Persia ",
Alexander Mosaic,
Naples National Archaeological Museum.
Alexander the Great
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Bust of a young Alexander the Great from the Hellenistic era,
British Museum
Alexander the Great
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Aristotle tutoring Alexander, by
Jean Leon Gerome Ferris
Alexander the Great
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Philip II of Macedon, Alexander's father.
29.
Ptolemy I Soter
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Ptolemy I Soter I, also known as Ptolemy Lagides, was a Macedonian Greek general under Alexander the Great, one of the three Diadochi who succeeded to his empire. Ptolemy became ruler of Egypt and founded a dynasty which ruled it for the three centuries, turning Egypt into a Hellenistic kingdom and Alexandria into a center of Greek culture. He assimilated some aspects of Egyptian culture, however, assuming the title pharaoh in 305/4 BC. The use of the title of pharaoh was often situational, pharaoh was used for an Egyptian audience, like all Macedonian nobles, Ptolemy I Soter claimed descent from Heracles, the mythical founder of the Argead dynasty that ruled Macedon. Ptolemy was one of Alexanders most trusted generals, and was among the seven somatophylakes attached to his person and he was a few years older than Alexander and had been his intimate friend since childhood. He was succeeded by his son Ptolemy II Philadelphus, Ptolemy served with Alexander from his first campaigns, and played a principal part in the later campaigns in Afghanistan and India. Ptolemy had his first independent command during the campaign against the rebel Bessus whom Ptolemy captured and handed over to Alexander for execution. During Alexanders campaign in the Indian subcontinent Ptolemy was in command of the guard at the siege of Aornos. When Alexander died in 323 BC, Ptolemy is said to have instigated the resettlement of the made at Babylon. Ptolemy quickly moved, without authorization, to subjugate Cyrenaica, by custom, kings in Macedonia asserted their right to the throne by burying their predecessor. Ptolemy then openly joined the coalition against Perdiccas, Perdiccas appears to have suspected Ptolemy of aiming for the throne himself, and may have decided that Ptolemy was his most dangerous rival. Ptolemy executed Cleomenes for spying on behalf of Perdiccas — this removed the check on his authority. In 321 BC, Perdiccas attempted to invade Egypt only to fall at the hands of his own men, Ptolemys decision to defend the Nile against Perdiccass attempt to force it ended in fiasco for Perdiccas, with the loss of 2000 men. This failure was a blow to Perdiccas reputation, and he was murdered in his tent by two of his subordinates. Ptolemy immediately crossed the Nile, to provide supplies to what had the day before been an enemy army, Ptolemy was offered the regency in place of Perdiccas, but he declined. Ptolemy was consistent in his policy of securing a power base and his first occupation of Syria was in 318, and he established at the same time a protectorate over the petty kings of Cyprus. When Antigonus One-Eye, master of Asia in 315, showed dangerous ambitions, Ptolemy joined the coalition against him, in Cyprus, he fought the partisans of Antigonus, and re-conquered the island. A revolt in Cyrene was crushed the same year, in 312, Ptolemy and Seleucus, the fugitive satrap of Babylonia, both invaded Syria, and defeated Demetrius Poliorcetes, the son of Antigonus, in the Battle of Gaza
Ptolemy I Soter
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Bust of Ptolemy I in the
Louvre Museum
Ptolemy I Soter
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Ptolemy as Pharaoh of Egypt, British Museum,
London.
Ptolemy I Soter
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The taking of Jerusalem by Ptolemy Soter ca. 320 BC, by
Jean Fouquet.
Ptolemy I Soter
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A rare coin of Ptolemy I, a reminder of his successful campaigns with Alexander in India. Obv: Ptolemy in profile at the beginning of his reign. Rev: Alexander triumphantly riding a chariot drawn by elephants.
30.
Ptolemaic Kingdom
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The Ptolemaic Kingdom was a Hellenistic kingdom based in Egypt. Alexandria became the city and a major center of Greek culture. To gain recognition by the native Egyptian populace, they named themselves the successors to the Pharaohs, the later Ptolemies took on Egyptian traditions by marrying their siblings, had themselves portrayed on public monuments in Egyptian style and dress, and participated in Egyptian religious life. The Ptolemies had to fight native rebellions and were involved in foreign and civil wars led to the decline of the kingdom. Hellenistic culture continued to thrive in Egypt throughout the Roman and Byzantine periods until the Muslim conquest. The era of Ptolemaic reign in Egypt is one of the most well documented periods of the Hellenistic Era. In 332 BC, Alexander the Great, King of Macedon invaded the Achaemenid satrapy of Egypt and he visited Memphis, and traveled to the oracle of Amun at the Oasis of Siwa. The oracle declared him to be the son of Amun, the wealth of Egypt could now be harnessed for Alexanders conquest of the rest of the Persian Empire. Early in 331 BC he was ready to depart, and led his forces away to Phoenicia and he left Cleomenes as the ruling nomarch to control Egypt in his absence. Following Alexanders death in Babylon in 323 BC, a crisis erupted among his generals. Perdiccas appointed Ptolemy, one of Alexanders closest companions, to be satrap of Egypt, Ptolemy ruled Egypt from 323 BC, nominally in the name of the joint kings Philip III and Alexander IV. However, as Alexander the Greats empire disintegrated, Ptolemy soon established himself as ruler in his own right, Ptolemy successfully defended Egypt against an invasion by Perdiccas in 321 BC, and consolidated his position in Egypt and the surrounding areas during the Wars of the Diadochi. In 305 BC, Ptolemy took the title of King, as Ptolemy I Soter, he founded the Ptolemaic dynasty that was to rule Egypt for nearly 300 years. All the male rulers of the dynasty took the name Ptolemy, while princesses and queens preferred the names Cleopatra, Arsinoe and Berenice. Because the Ptolemaic kings adopted the Egyptian custom of marrying their sisters, many of the kings ruled jointly with their spouses and this custom made Ptolemaic politics confusingly incestuous, and the later Ptolemies were increasingly feeble. The only Ptolemaic Queens to officially rule on their own were Berenice III, Cleopatra V did co-rule, but it was with another female, Berenice IV. Cleopatra VII officially co-ruled with Ptolemy XIII Theos Philopator, Ptolemy XIV, and Ptolemy XV, upper Egypt, farthest from the centre of government, was less immediately affected, even though Ptolemy I established the Greek colony of Ptolemais Hermiou to be its capital. But within a century Greek influence had spread through the country, nevertheless, the Greeks always remained a privileged minority in Ptolemaic Egypt
Ptolemaic Kingdom
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Eagle of Zeus
Ptolemaic Kingdom
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Bust of
Ptolemy I Soter, king of Egypt (305 BC–282 BC) and founder of the Ptolemaic dynasty
Ptolemaic Kingdom
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A bust depicting King
Ptolemy II Philadelphus 309–246 BCE
