1.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, change. There is a range of views among philosophers as to the exact scope and definition of mathematics. Mathematicians use them to formulate new conjectures. Mathematicians resolve the falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of logic, mathematics developed from counting, calculation, measurement, the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Galileo Galilei said, "The universe can not become familiar with the characters in which it is written. Without these, one is wandering about in a dark labyrinth." Carl Friedrich Gauss referred as "the Queen of the Sciences". Benjamin Peirce called mathematics "the science that draws necessary conclusions". David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules.
Mathematics
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Euclid (holding calipers), Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.
Mathematics
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Greek mathematician Pythagoras (c. 570 – c. 495 BC), commonly credited with discovering the Pythagorean theorem
Mathematics
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Leonardo Fibonacci, the Italian mathematician who established the Hindu–Arabic numeral system to the Western World
Mathematics
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Carl Friedrich Gauss, known as the prince of mathematicians
2.
Ancient Egypt
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It is one of six civilizations to arise independently. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh Narmer. In the aftermath of Alexander one of his generals, Ptolemy Soter, established himself as the new ruler of Egypt. This Greek Ptolemaic Kingdom ruled Egypt until 30 BC, when, under Cleopatra, it became a Roman province. The success of Egyptian civilization came partly from its ability to adapt to the conditions of the Nile River valley for agriculture. The predictable flooding and controlled irrigation of the fertile valley produced surplus crops, which supported social development and culture. Egypt left a lasting legacy. Its antiquities carried off to far corners of the world. Its monumental ruins have inspired the imaginations of writers for centuries. The Nile has been the lifeline of its region for much of human history. Nomadic human hunter-gatherers began living in the Nile valley through the end of the Middle Pleistocene some 120,000 years ago. In Predynastic and Early Dynastic times, the Egyptian climate was much less arid than it is today. Large regions of Egypt were traversed by herds of grazing ungulates. The Nile region supported large populations of waterfowl. This is also the period when many animals were first domesticated.
Ancient Egypt
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The Great Sphinx and the pyramids of Giza are among the most recognizable symbols of the civilization of ancient Egypt.
Ancient Egypt
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A typical Naqada II jar decorated with gazelles. (Predynastic Period)
Ancient Egypt
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The Narmer Palette depicts the unification of the Two Lands.
3.
Abydos, Egypt
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It is located about 11 kilometres west of the Nile at latitude 26 ° 10' N, near the Egyptian towns of el - ` Araba el Madfuna and al-Balyana. In the Egyptian language, the city was called Abdju. The English name Abydos comes from the Greek Ἄβυδος, a name borrowed by Greek geographers on the Hellespont. It is a chronological list showing cartouches of most dynastic pharaohs of Egypt from Menes until Seti I's father, Ramesses I. Most of the ancient town are buried under the modern buildings to the north of the Seti temple. Many of the artifacts within them are considered irretrievable and lost; many may have been destroyed by the new construction. Abydos was occupied by the rulers of the Predynastic period, whose town, temple and tombs have been found there. The cemetery was used continuously. The pharaohs of the first dynasty were buried including Narmer, regarded as founder of the first dynasty, his successor, Aha. It was in this period that the Abydos boats were constructed. Some pharaohs of the second dynasty were also buried in Abydos. The temple was enlarged by these pharaohs as well. From the fifth dynasty, foremost of the Westerners, came to be seen as a manifestation of the dead pharaoh in the underworld. Abydos became the centre of the worship of the Isis and Osiris cult. Khentiamentiu's name became an epithet of Osiris.
Abydos, Egypt
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Façade of the Temple of Seti I in Abydos
Abydos, Egypt
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Part of the Abydos King List
Abydos, Egypt
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Tomb relief depicting the vizier Nespeqashuty and his wife, KetjKetj, making the journey of the dead to the holy city of Abydos – from Deir el-Bahri, Late Period, twenty-sixth dynasty of Egypt, reign of Psammetichus I
Abydos, Egypt
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Panel from the Osiris temple: Horus presents royal regalia to a worshipping pharaoh.
4.
Narmer Macehead
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The Narmer macehead is an ancient Egyptian decorative stone mace head. It was found during a dig at the site of Hierakonpolis. It is dated to the Early Dynastic reign of king Narmer whose serekh is engraved on it. The macehead is now kept at the Ashmolean Museum, Oxford. The Narmer macehead has had various interpretations. Directly in front of him is another dais or possibly litter on which sits facing a cloaked figure. This figure has been interpreted as a princess being presented to the king for marriage, a deity. Behind it are three registers. In the center register attendants are running behind the dais. Behind the enclosure four standard-bearers approach the throne. In front of the fan-bearers, are seen what looks like a collection of offerings. He is followed by a man carrying a long pole. Above him three men are walking, two of them likewise carrying long poles. The serekh displaying the signs for Narmer can be seen above these. The top field to the right of the field shows a building, perhaps a shrine, with a heron perched on its roof.
Narmer Macehead
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Narmer Macehead Centre left: Pharaoh Narmer seated in a naos
5.
Old Kingdom
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The Old Kingdom is most commonly regarded through to the Sixth Dynasty. Many Egyptologists also include the Memphite Seventh and Eighth Dynasties in the Old Kingdom as a continuation of the administration centralized at Memphis. During the Old Kingdom, the king of Egypt became a living god who could demand the services and wealth of his subjects. A new era of building was initiated under his reign. King Djoser's architect, Imhotep is credited with the development of building with the conception of the new architectural form -- the Step Pyramid. Indeed, the Old Kingdom is perhaps best known for the large number of pyramids constructed at this time as pharaonic burial places. For this reason, the Old Kingdom is frequently referred to as "the Age of the Pyramids." The first king of the Old Kingdom was Djoser of the third dynasty, who ordered the construction of a pyramid in Saqqara. An important person during the reign of Djoser was his vizier, Imhotep. It was in this era that formerly independent Egyptian states became known as nomes, under the rule of the pharaoh. The former rulers were forced to assume the role of governors or otherwise work in collection. Egyptians in this era worshipped their pharaoh as a god, believing that he ensured the annual flooding of the Nile, necessary for their crops. They also perceived themselves as a specially selected people. Its royal power reached a zenith under the Fourth Dynasty, which began with Sneferu. However, the full development of the style of building was reached not at Saqqara, but during the building of the "great pyramids" at Giza.
Old Kingdom
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During the Old Kingdom of Egypt (circa 2686 B.C.E. — circa 2181 B.C.E.), Egypt consisted of the Nile River region and the area along the river south to Elephantine.
Old Kingdom
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The Pyramid of Djoser at Saqqara.
Old Kingdom
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Temple of Djoser at Saqqara
6.
Mastaba
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These edifices marked the burial sites of eminent Egyptians during Egypt's Early Dynastic Period and Old Kingdom. Egyptologists call these tombs mastaba, the Arabic word for bench. The afterlife ruled every aspect of the society. This is reflected prominently by the enormous amounts of time, money, manpower involved in the building of their tombs. Ancient Egyptians believed the soul could live only if the body was depredation as well as fed. The Ancient Egyptians initially began by burying their dead in pit graves dug out from the sand. The body of the deceased was buried usually along with some items believed to help them in the afterlife. The first structure that the Egyptians built was the mastaba. Mastabas provided better protection from grave robbers. However, the human remains were not in contact with the dry sand, so natural mummification could not take place. Use of the more secure mastabas required Ancient Egyptians to devise a system of artificial mummification. Until at least First Intermediate Period, only high officials and royalty would be buried in these mastabas. When seen from a distance a mastaba does resemble a bench. Historians speculate that the Egyptians may have borrowed architectural ideas from Mesopotamia since at the time they were both building similar structures. The above-ground structure of a mastaba is rectangular with inward-sloping sides and a flat roof.
Mastaba
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Example of a mastaba
7.
Meidum
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Meidum or Maidum is an archaeological site in Lower Egypt. It contains several mud-brick mastabas. The area is located around 62 miles south of modern Cairo. The pyramid at Meidum was continued by Sneferu. The architect was a successor to the inventor of the stone built pyramid. Because of its unusual appearance, the pyramid is called el-heram el-kaddaab — in Egyptian Arabic. The second extension turned the original step pyramid design by filling in the steps with limestone encasing. While this approach is consistent with the design of the true pyramids, Meidum was affected by construction errors. Firstly, the outer layer was founded like the inner layers. Secondly, the inner step pyramids had been designed as the final stage. The platforms of the steps were not horizontal, but fell off to the outside. There are a number of facts contradicting this theory. The Meidum Pyramid seems never to have been completed. Beginning to the 12th dynasty all pyramids had a valley temple, missing at Meidum. The mortuary temple, found under the rubble at the base of the pyramid, never was finished.
Meidum
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View of the Pyramid
Meidum
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Lantern Slide Collection: Views, Objects: Egypt. Meidum. Old Kingdom. Step Pyramid of Meidum, 4th Dyn., n.d. Brooklyn Museum Archives
Meidum
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Passageway in the Meidum Pyramid
Meidum
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Another view of Meidum Pyramid
8.
Cubit
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The cubit is an ancient unit based on the forearm length from the middle finger tip to the elbow bottom. Cubits of various lengths were employed in many parts of the world in antiquity, during the Middle Ages and as recently Early Modern Times. The term is still used in the length of the forearm being frequently used to determine the interval between stakes placed within the hedge. The Egyptian royal cubit is the earliest attested standard measure. Cubit rods were used for the measurement of length. Fourteen such rods, including one cubit rod, were described and compared by Lepsius in 1865. The bar dates from c. 2650 BC and Unger claimed it was used as a standard. This irregularly formed and irregularly marked rule supposedly defined the Sumerian cubit as about 518.6 mm. The Near Eastern or Biblical cubit is usually estimated as approximately 457.2 mm. The Greek cubit, called a pēchys, measured approximately 462.4 mm. The short cubit from the wrist to the elbow, called the pygmē, measured approximately 345.4 mm. According to Vitruvius, a cubit was equal to 1 1⁄2 Roman feet or 6 palm widths. A cubit arm in heraldry may be sinister. It may be vested and may be shown in various positions, most commonly erect, but also fesswise, is often shown grasping objects. It is most often used erect by the families of Poyntz of Iron Acton Rolle of Stevenstone and Turton.
Cubit
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Egyptian cubit rod in the Liverpool World Museum
Cubit
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Cubit rod of Maya, 1336-1327 BC (Eighteenth Dynasty)
Cubit
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Cubit rod from the Turin Museum.
Cubit
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The Nippur cubit-rod in the Archeological Museum of Istanbul, Turkey
9.
Ancient Egyptian units of measurement
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Ancient Egyptian units of measure include units for length, area and volume. Units of length date back to at least the Early Dynastic Period. In the Palermo stone, for instance, the level of the Nile river is recorded. During the reign of Pharaoh Djer the height of the Nile was given as measuring 1 palm. This is equivalent to approximately 3.2 m. A third dynasty diagram shows how to construct an elliptical vault using simple measures along an arc. The ostracon depicting this diagram was found in the area of the Step Pyramid in Saqqara. The height of the curve is given in each of the sections. Fourteen such rods, including one cubit rod, were compared by Lepsius in 1865. Two examples are known from the tomb of Maya – the treasurer of Tutankhamun – in Saqqara. Another was found in the tomb of Kha in Thebes. A scene in the tomb of Menna in Thebes shows surveyors measuring a plot of land using rope with knots tied at regular intervals. Similar scenes can be found in the tombs of Amenhotep-Sesi, Khaemhat and Djeserkareseneb. The balls of rope are also shown in New Kingdom statues of officials such as Senenmut, Amenemhet-Surer and Penanhor. The records of areas of land date back to the early dynastic period.
Ancient Egyptian units of measurement
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Cubit rod from the Turin Museum.
Ancient Egyptian units of measurement
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Problem 80 on the Rhind Mathematical Papyrus
10.
Moscow Mathematical Papyrus
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Golenishchev bought the papyrus in 1892 or 1893 in Thebes. It later entered the collection of the Pushkin State Museum of Fine Arts in Moscow, where it remains today. It is a mathematical papyrus along with the Rhind Mathematical Papyrus. The Moscow Mathematical Papyrus is older than the Rhind Mathematical Papyrus, while the latter is the larger of the two. The papyrus is well known for some of its geometry problems. Problems 10 and 14 compute a surface area and the volume of a frustum respectively. The remaining problems are more common in nature. 3 are ship's part problems. Aha problems involve finding unknown quantities if the sum of the part of it are given. The Rhind Mathematical Papyrus also contains four of these type of problems. Problems 1, 25 of the Moscow Papyrus are Aha problems. For problem 19 asks one to calculate a quantity taken 1 and 1/2 times and added to 4 to make 10. The pefsu number is mentioned in many offering lists. Calculate 1/2 of the result will be 2 1/2 Take this 2 1/2 four times The result is 10. Then you say to him: "Behold!
Moscow Mathematical Papyrus
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14th problem of the Moscow Mathematical Papyrus (V. Struve, 1930)
Moscow Mathematical Papyrus
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The neutrality of this article is disputed. Relevant discussion may be found on the talk page. Please do not remove this message until the dispute is resolved. (July 2015)
11.
Kahun Papyri
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The Kahun Papyri are a collection of ancient Egyptian texts discussing administrative, mathematical and medical topics. Its many fragments are kept at the University College London. This collection of papyri is one of the largest ever found. Most of the texts are dated to ca. 1825 BC, to the reign of Amenemhat III. In general the collection spans the Middle Kingdom of Egypt. The texts span a variety of topics: Business papers of the cult of Senusret II Hymns to king Senusret III. The Kahun Gynaecological Papyrus, which deals with gynaecological illnesses and conditions. Legon PlanetMath: Kahun Papyrus and Arithmetic Progressions
Kahun Papyri
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Fragments of the Kahun Papyrus on veterinary medicine
12.
Berlin Papyrus 6619
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The two readable fragments were published by Hans Schack-Schackenburg in 1902. The papyrus is one of the primary sources of Egyptian mathematics. The Berlin Papyrus contains two problems, the first stated as "the area of a square of 100 is equal to that of two smaller squares. The side of one is + 1/4 the side of the other." Papyrology Timeline of mathematics Egyptian fraction Simultaneous equation examples from the Berlin papyrus Two algebra problems compared to RMP algebra Two suggested solutions
Berlin Papyrus 6619
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Berlin Papyrus 6619, as reproduced in 1900 by Schack-Schackenburg
13.
Rhind Mathematical Papyrus
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The Rhind Mathematical Papyrus is one of the best known examples of Egyptian mathematics. It dates to around BC. It is one of the two well-known Mathematical Papyri along with the Moscow Mathematical Papyrus. The Rhind Papyrus is larger than the Moscow Mathematical Papyrus, while the latter is older than the former. The Rhind Mathematical Papyrus dates to the Second Intermediate Period of Egypt. It was copied from a now-lost text from the reign of king Amenemhat III. Written in the hieratic script, this Egyptian manuscript consists of multiple parts which in total make it over 5m long. The papyrus began to be mathematically translated in the late 19th century. The mathematical aspect remains incomplete in several respects. The Ahmose writes this copy. A handful of these stand out. A more recent overview of the Rhind Papyrus was published by Robins and Shute. The first part of the Rhind papyrus consists of a collection of 21 arithmetic and 20 algebraic problems. The problems start out followed by completion problems and more involved linear equations. The first part of the papyrus is taken up by the 2/n table.
Rhind Mathematical Papyrus
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A portion of the Rhind Papyrus
Rhind Mathematical Papyrus
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Building
14.
Second Intermediate Period
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It is best known as the period when the Hyksos made their appearance in Egypt and whose reign comprised the Fifteenth dynasty. The Twelfth Dynasty of Egypt came to an end at the end of the 19th century BCE with the death of Queen Sobekneferu. Retaining the seat of the twelfth dynasty, the thirteenth dynasty ruled from Itjtawy near Memphis and Lisht, just south of the apex of the Nile Delta. The Thirteenth Dynasty is notable for the accession of the first formally recognised Semitic-speaking king, Khendjer. The Fifteenth Dynasty dates approximately from 1650 to 1550 BC. Known rulers of the Fifteenth Dynasty are as follows: Salitis Sakir-Har Khyan Apophis, c. 1590? BC-1550 BC Khamudi, c. 1550-1540 BC The Fifteenth Dynasty of Egypt was the first Hyksos dynasty, ruled from Avaris, without control of the entire land. The Hyksos preferred to stay in northern Egypt since they infiltrated from the north-east. The names and order of kings is uncertain. The Turin King list indicates that there were six Hyksos kings, with an obscure Khamudi listed as the final king of the Fifteenth Dynasty. This is also supported by the fact that this king employed a third prenomen during his reign: Nebkhepeshre. Apepi likely employed several different prenomens throughout various periods of his reign. The Sixteenth Dynasty ruled the Theban region in Upper Egypt for 70 years. Of the two chief versions of Manetho's Aegyptiaca, Dynasty XVI is described as Theban.
Second Intermediate Period
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The political situation in the Second Intermediate Period of Egypt (circa 1650 B.C.E. — circa 1550 B.C.E.) Thebes was briefly conquered by the Hyksos circa 1580 B.C.E.
Second Intermediate Period
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Thebes (Luxor Temple pictured) was the capital of many of the Dynasty XVI pharaohs.
15.
Ancient Egyptian
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It is one of six civilizations to arise independently. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh Narmer. In the aftermath of Alexander one of his generals, Ptolemy Soter, established himself as the new ruler of Egypt. This Greek Ptolemaic Kingdom ruled Egypt until 30 BC, when, under Cleopatra, it became a Roman province. The success of Egyptian civilization came partly from its ability to adapt to the conditions of the Nile River valley for agriculture. The predictable flooding and controlled irrigation of the fertile valley produced surplus crops, which supported social development and culture. Egypt left a lasting legacy. Its antiquities carried off to far corners of the world. Its monumental ruins have inspired the imaginations of writers for centuries. The Nile has been the lifeline of its region for much of human history. Nomadic human hunter-gatherers began living in the Nile valley through the end of the Middle Pleistocene some 120,000 years ago. In Predynastic and Early Dynastic times, the Egyptian climate was much less arid than it is today. Large regions of Egypt were traversed by herds of grazing ungulates. The Nile region supported large populations of waterfowl. This is also the period when many animals were first domesticated.
Ancient Egyptian
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The Great Sphinx and the pyramids of Giza are among the most recognizable symbols of the civilization of ancient Egypt.
Ancient Egyptian
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A typical Naqada II jar decorated with gazelles. (Predynastic Period)
Ancient Egyptian
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The Narmer Palette depicts the unification of the Two Lands.
16.
Egyptian fraction
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An Egyptian fraction is a finite sum of distinct unit fractions, such as 1 2 + 1 3 + 1 16. The value of an expression of this type is a positive rational a/b; for instance the Egyptian fraction above sums to 43/48. Every rational number can be represented by an Egyptian fraction. In mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation. Beyond their historical use, Egyptian fractions have some practical advantages over other representations of fractional numbers. For instance, Egyptian fractions can help in dividing a number of objects into equal shares. For more information on this subject, see Egyptian numerals, Egyptian mathematics. Egyptian notation was developed in the Middle Kingdom of Egypt, altering the Old Kingdom's Eye of Horus numeration system. The Rhind Mathematical Papyrus, introduced improved ways of writing Egyptian fractions. Solutions to each problem were written out with the final answers of all 84 problems being expressed in Egyptian fraction notation. 2/n tables similar to the one on the Rhind papyrus also appear on some of the other texts. However, as the Kahun Papyrus shows, vulgar fractions were also used by scribes within their calculations. Similarly in hieratic script they drew a line over the letter representing the number. These have been called "Horus-Eye fractions" after a theory that they were based on the parts of the Eye of Horus symbol. In particular, study in this area has concentrated on understanding the tables of expansions for numbers of the 2/n in the Rhind papyrus.
Egyptian fraction
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Eye of Horus
17.
New Kingdom
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Radiocarbon dating places the exact beginning of the New Kingdom between 1570–1544 BC. The New Kingdom was succeeded by the Third Intermediate Period. It marked the peak of its power. The later part of this period, under the Nineteenth and Twentieth Dynasties is also known as the Ramesside period. It is named after the eleven pharaohs that took the name of founder of the 19th Dynasty. Egyptian armies fought Hittite armies for control of modern-day Syria. The Eighteenth Dynasty contained some of Egypt's most famous Pharaohs, including Ahmose I, Hatshepsut, Thutmose III, Amenhotep III, Tutankhamun. Queen Hatshepsut concentrated on expanding Egypt's external trade by sending a commercial expedition to the land of Punt. Thutmose III wielded it with great success to consolidate the empire created by his predecessors. This resulted during the reign of Amenhotep III. During the reign of Thutmose III, Pharaoh, originally referring to the king's palace, became a form of address for the person, king. Akhenaten's religious fervor is cited as the reason why he was subsequently written out of Egyptian history. Under his reign, in the 14th BC, Egyptian art flourished and attained an unprecedented level of realism. Towards the end of the 18th Dynasty, the situation had changed radically. Ramesses II sought to recover territories in the Levant, held by the 18th Dynasty.
New Kingdom
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New Kingdom at its maximum territorial extent in the 15th century BC.
New Kingdom
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Relief of a Nobleman, ca. 1295-1070 B.C.E. Brooklyn Museum
New Kingdom
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Queen Ahmose-Nefertari
18.
Papyrus Anastasi I
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Papyrus Anastasi I is an ancient Egyptian papyrus containing a satirical text used for the training of scribes during the Ramesside Period. This papyrus is important to Bible scholars above all for the information it supplies about towns in Syria and Canaan during the New Kingdom. The border lands of Egypt's province of Caanan with Kadesh are defined in the Gardiner p. 19. Hori goes on to show that Amenemope is not skilled in the role of a maher. Hori then relates what appears to be an actual anecdote for which Amenemope is apparently infamous. It contains a lot of detail comparing him to Qedjerdi, the chief of Isser. This touches amongst the scribes for which the idiom is "Much in the mouths of." Amenemope gets ambushed possibly at a battle in the campaigns against Kadesh which go on throughout the 18th and 19th dynasties. Hori makes clear that these involve routes that should be well known to scouts in the battles. Illustrations from the battle of Kadesh provide an excellent background for Hori's tale showing the size of the Shashu. Amenemope's lack of experience causes him not to be apprehensive when he should be and then panicking when he should remain calm. Amenmope's chariot is on a narrow pass above a ravine in which some four or five cubit tall Shashu are lurking. The Shashu look dangerous and fierce. Amenmope has to cut it loose with a knife from some trees it is tangled up in. He cuts himself trying to get the traces free of the branches.
Papyrus Anastasi I
19.
Ramesses III
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His long reign saw the decline of Egyptian economic power, linked to a series of invasions and internal economic problems. Ramesses III was the son of Setnakhte and Queen Tiy-Merenese. He was probably murdered by an assassin in a conspiracy led by one of his secondary wives, her son Pentaweret. Ramesses' two main names transliterate as wsr-mꜢʿt-rʿ–mry-ỉmn rʿ-ms-s–ḥḳꜢ-ỉwnw. They are normally realised as Usermaatre-meryamun Ramesse-hekaiunu, meaning "Beloved of Amun, Born of Ra, Ruler of Heliopolis". Ramses III had haplogroup E1b1a. Ramesses III is believed to have reigned to April 1155 BC. Alternate dates for his reign are 1187 to 1156 BC. In Year 8 of his reign, the Sea Peoples, including Tjekker, invaded Egypt by land and sea. Ramesses III defeated them in two great sea battles. Although the Egyptians had a reputation as poor seamen, they fought tenaciously. Then, the Egyptian navy attacked using grappling hooks to haul in the enemy ships. In the hand-to-hand fighting which ensued, the Sea People were utterly defeated. The Harris Papyrus states: As for those who reached my frontier, their seed is not, their soul are finished forever and ever. Ramesses III was also compelled to fight invading Libyan tribesmen in two major campaigns in Egypt's Western Delta in his Year Year 11 respectively.
Ramesses III
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Relief from the sanctuary of the Temple of Khonsu at Karnak depicting Ramesses III
Ramesses III
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Ramses III offering incense, wall painting in KV11.
Ramesses III
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Osirid statues of Ramses III at his temple in Karnak (in the first courtyard of the Great Temple of Amun).
Ramesses III
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Red granite sarcophagus of Ramesses III (Louvre)
20.
Deir el-Medina
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During the Christian era, the temple of Hathor was converted into a church from which the Arabic el-Medina is derived. This work has resulted in one of the most thoroughly documented accounts of life in the ancient world that spans almost hundred years. There is no comparable site in which social interactions, living conditions of a community can be studied in such detail. The site is located on the west bank of the Nile, across the river from modern-day Luxor. The archaeological site was first seriously excavated by Ernesto Schiaparelli between 1905–1909 which uncovered large amounts of ostraca. A French team directed by Bernard Bruyère excavated the entire site, including village, dump and cemetery, between 1922–1951. Around thousand ostraca of assorted works of literature were found in a well close to the village. The peak overlooking the village was renamed "Mont Cernabru" in recognition of Černý and Bruyère's work on the village. The main road through the village may have been covered to shelter the villagers from the intense glare and heat of the sun. The size of the habitations varied, with an average floor space of 70 m2, but the same construction methods were used throughout the village. Walls were made of mudbrick, built on top of stone foundations. A wooden front door might have carried the occupants name. Houses consisted of four to five rooms comprising an entrance, main room, staircase leading to the roof. The full glare of the sun was avoided by situating the windows high up on the walls. The main room contained a platform with steps which may have been used as a birthing bed.
Deir el-Medina
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Ruins of Deir el-Medina. A UNESCO World Heritage Site
Deir el-Medina
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Statue from the intact Tomb of Kha and Merit (Turin Museum)
Deir el-Medina
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Ra slays Apep (tomb scene in Deir el-Medina)
Deir el-Medina
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A worker's tomb
21.
Ostracon
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An ostracon is a piece of pottery, usually broken off from a vase or other earthenware vessel. In an epigraphical context, ostraca refer to sherds or even small pieces of stone that have writing scratched into them. In Classical Athens, the public would write or scratch the name of a person in the sherd of pottery. Anything with a smooth surface could be used as a surface. The importance of ostraca for Egyptology is immense. The combination of the Egyptian climate have preserved texts, from the medical to the mundane, which in other cultures were lost. These can often serve than literary treatises preserved in libraries. The many ostraca found at Deir el-Medina provide a deeply compelling view into the medical workings of the New Kingdom. The ostraca from Deir el-Medina also differed in their circulation. From Bryan Emery excavated at Saqqara in search of Imhotep's tomb; instead, the extensive catacombs of animal mummies were uncovered. Apparently it was a site, with as many as 1 1/2 million ibis birds interred. This 2nd-century BC site contained extensive debris from the site offerings of the pilgrims. Emery's excavations uncovered the "Ostraca", created by a scribe named Hor of Sebennytos. He transferred his divinely-inspired dreams onto ostraca. The Dream Ostraca are 65 Demotic texts written on limestone.
Ostracon
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Ostrakon of Cimon, an Athenian statesman, showing his name (as "Kimon [son] of Miltiades")
Ostracon
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Ostrakon of Megacles, son of Hippocrates (inscription: ΜΕΓΑΚΛΕΣ ΗΙΠΠΟΚΡΑΤΟΣ), 487 BC. On display in the Ancient Agora Museum in Athens, housed in the Stoa of Attalus
Ostracon
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Voting ostraca (for ostracism, Ancient Greece)
Ostracon
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One of four official letters to vizier Khay copied onto a limestone ostracon, in Egyptian Hieratic
22.
Ahmes
Ahmes
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A portion of the Rhind Mathematical Papyrus
23.
Middle Kingdom of Egypt
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Some scholars also include the Thirteenth Dynasty of Egypt wholly into this period as well, in which case the Middle Kingdom would finish c. 1650, while others only include it until Merneferre Ay c. 1700 BC, last king of this dynasty to be attested in both Upper and Lower Egypt. During the Middle Kingdom period, Osiris became the most important deity in popular religion. The period comprises the 11th Dynasty, which ruled from Thebes and the 12th Dynasty onwards, centered on el-Lisht. After the collapse of the Old Kingdom, Egypt entered a period of decentralization called the First Intermediate Period. Towards the end of this period, two rival dynasties, known as the Tenth and Eleventh, fought for power over the entire country. The Theban 11th Dynasty only ruled southern Egypt to the Tenth Nome of Upper Egypt. To the north, Lower Egypt was ruled by the 10th Dynasty from Herakleopolis. The struggle was to be concluded by Mentuhotep II, who ascended the Theban throne in 2055 B.C. During Mentuhotep II's fourteenth he took advantage of a revolt in the Thinite Nome to launch an attack on Herakleopolis, which met little resistance. For this reason, Mentuhotep II is regarded as the founder of the Middle Kingdom. Mentuhotep II commanded military campaigns south far as the Second Cataract in Nubia, which had gained its independence during the First Intermediate Period. He also restored Egyptian hegemony over the Sinai region, lost since the end of the Old Kingdom. Mentuhotep III was succeeded by Mentuhotep IV, whose name significantly is omitted from all Egyptian king lists. The Turin Papyrus claims after Mentuhotep III came "seven kingless years."
Middle Kingdom of Egypt
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An Osiride statue of the first pharaoh of the Middle Kingdom, Mentuhotep II
Middle Kingdom of Egypt
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The head of a statue of Senusret I.
Middle Kingdom of Egypt
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Statue head of Senusret III
24.
Egyptian numerals
–
The system of ancient Egyptian numerals was used in Ancient Egypt around 3000 BC until the early first millennium AD. The hieratic form of numerals stressed an exact finite series notation, ciphered one to one onto the Egyptian alphabet. For instance, a stone carving from Karnak shows the number 4622 as Egyptian hieroglyphs could be written in both directions. Rational numbers could also be expressed, but only as sums of unit fractions, i.e. sums of reciprocals of positive integers, except for 2⁄3 and 3⁄4. Instances of numerals written in hieratic can be found as far back as the Early Dynastic Period. The Old Kingdom Abusir Papyri are a particularly important corpus of texts that utilize hieratic numerals. A large number like 9999 could thus be written with only four signs—combining the signs for 9000, 900, 90, 9—as opposed to 36 hieroglyphs. Boyer saw the new hieratic numerals as ciphered, mapping one number onto one Egyptian letter for the first time in human history. Greeks adopted the new system, mapping their counting numbers onto two of their alphabets, the Doric and Ionian. In the oldest hieratic texts the individual numerals were clearly written in a ciphered relationship to the Egyptian alphabet. But during the Old Kingdom a series of standardized writings had developed for sign-groups containing more than one numeral, repeated as Roman numerals practiced. However, repetition of the same numeral for each place-value was not allowed in the hieratic script. As the hieratic writing system developed over time, these sign-groups were further simplified for quick writing; this process continued into Demotic as well. Two famous mathematical papyri using hieratic script are the Moscow Mathematical Papyrus and the Rhind Mathematical Papyrus. The majuscule letter "A" in some reconstructed forms means that the quality of that vowel remains uncertain: Ancient Egypt Egyptian language Egyptian mathematics Allen, James Paul.
Egyptian numerals
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Numeral systems
25.
Egyptian hieroglyphs
–
Egyptian hieroglyphs were the formal writing system used in Ancient Egypt. It combined alphabetic elements, with a total of some 1,000 distinct characters. Cursive hieroglyphs were used for religious literature on papyrus and wood. Egyptian scripts are derived from hieroglyphic writing; Meroitic was a late derivation from Demotic. The system continued to be used throughout the Late Period, well as the Persian and Ptolemaic periods. Late survivals of hieroglyphic use are found well into the Roman period, extending into the 4th century AD. The decipherment of hieroglyphs would only be solved with the help of the Rosetta Stone. The hieroglyph comes from a compound of ἱερός and γλύφω, supposedly a calque of an Egyptian phrase mdw · w-nṯr "god's words". The glyphs themselves were called τὰ ἱερογλυφικὰ γράμματα "the sacred engraved letters". The hieroglyph has become a noun in English, standing for an hieroglyphic character. As used in the previous sentence, the word hieroglyphic is an adjective, but hieroglyphic has also become a noun in English, at least in non-academic usage. Hieroglyphs emerged from the preliterate artistic traditions of Egypt. For example, symbols on Gerzean pottery from c. 4000 BC have been argued to resemble hieroglyphic writing. There are around 800 hieroglyphs dating back to New Kingdom Eras. By the Greco-Roman period, there are more than 5,000.
Egyptian hieroglyphs
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A section of the Papyrus of Ani showing cursive hieroglyphs.
Egyptian hieroglyphs
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Hieroglyphs on a funerary stela in Manchester Museum
Egyptian hieroglyphs
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The Rosetta Stone in the British Museum
Egyptian hieroglyphs
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Hieroglyphs typical of the Graeco-Roman period
26.
Hieratic
–
It is a cursive writing system used in the provenance of the pharaohs in Egypt and Nubia. Hieratic developed alongside cursive hieroglyphs, from which it is separate yet intimately related. Hieratic was primarily written with a reed brush on papyrus allowing scribes to write quickly without resorting to the time-consuming hieroglyphs. In the 2nd AD, the term hieratic was first used by Saint Clement of Alexandria. It can also be an adjective meaning "f or associated with sacred offices; sacerdotal." In the Proto-Dynastic Period of Egypt, hieratic first developed alongside the more formal hieroglyphic script. Hieratic is an error to view hieratic as a derivative of hieroglyphic writing. Indeed, the earliest texts from Egypt are produced with no indication their signs are descendants of hieroglyphs. Monumental hieroglyphs carved in stone did not appear until the 1st Dynasty, well after hieratic had been established as a scribal practice. The two writing systems, therefore, are parallel developments, rather than a single linear one. It was used into the Graeco-Roman Period. During the Græco-Roman period, when Demotic had become the administrative script, hieratic was limited primarily to religious texts. In general, hieratic was much more important than hieroglyphs throughout Egypt's history, being the script used in daily life. Hieratic was also the system first taught to students, knowledge of hieroglyphs being limited to a small minority who were given additional training. In fact, Hieratic is often possible to detect errors in hieroglyphic texts that came about due to a misunderstanding of an hieratic text.
Hieratic
–
One of four official letters to vizier Khay copied onto fragments of limestone (an ostracon).
Hieratic
–
Hieratic
Hieratic
–
Exercise tablet with hieratic excerpt from The Instructions of Amenemhat. Dynasty XVIII, reign of Amenhotep I, c. 1514–1493 BC. Text reads: "Be on your guard against all who are subordinate to you... Trust no brother, know no friend, make no intimates."
27.
Hobble (device)
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A hobble is a device that prevents or limits the locomotion of a human or an animal, by tethering one or more legs. Although hobbles are most commonly used on horses, they are sometimes used also on other animals. On dogs, they are used especially during force-fetch training to limit the movement of a dog's front paws when training it to stay still. They are made from leather, synthetic materials such as nylon or Neoprene. There are various designs for breeding, mounting horses. "Western" - horse hobbles are tied around the pasterns or cannon bones of the horse's front legs. This hobble is made with two rings, plus a buckle fastening. The twist hobble, made of soft leather or rope, with a twist between the horse's legs. The above patterns are unsuitable for training as they can tighten around a leg and injury. Hobbles also allow yet prevent the horse from running off too far. Hobble desensitizing a horse to accept restraints on its legs. This helps a horse accept pressure on its legs in case it ever becomes entangled in barbed fencing. Service hobbles usually fasten around a mare's hocks, pass between her front legs to a neck strap. They are used to protect a stallion from kicks. Casting hobbles are the same as the above, but with another strap attached to the other hind foot.
Hobble (device)
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A hobbled donkey in Sardinia
Hobble (device)
–
Hind leg pull up strap
Hobble (device)
–
Drovers' and cattle hobbles
Hobble (device)
–
Pacing hopples
28.
Neferetiabet
–
Nefertiabet was an ancient Egyptian princess of the 4th dynasty. She was possibly a daughter of Pharaoh Khufu. Her tomb at Giza is known. The mastaba is about 24.25 x 11.05 m. in size. A statue of her, now in Munich, probably originates from her tomb. She is best known from her beautiful stela, now in the Louvre. Nefertiabet is shown seated facing to right. She is depicted with a panther skin garment. Her right hand is extended to table. A table in front of her is piled with bread. Under the table offerings are on the right offerings of bread, beer, oryx, bull. On the right of the slab a list is depicted. The tomb originally contained one shaft which contained the burial of Nefertiabet. The shaft contains a chamber. Fragments of a white coffin with a flat lid were found.
Neferetiabet
–
Nefertiabet, stela
Neferetiabet
–
Nefertiabet's stela from her tomb in Giza.
29.
Louvre
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The Louvre or the Louvre Museum is the world's largest museum and a historic monument in Paris, France. A central landmark of the city, it is located in the city's 1st arrondissement. Nearly 35,000 objects from prehistory to the 21st century are exhibited over an area of 72,735 square metres. The Louvre is the world's second most visited museum after the Palace Museum in China, receiving more than million visitors in 2014. The museum is housed in the Louvre Palace, originally built under Philip II. Remnants of the fortress are visible in the basement of the museum. The building was extended many times to form the present Louvre Palace. The Académie remained for 100 years. During the French Revolution, the National Assembly decreed that the Louvre should be used as a museum to display the nation's masterpieces. The museum confiscated church property. Because of structural problems with the building, the museum was closed until 1801. During the Second French Empire the museum gained 20,000 pieces. Holdings have grown steadily since the Third Republic. Whether this was the first building on that spot is not known; it is possible that Philip modified an existing tower. According to the authoritative Grand Larousse encyclopédique, the name derives from an association with wolf den.
Louvre
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the Richelieu wing (2005)
Louvre
–
The only portion of the medieval Louvre still visible
Louvre
–
Antonio Canova 's Psyche Revived by Cupid's Kiss was commissioned in 1787, donated in 1824.
Louvre
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The Venus de Milo was added to the Louvre's collection during the reign of Louis XVIII.
30.
Predynastic Egypt
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This Predynastic era is traditionally equivalent to the Neolithic period, beginning c. 6000 BC and including the Protodynastic period. The Predynastic period is generally divided into cultural periods, each named after the place where a certain type of Egyptian settlement was first discovered. The Late Paleolithic in Egypt started around 30,000 BC. The Nazlet Khater skeleton was found in 1980 and dated in 1982 from nine samples ranging between 35,100 and 30,360 years. This specimen is the only complete modern human skeleton from the earliest Late Stone Age in Africa. Excavation of the Nile has exposed early stone tools. The earliest of these lithic industries were located within the 100-foot terrace, were Chellean, primitive Acheulean and an Egyptian form of the Clactonian. Within the 50-foot terrace was developed Acheulean. Originally reported as Early Mousterian but since changed to Levalloisean, other implements were located in the 30-foot terrace. The 15- and 10-foot terraces saw a more developed version of the Levalloisean, also initially reported as an Egyptian version of Mousterian. Finally, tools of the Egyptian Sebilian technology and an Egyptian version of the Aterian technology were also located. Some of the oldest known buildings were discovered in Egypt by archaeologist Waldemar Chmielewski along the southern border near Wadi Halfa. They were mobile structures—easily disassembled, moved, reassembled—providing hunter-gatherers with semi-permanent habitation. Aterian tool-making reached Egypt c. 40,000 BC. The Khormusan industry in Egypt began between 40,000 and 30,000 BC.
Predynastic Egypt
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Predynastic artifacts: clockwise from top left: a Bat figurine, a Naqada jar, an ivory figurine, cosmetic palette, a flint knife, and a diorite vase.
Predynastic Egypt
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Female Figure, ca. 3500-3400 B.C.E. Terracotta, painted, 11 1/2 x 5 1/2 x 2 1/4 in. (29.2 x 14 x 5.7 cm). Brooklyn Museum
Predynastic Egypt
–
A typical Naqada II pot with ship theme
31.
Cattle count
–
The cattle count was controlled by high officials, was connected to several cultic feasts. To perform the cattle count, all cattles were counted. Following the count, the percentage of cattles to be taxed by the state would be calculated. The cattle count was performed in every nomes of Egypt. Frauds were harshly punished. From the 2nd dynasty onwards, the cattle count was connected with the "Following of Horus" which occurred every two years. This last point being for correct datation of reign lengths, it is highly disputed up to this day. After this period, however, it was performed yearly. The first pharaoh during whose reign yearly counts are known for sure to have taken place is king Pepy I of the 6th dynasty. This does not exclude that the cattle count necessarily took every second year before Pepi I. An example of conflicting evaluations for a duration via cattle count is the case of king Khufu. The highest known numbers of counts under Khufu are found in workmen's graffiti inside the relieving chambers of the Khufu pyramid. The inscription reports the "17th occasion of the cattle count". This calculation is rejected by several Egyptologists, because the Turin canon, credits Khufu with a reign of merely 23 years. At the opposite, the Greek historian Herodotus claims that Khufu ruled for 50 years, now seen as an exaggeration.
Cattle count
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Cattle count after a relief in Mastaba tomb G75 at Giza.
32.
Carl Richard Lepsius
–
Karl Richard Lepsius was a pioneering Prussian Egyptologist and linguist and pioneer of modern archaeology. He was born in Naumburg an der Saale, Saxony, Peter Carl Lepsius, Naumburg County Commissioner. Karl Richard's grandfather was Johann August Lepsius, Mayor of Naumburg upon Saale. Karl Richard Lepsius studied Greek and Roman archaeology at the University of Leipzig, the Frederick William University of Berlin. In 1836 Lepsius travelled to Tuscany to meet with Ippolito Rosellini, who had led a joint expedition with Champollion in 1828-1829. The Prussian expedition was consisted of surveyors, draftsmen, other specialists. They discovered more than 130 tombs of noblemen in the area. In 1843 he copied some of the inscriptions and representations of the temple standing there. Afterwards they stopped at Coptos, the Sinai, sites before returning to Europe in 1846. While at the editorial helm, Lepsius commissioned typographer Ferdinand Theinhardt to cut the so-called Theinhardt font, which remains in use today. Much of his work is fundamental to the field. Indeed, Lepsius even coined the Totenbuch. He was also a leader in the field of African linguistics, though his ideas are now mainly considered to be outdated. On 5 July 1846 Lepsius married Elisabeth Klein, great-granddaughter of Friedrich Nicolai. 1842.
Carl Richard Lepsius
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Karl Richard Lepsius
Carl Richard Lepsius
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Plates of El-Lahun and Tura from Denkmäler aus Aegypten und Aethiopien.
33.
Binary numeral system
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The base-2 system is a positional notation with a radix of 2. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by almost all modern computers and computer-based devices. Each digit is referred to as a bit. The modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de l'Arithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, India. Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions. The method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, which dates to around 1650 BC. The I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique. It is based on taoistic duality of yin and yang. The Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, making it similar to Morse code. Pingala's Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter.
Binary numeral system
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Numeral systems
Binary numeral system
–
Gottfried Leibniz
Binary numeral system
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George Boole
34.
Multiplication
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Multiplication is one of the four elementary, mathematical operations of arithmetic; with the others being addition, subtraction and division. Multiplication can also be visualized as counting objects arranged in a rectangle or as finding the area of a rectangle whose sides have given lengths. The area of a rectangle does not depend on which side is measured first, which illustrates the commutative property. The inverse operation of multiplication is division. For example, since 4 multiplied by 3 equals 12, then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number. Multiplication is also defined for other types of numbers, such as complex numbers, more abstract constructs, like matrices. For these more abstract constructs, the order that the operands are multiplied sometimes does matter. A listing of the different kinds of products that are used in mathematics is given in the page. In arithmetic, multiplication is often written using the sign" ×" in notation. There are mathematical notations for multiplication: Multiplication is also denoted by dot signs, usually a middle-position dot: 5 ⋅ 5. When the character is not accessible, the interpunct is used. In other countries that use a comma as a decimal mark, either the period or a middle dot is used for multiplication. In algebra, multiplication involving variables is often written as a juxtaposition. The notation can also be used for quantities that are surrounded by parentheses.
Multiplication
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4 × 5 = 20, the rectangle is composed of 20 squares, having dimensions of 4 by 5.
Multiplication
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Four bags of three marbles gives twelve marbles (4 × 3 = 12).
35.
Rhind mathematical papyrus
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The Rhind Mathematical Papyrus is one of the best known examples of Egyptian mathematics. It dates to around BC. It is one of the two well-known Mathematical Papyri along with the Moscow Mathematical Papyrus. The Rhind Papyrus is larger than the Moscow Mathematical Papyrus, while the latter is older than the former. The Rhind Mathematical Papyrus dates to the Second Intermediate Period of Egypt. It was copied from a now-lost text from the reign of king Amenemhat III. Written in the hieratic script, this Egyptian manuscript consists of multiple parts which in total make it over 5m long. The papyrus began to be mathematically translated in the late 19th century. The mathematical aspect remains incomplete in several respects. The Ahmose writes this copy. A handful of these stand out. A more recent overview of the Rhind Papyrus was published by Robins and Shute. The first part of the Rhind papyrus consists of a collection of 21 arithmetic and 20 algebraic problems. The problems start out followed by completion problems and more involved linear equations. The first part of the papyrus is taken up by the 2/n table.
Rhind mathematical papyrus
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A portion of the Rhind Papyrus
Rhind mathematical papyrus
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Building
36.
Moscow mathematical papyrus
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Golenishchev bought the papyrus in 1892 or 1893 in Thebes. It later entered the collection of the Pushkin State Museum of Fine Arts in Moscow, where it remains today. It is a mathematical papyrus along with the Rhind Mathematical Papyrus. The Moscow Mathematical Papyrus is older than the Rhind Mathematical Papyrus, while the latter is the larger of the two. The papyrus is well known for some of its geometry problems. Problems 10 and 14 compute a surface area and the volume of a frustum respectively. The remaining problems are more common in nature. 3 are ship's part problems. Aha problems involve finding unknown quantities if the sum of the part of it are given. The Rhind Mathematical Papyrus also contains four of these type of problems. Problems 1, 25 of the Moscow Papyrus are Aha problems. For problem 19 asks one to calculate a quantity taken 1 and 1/2 times and added to 4 to make 10. The pefsu number is mentioned in many offering lists. Calculate 1/2 of the result will be 2 1/2 Take this 2 1/2 four times The result is 10. Then you say to him: "Behold!
Moscow mathematical papyrus
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14th problem of the Moscow Mathematical Papyrus (V. Struve, 1930)
Moscow mathematical papyrus
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The neutrality of this article is disputed. Relevant discussion may be found on the talk page. Please do not remove this message until the dispute is resolved. (July 2015)
37.
Linear equation
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A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The distinction between parameters may depend on the problem. Linear equations can have one or more variables. Linear equations occur frequently in most subareas of mathematics and especially in applied mathematics. An equation is linear if the sum of the exponents of the variables of each term is one. Equations with exponents greater than one are non-linear. An example of a non-linear equation of two variables is axy + b = 0, where b are a ≠ 0. It is non-linear because the sum of the exponents of the variables in axy, is two. This article considers the case of a single equation for which one searches the real solutions. All its content more generally for linear equations with solutions in any field. A linear equation in one unknown x may always be rewritten a x = b. If a ≠ 0, there is a unique solution x = b a. The origin of the name "linear" comes from the fact that the set of solutions of such an equation forms a straight line in the plane. Linear equations can be rewritten using the laws of elementary algebra into several different forms. These equations are often referred to as the "equations of the straight line."
Linear equation
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Graph sample of linear equations.
38.
Method of false position
–
False position method and regula falsi method are two early, still current, names for a very old method for solving an equation in one unknown. Many equations, including most of the more complicated ones, can be solved only by numerical approximation. That consists of error, in which various values of the unknown quantity, referred to here as "x", are tried. That trial-and-error may be informed by a calculated estimate for the solution. That transforms the problem into one of finding the x-value at which f = 0. That x-value is the equation’s solution. In this section, the symbol "y" reduces clutter. Here, “y” means “y” means “f”. They mean the same thing. The symbol "y" is familiar, as the often-used name for the vertical co-ordinate on a graph, often a function of the horizontal co-ordinate. Example Let's solve the equation x + 1/4x = 15 by false position. Try with x = 4. We get 1/4 * 4 = 5. Notice 4 is not the solution. Lets now multiply on both sides to get 12 + 1/4 * 12 = 15.
Method of false position
–
The first two iterations of the false position method. The red curve shows the function f and the blue lines are the secants.
39.
Quadratic equation
–
If a = 0, then the equation is linear, not quadratic. Because the quadratic equation involves only one unknown, it is called "univariate". Solutions to problems equivalent to the quadratic equation were known early as 2000 BC. A quadratic equation with complex coefficients has two solutions, called roots. They may or may not be real. It may be possible to express a quadratic equation + bx + c = 0 as a product = 0. Solving these two linear equations provides the roots of the quadratic. For most students, factoring by inspection is the first method of solving quadratic equations to which they are exposed. As an example, x2 + 5x + 6 factors as. For special cases such as where b = 0 or c = 0, factoring by inspection only works for quadratic equations that have rational roots. This means that the great majority of quadratic equations that arise in practical applications cannot be solved by factoring by inspection. Starting with a quadratic equation in standard form, + bx + c = 0 Divide each side by a, the coefficient of the squared term. Subtract the constant c/a from both sides. Add the square of one-half of the coefficient of x, to both sides. This "completes the square", converting the left side into a perfect square.
Quadratic equation
–
The trajectory of the cliff jumper is parabolic because horizontal displacement is a linear function of time, while vertical displacement is a quadratic function of time. As a result the path follows quadratic equation, where and are horizontal and vertical components of the original velocity, a is gravity and h is original height.
Quadratic equation
–
Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0)
40.
Egyptian geometry
–
Egyptian geometry refers to geometry as it was developed and used in Ancient Egypt. Egyptian mathematics as discussed here spans a time period ranging from ca. 3000 BC to ca 300 BC. We only have a limited number of problems from ancient Egypt that concern geometry. Geometric problems appear in the Rhind Mathematical Papyrus. The examples demonstrate that the Ancient Egyptians knew how to compute the volumes of cylinders and pyramids. Also the Egyptians used many geometric shapes such as squares and triangles on temples and obelisks. The Ancient Egyptians wrote out their problems in multiple parts. The problems were written in prose form. The solutions were written out in steps, outlining the process. Triangles: The Ancient Egyptians knew that the area of a triangle is A = 1 2 b h where b = base and h = height. Calculations of the area of a triangle appear in both the MMP. This problem seems to be identical to one of the Lahun Mathematical Papyri in London. The problem is also interesting because it is clear that the Egyptians were familiar with square roots. They even had a special hieroglyph for finding a square root. It appears in the fifth line of the problem.
Egyptian geometry
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Image of Problem 14 from the Moscow Mathematical Papyrus. The problem includes a diagram indicating the dimensions of the truncated pyramid.
41.
Babylonian mathematics
–
Babylonian mathematical texts are plentiful and well edited. In respect of content there is scarcely any difference between the two groups of texts. Thus Babylonian mathematics remained constant, in character and content, for nearly two millennia. In contrast to the scarcity of sources in Egyptian mathematics, our knowledge of Babylonian mathematics is derived from some 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed while the clay was moist, baked hard in an oven or by the heat of the sun. The Babylonian tablet YBC 7289 gives an approximation to 2 accurate to three significant sexagesimal digits. Babylonian mathematics is a range of numeric and more advanced mathematical practices in the ancient Near East, written in cuneiform script. Study has historically focused on the Old Babylonian period in the early second millennium BC due to the wealth of data available. There has been debate over the earliest appearance of Babylonian mathematics, with historians suggesting a range of dates between the 5th and 3rd millennia BC. Babylonian mathematics was primarily written on clay tablets in cuneiform script in the Akkadian or Sumerian languages. The Babylonian system of mathematics was sexagesimal numeral system. From this we derive the modern day usage of 60 seconds in a minute, 60 minutes in an hour, 360 degrees in a circle. The Babylonians were able to make great advances in mathematics for two reasons. Additionally, unlike the Egyptians and Romans, the Babylonians had a true place-value system, where digits written in the left column represented larger values. The ancient Sumerians of Mesopotamia developed a complex system of metrology from 3000 BC.
Babylonian mathematics
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Babylonian clay tablet YBC 7289 with annotations. The diagonal displays an approximation of the square root of 2 in four sexagesimal figures, 1 24 51 10, which is good to about six decimal digits. 1 + 24/60 + 51/60 2 + 10/60 3 = 1.41421296... The tablet also gives an example where one side of the square is 30, and the resulting diagonal is 42 25 35 or 42.4263888...
42.
Hellenistic mathematics
–
Greek mathematicians were united by culture and language. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. The word "mathematics" itself derives from the Greek μάθημα, meaning "subject of instruction". The origin of Greek mathematics is not well documented. The earliest advanced civilizations in Europe were the Minoan and later Mycenaean civilization, both of which flourished during the 2nd millennium BC. While these civilizations were capable of advanced engineering, including four-story palaces with drainage and beehive tombs, they left behind no mathematical documents. Though no direct evidence is available, it is generally thought that 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. Despite this, it is generally agreed that Thales is the first of the seven wise men of Greece. Thales' theorem and Intercept theorem are attributed to Thales. It is for this reason that Thales is often hailed as the first true mathematician. Thales is also thought to be the earliest known man in history to whom mathematical discoveries have been attributed. Another important figure in the development of Greek mathematics is Pythagoras of Samos. Like Thales, Pythagoras also settled in Croton, Magna Graecia. And since in antiquity it was customary to give all credit to the master, Pythagoras himself was given credit for the discoveries made by his order.
Hellenistic mathematics
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Statue of Euclid in the Oxford University Museum of Natural History
Hellenistic mathematics
–
An illustration of Euclid 's proof of the Pythagorean Theorem
Hellenistic mathematics
–
The Antikythera mechanism, an ancient mechanical calculator.
43.
Roman math
–
The Ancient Romans developed the Roman hand abacus, a portable, but less capable, base-10 version of the previous Babylonian abacus. It was the portable calculating device for engineers, merchants and presumably tax collectors. It greatly reduced the time needed to perform the basic operations of arithmetic using Roman numerals. But the most reliable and conservative guardian of a past culture, has come to our rescue once more. What the Greeks called psephoi, the Romans called calculi. The Latin calx means ` pebble' or ` gravel stone'; calculi are thus little stones." Both the Chinese suanpan have been used since ancient times. The rightmost two grooves were for fractional counting. The abacus was made of a plate where the beads ran in slots. The size was such that it could fit in a modern pocket. The beads in the upper shorter grooves denote fives—five units, five tens, etc. essentially in a bi-quinary coded decimal place value system. Computations are made by means of beads which would probably have been slid down the grooves to indicate the value of each column. These latter two slots are for a development unique to the Roman hand abacus described in following sections. 3 slots with one, one and two beads respectively top to bottom. In either case, three symbols were included beside one symbol per slot for the three slot version.
Roman math
–
A reconstruction of a Roman hand abacus, made by the RGZ Museum in Mainz, 1977. The original is bronze and is held by the Bibliothèque nationale de France, in Paris.
44.
Islamic mathematics
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Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics and Indian mathematics. Arabic works also played an important role in the transmission of mathematics to Europe during the 10th to 12th centuries. The study of algebra, which itself is derived from the Arabic word meaning completion or "reunion of broken parts", flourished during the Islamic golden age. Muhammad ibn Musa al-Khwarizmi, a scholar in the House of Wisdom in Baghdad, is along with the Greek mathematician Diophantus, known as the father of algebra. He also introduces the method of reduction, unlike Diophantus, gives general solutions for the equations he deals with. Al-Khwarizmi's algebra was rhetorical, which means that the equations were written out in full sentences. This was unlike the algebraic work of Diophantus, syncopated, meaning that some symbolism is used. The transition to symbolic algebra, where only symbols are used, can be seen in the work of Ibn al-Banna' al-Marrakushi and Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics, essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc. to all be treated as "algebraic objects". Several other mathematicians during this time period expanded on the algebra of Al-Khwarizmi. Omar Khayyam, along with Sharaf al-Dīn al-Tūsī, found several solutions of the cubic equation. Omar Khayyam found the general geometric solution of a cubic equation. Omar Khayyám wrote the Treatise on Demonstration of Problems of Algebra containing the systematic solution of cubic or third-order equations, going beyond the Algebra of al-Khwārizmī.
Islamic mathematics
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A page from the The Compendious Book on Calculation by Completion and Balancing by Al-Khwarizmi.
Islamic mathematics
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Engraving of Abū Sahl al-Qūhī 's perfect compass to draw conic sections.
Islamic mathematics
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The theorem of Ibn Haytham.
45.
Egyptian hieroglyphics
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Egyptian hieroglyphs were the formal writing system used in Ancient Egypt. It combined logographic, syllabic and alphabetic elements, with a total of some 1,000 distinct characters. Cursive hieroglyphs were used for religious literature on papyrus and wood. The later hieratic and demotic Egyptian scripts are derived from hieroglyphic writing; Meroitic was a late derivation from Demotic. The writing system continued to be used throughout the Late Period, as well as the Persian and Ptolemaic periods. Late survivals of hieroglyphic use are found well into the Roman period, extending into the 4th century AD. The decipherment of hieroglyphs would only be solved in the 1820s by Jean-François Champollion, with the help of the Rosetta Stone. The word hieroglyph comes from the Greek adjective ἱερογλυφικός, a compound of ἱερός and γλύφω, supposedly a calque of an Egyptian phrase mdw·w-nṯr "god's words". The glyphs themselves were called τὰ ἱερογλυφικὰ γράμματα "the sacred engraved letters". The word hieroglyph has become a noun in English, standing for an individual hieroglyphic character. As used in the previous sentence, the word hieroglyphic is an adjective, but hieroglyphic has also become a noun in English, at least in non-academic usage. Hieroglyphs emerged from the preliterate artistic traditions of Egypt. For example, symbols on Gerzean pottery from c. 4000 BC have been argued to resemble hieroglyphic writing. There are around 800 hieroglyphs dating back to the Old Kingdom, Middle Kingdom and New Kingdom Eras. By the Greco-Roman period, there are more than 5,000.
Egyptian hieroglyphics
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A section of the Papyrus of Ani showing cursive hieroglyphs.
Egyptian hieroglyphics
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Hieroglyphs on a funerary stela in Manchester Museum
Egyptian hieroglyphics
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The Rosetta Stone in the British Museum
Egyptian hieroglyphics
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Hieroglyphs typical of the Graeco-Roman period
46.
Transliteration of Ancient Egyptian
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This process facilitates the publication of texts where the inclusion of drawings of an actual Egyptian document is impractical. It should be emphasised that transliteration is not the same as transcription. Transcription seeks to reproduce the pronunciation of a text. Egyptologists, therefore, rely on transliteration in scientific publications. Important as transliteration is to the field of Egyptology, there is no one standard scheme in use for hieratic texts. Some might even argue that there are as many systems of transliteration as there are Egyptologists. However, there are a few closely related systems that can be regarded as conventional. However, there is a growing trend, even among English-speaking scholars, to adopt a modified version of the method used in the Wörterbuch. It is being used fairly widely in Germany and other German-speaking countries. Its usage is not presently common. Unfortunately this perceived accuracy is debatable. It is widely used in e-mail discussion lists and internet forums catering to the interested public. This system is used by various software packages developed for typesetting hieroglyphic texts. The following table only lists the special characters used in various transliteration schemes. Three additional characters are required for transliterating Egyptian: Alef; Ayin; Yod.
Transliteration of Ancient Egyptian
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ꜣ (, 3)
Transliteration of Ancient Egyptian
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ꜣ ()
47.
Ancient Egyptian technology
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Ancient Egyptian technology describes devices and technologies invented or used in Ancient Egypt. The Egyptians used many simple machines, such as the ramp and the lever, to aid construction processes. They used rope trusses to stiffen the beam of ships. Pottery were mass-produced and exported throughout the Mediterranean basin. Chariots only came into use after the Second Intermediate period. The Egyptians also played an important role in developing Mediterranean technology including ships and lighthouses. Significant advances during the dynastic period include astronomy, mathematics, medicine. Their geometry was a necessary outgrowth of surveying to preserve the ownership of farmland, flooded annually by the Nile river. The 3,4,5 right triangle and other rules of thumb served to represent the post and lintel architecture of Egypt. Egypt also was a center of alchemy research for much of the western world. The paper comes from the Greek term for the ancient Egyptian writing material called papyrus, formed from beaten strips of papyrus plants. Papyrus was sold to ancient Greece and Rome. The establishment of the Library of Alexandria limited the supply of papyrus for others. This however is a myth; parchment had elsewhere long before the rise of Pergamon. A phonetic writing system, served as the basis for the Phoenician alphabet from which later alphabets were derived.
Ancient Egyptian technology
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Ancient Egyptian depiction of women engaged in mechanical rope making, the first graphic evidence of the craft, shown in the two lower rows of the illustration
Ancient Egyptian technology
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A section of the Egyptian Book of the Dead, which is written and drawn on papyrus
Ancient Egyptian technology
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The Lighthouse of Alexandria on the island of Pharos.
Ancient Egyptian technology
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Giza Plateau, Cairo. Khafre's pyramid in the background
48.
Mathematics and architecture
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Mathematics and architecture are related, since, as with other arts, architects use mathematics for several reasons. In Islamic architecture, geometric shapes and geometric tiling patterns are used to decorate buildings, both outside. Some Hindu temples have a fractal-like structure where parts resemble the whole, conveying a message about the infinite in Hindu cosmology. In the twenty-first century, mathematical ornamentation is again being used to cover public buildings. In the twentieth century, styles such as Deconstructivism explored different geometries to achieve desired effects. But, they argue, the two have been since antiquity. A builder at the top of his profession was given the title of architect or engineer. In the Renaissance, the quadrivium of arithmetic, geometry, astronomy became an extra syllabus expected of the Renaissance man such as Leon Battista Alberti. Similarly in England, Sir Christopher Wren, known today as an architect, was firstly a noted astronomer. They argue that architects have avoided looking in revivalist times. This would explain why in revivalist periods, such as the Gothic Revival in 19th century England, architecture had little connection to mathematics. In contrast, the revolutionary 20th century movements such as Futurism and Constructivism actively rejected old ideas, embracing mathematics and leading to Modernist architecture. Architects use mathematics for several reasons, leaving aside the necessary use of mathematics in the engineering of buildings. Firstly, they use geometry because it defines the spatial form of a building. Secondly, they use mathematics to design forms that are considered harmonious.
Mathematics and architecture
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"The Gherkin", 30 St Mary Axe, London, completed 2003, is a parametrically designed solid of revolution.
Mathematics and architecture
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Kandariya Mahadeva Temple, Khajuraho, India, is an example of religious architecture with a fractal -like structure which has many parts that resemble the whole. c. 1030
Mathematics and architecture
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In the Renaissance, an architect like Leon Battista Alberti was expected to be knowledgeable in many disciplines, including arithmetic and geometry.
Mathematics and architecture
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Plan of a Greek house by Vitruvius
49.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each variation of a book. For example, an e-book, a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned after 1 January 2007, 10 digits long if assigned before 2007. The method of assigning an ISBN varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated based upon the 9-digit Standard Book Numbering created in 1966. The 10-digit ISBN format was published in 1970 as international standard ISO 2108. The International Standard Serial Number, identifies periodical publications such as magazines; and the International Standard Music Number covers for musical scores. The ISBN configuration of recognition was generated in 1967 in the United Kingdom by Emery Koltay. The 10-digit ISBN format was published as international standard ISO 2108. The United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978. An SBN may be converted by prefixing the digit "0". This can be converted to ISBN 0-340-01381-8; the digit does not need to be re-calculated. Since 1 ISBNs have contained 13 digits, a format, compatible with "Bookland" European Article Number EAN-13s.
International Standard Book Number
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A 13-digit ISBN, 978-3-16-148410-0, as represented by an EAN-13 bar code
50.
Raymond Clare Archibald
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Raymond Clare Archibald was a prominent Canadian-American mathematician. He is known as an historian of mathematics, his editorships of mathematical journals and his contributions to the teaching of mathematics. Raymond Clare Archibald was born in South Branch, Stewiacke, Nova Scotia on 7 October 1875. He was the son of Mary Mellish Archibald. He was the fourth cousin twice removed of mathematician Simon Newcomb. Archibald graduated in 1894 in mathematics and teacher's certificate in violin. He then traveled to Europe where he received a Ph.D.cum laude from the University of Strassburg in 1900. Title of his dissertation was The Cardioide and Some of its Related Curves. He taught mathematics and violin at the Mount Allison Ladies' College until 1907. After a one-year appointment at Acadia University he accepted an invitation of join the department at Brown University. He stayed for the rest of his career becoming a Professor Emeritus in 1943. While at Brown he created one of the finest mathematical libraries in the western hemisphere. Archibald returned to Mount Allison in 1954 to curate the library he had founded in 1905 to honor his mother. At his death the library contained 23,000 volumes, 70,000 songs in American and English poetry and drama. Raymond Clare Archibald was a world-renowned historian of mathematics with a lifelong concern for the teaching of mathematics in secondary schools.
Raymond Clare Archibald
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Raymond Clare Archibald
51.
Bharath Sriraman
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Bharath Sriraman is a professor of mathematics at the University of Montana – Missoula with an adjunct appointment in the department of Central and Southwest-Asian Studies. Sriraman is the editor-in-chief of The Mathematics Enthusiast, an independent open access journal hosted by University of Montana. He is the co-founder/co-editor-in - chief of two series with Springer Science + Business Media namely Advances in Action in Education. He previously received the School Science and Mathematics Association Early Scholar Award in 2007. In 2016 he was the recipient of the University of Montana Distinguished Scholar Award Beghetto, Ron. Sriraman, Bharath. . . Complexity and Creativity: Deconstructing Clichés. Sense Publishers, Rotterdam, Netherlands, ISBN 978-9-46209771-1 Chernoff, Egan. Bharath Sriraman Probabilistic Thinking: Presenting Plural Perspectives. Springer Science+Business Media, Dodrecht, Netherlands, ISBN 978-94-007-7154-3 Ambrose, Don. Sriraman, Bharath. Cross, Tracy. . Taylor and Francis London, New York Sriraman, Bharath; English, Lyn. Theories of Mathematics Education: Seeking New Frontiers. Advances in Mathematics Education. 1.
Bharath Sriraman
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Sriraman, Universidad Antonio Narino, 2015
52.
Princeton University Press
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The Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship at large. The press was founded by Whitney Darrow, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's Lectures on Moral Philosophy. Six books from the Princeton University Press have won Pulitzer Prizes. The Princeton University Press Bollingen Series had its beginnings in a 1943 project of Paul Mellon's Old Dominion Foundation. From 1945, the foundation had independent status, providing fellowships and grants in several areas of study including archaeology, poetry, psychology. The Bollingen Series was given to the university in 1969. First copyright 1950, 27th printing 1997. "Book of Lists: Princeton University Press at 100". Artforum International. Staff of Princeton University Press. A Century in Books:Princeton University Press 1905-2005. ISBN 9780691122922.
Princeton University Press
Princeton University Press
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Princeton University Press
Princeton University Press
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Academics
53.
Ancient Egyptian architecture
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The core of the pyramids consisted of locally quarried stone, mudbricks, gravel. For the casing stones were used that had to be transported from upper Egypt. Egyptian houses were made out of mud collected from the Nile river. It was left to dry in the hot sun to harden for use in construction. New buildings having been erected on ancient ones. Fortunately, the hot climate of Egypt preserved some mud brick structures. Examples include the village Deir al-Madinah, the fortresses at Buhen and Mirgissa. Also, many tombs have survived because they were built on high ground unaffected by the Nile flood and were constructed of stone. In a similar manner, the incised and flatly modeled adornment of the stone buildings may have derived from mud wall ornamentation. Interior walls, as well as the columns and piers, were covered with hieroglyphic and pictorial frescoes and carvings painted in brilliant colors. Many motifs of Egyptian ornamentation are symbolic, such as the scarab, or sacred beetle, the vulture. Common motifs include palm leaves, the papyrus plant, the buds and flowers of the lotus. Hieroglyphs spells. In addition, carvings allow us to understand how the Ancient Egyptians lived, statuses, wars that were fought and their beliefs. This was especially true when exploring the tombs of Egyptian officials in recent years.
Ancient Egyptian architecture
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The well preserved Temple of Horus at Edfu is an example of Egyptian architecture and architectural sculpture.
Ancient Egyptian architecture
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Drawings of the types of the architectural capitals specific for the Ancient Egyptian civilization.
Ancient Egyptian architecture
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The Pyramids of Giza
Ancient Egyptian architecture
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The hypostyle hall of Karnak Temple
54.
Egyptian Revival architecture
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Egyptian revival is an architectural style that uses the motifs and imagery of ancient Egypt. Napoleon took a scientific expedition with him to Egypt. The Description de l'Égypte, was published as a series through 1826. The most important example is probably Gian Lorenzo Bernini's obelisk in the Piazza Navona in Rome. Others may be found at County Meath. The Casteltown Folly in County Kildare is probably the best known, albeit the least Egyptian-styled. Egyptian buildings had also been built as garden follies. The most elaborate was probably the one built by Frederick I, Duke of Württemberg in the gardens of the Château de Montbéliard. Designed included an Egyptian bridge across which guests walked to reach an island with an Egyptian-influenced house. Designed by Jean Baptiste Kleber, the building had a "bagnio". In France and Britain this was at least partially inspired by successful war campaigns undertaken by each country while in Egypt. According to Diana Muir Appelbaum, Designed was "the public building in the Egyptian style." In 1828 a building with Egyptianizing detail including large Hathor heads and a freize by sculptor J. G. Garraudwas built at No. 2. Place du Caire. Among the earliest monuments of the Egyptian revival in Paris is the Fontaine du Fellah in Paris, built in 1806.
Egyptian Revival architecture
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Egyptian Hall (1812) in London
Egyptian Revival architecture
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Foire du Caire building (1828) in Paris
Egyptian Revival architecture
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The Egyptian Gates (1827–30) in Tsarskoe Selo, St. Petersburg
Egyptian Revival architecture
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4th Precinct Police Station (1836) in New Orleans
55.
Art of ancient Egypt
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Egyptian art reached a high level in painting and sculpture, was both highly stylized and symbolic. Egyptian styles changed remarkably little over more than three thousand years. Egyptian art included paintings, sculpture in wood, stone and ceramics, drawings on papyrus, faience, jewelry, ivories, other art media. It displays an extraordinarily vivid representation of the ancient Egyptian's socioeconomic belief systems. Other conventions make statues of males darker than ones. Egyptian art uses hierarchical proportion, where the size of figures indicates their relative importance. Symbolism can be played an important role in establishing a sense of order. The pharaoh's regalia, for example, represented his power to maintain order. Animals were also highly symbolic figures in Egyptian art. Less prestigious works in tombs, temples and palaces were merely painted on a flat surface. Pigments were mostly mineral, chosen to withstand strong sunlight without fading. The binding medium used in painting remains unclear: various gums and resins have been suggested. It is clear that true fresco, painted into a thin layer of wet plaster, was not used. Instead the paint was applied in what is called "fresco a secco" in Italian. Small objects including wooden statuettes were often painted using similar techniques.
Art of ancient Egypt
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Thutmose, Bust of Nefertiti, 1345 BC, Egyptian Museum of Berlin
Art of ancient Egypt
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Sunk relief of the crocodile god Sobek
Art of ancient Egypt
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Tomb of Sarenput II.
Art of ancient Egypt
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Wall painting of Nefertari
56.
Egyptian astronomy
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Egyptian astronomy begins in prehistoric times, in the Predynastic Period. In the 5th millennium BCE, the stone circles at Nabta Playa may have made use of astronomical alignments. The temple of Amun-Re at Karnak was aligned on the rising of the midwinter sun. Roman Egypt produced the greatest astronomer of Ptolemy. His works including the Almagest, became the most influential books in the history of Western astronomy. Following the Muslim conquest of Egypt, the region came to be dominated by Islamic astronomy. His observations on eclipses were still used centuries later. In the 14th century, Najm al-Din al-Misri wrote a treatise describing over 100 different types of astronomical instruments, many of which he invented himself. Egyptian astronomy begins in prehistoric times. The constellation system used among the Egyptians also appears to have been essentially of native origin. The length of the corridor down which sunlight would travel would have limited illumination at other times of the year. Astronomy played a considerable part for fixing the dates of festivals and determining the hours of the night. The titles of several temple books are preserved recording the phases of the sun, moon and stars. The rising of Sirius at the beginning of the inundation was a particularly important point to fix in the yearly calendar. One of the most important Egyptian astronomical texts was the Book of Nut, going earlier.
Egyptian astronomy
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Chart from Senemut's tomb, 18th dynasty
Egyptian astronomy
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Nut, Egyptian goddess of the sky, with the star chart in the tomb of Ramses VI
Egyptian astronomy
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' Star clock ' method from the tomb of Rameses VI
Egyptian astronomy
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An Egyptian 30th-dynasty (Ptolemaic) terracotta astrological disc at the Los Angeles County Museum of Art.
57.
Ancient Egyptian burial customs
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The ancient Egyptians had an elaborate set of funerary practices that they believed were necessary to ensure their immortality after death. Burial with specific grave goods thought to be needed in the Egyptian afterlife. Though no writing survives from Predynastic Egypt, scholars believe the importance of its preservation originated there. This would explain why people of that time did not follow the common practice of cremation, but rather buried the dead. Some also believe they may have feared the bodies would rise again if mistreated after death. Early bodies were buried with a few burial goods. Sometimes multiple animals were placed in the same grave. Over time, graves became more complex, with the body placed in a basket, then later in wooden or terracotta coffins. The latest tombs Egyptians made were sarcophaguses. These graves contained burial goods like jewelry, food, games and splint. This may be because admission required that the deceased must be able to serve a purpose there. Others needed to have some role there. Human sacrifices found in early royal tombs reinforce this view. These people were probably meant to serve the pharaoh during his eternal life. Eventually, figurines and wall paintings begin to replace human victims.
Ancient Egyptian burial customs
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Professional mourners in an eloquent gesture of mourning.
Ancient Egyptian burial customs
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Female Figure, ca. 3500-3400 B.C.E., Brooklyn Museum
Ancient Egyptian burial customs
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Mask from a Coffin. Cartonnage, 37.1387E, Brooklyn Museum
58.
Egyptian chronology
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The majority of Egyptologists agree on the outline and many details of the chronology of Ancient Egypt. Scholarly consensus on the general outline of the conventional current in Egyptology has not fluctuated much over the last 100 years. This is illustrated by comparing the chronology as given by two Egyptologists, the second in 2000. The disparities between the two sets of dates result from refined understanding of the still very incomplete source evidence. For example, Breasted adds a ruler in the Twentieth dynasty that further research showed did not exist. Following Manetho, Breasted also believed all the dynasties were sequential, whereas it is now known that several existed at the same time. These revisions have resulted by up to 400 years at the beginning of Dynasty I. The backbone of Egyptian chronology are the regnal years as recorded in Egyptian king lists. In addition, some Egyptian dynasties may have overlapped, with different pharaohs ruling at the same time, rather than serially. Not knowing whether monarchies were simultaneous or sequential results in widely differing chronological interpretations. However, further research has shown after two or more years had passed. Once again, this may not be the usual practice in all cases. In the early days of Egyptology, the compilation of regnal periods may also have been hampered due to biblical bias on the part of the Egyptologists. This was most pervasive before the 19th century, when Manetho's figures were recognized as conflicting with biblical chronology based on Old Testament references to Egypt. In the 20th century, biblical bias has mostly been confined to alternative chronologies outside of scholarly mainstream.
Egyptian chronology
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Astronomical ceiling from the tomb of Seti I showing stars and constellations used in calendar calculations
Egyptian chronology
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'Diagonal star table' from the 11th Dynasty coffin lid; found at Asyut, Egypt. Roemer- und Pelizaeus-Museum Hildesheim
59.
Urban planning in ancient Egypt
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The use of urban planning in ancient Egypt is a matter of continuous debate. The Egyptians referred as either nwt or dmi. Sites that do survive do not show much evidence of urban planning. Almost all the houses follow a plan which faces their doorways to the northwest, to avoid the prevailing wind. Other known pre-dynastic settlements, such as those of the Badarian and Naqada cultures, lack a defining plan. These villages mostly consisting of small huts situated around circular storage pits. The workmen's village at el-Lahun was inhabited during the reign of Senusret II of the Twelfth Dynasty. The village was apparently fully inhabited during the king's reign. The village was organized according to a regular plan. The smaller western quarter contained the relatively humble dwellings of the workers that were laid out on a rectangular pattern. Flinders Petrie, who first excavated the site, noted how the layout of the neighborhood would allow a single nightwatchman to easily guard the area. They were evenly spaced along the parallel streets. Stone drainage channels built into them, leading to a central drain, allowed the disposal of dirty water from the houses. The village is built around a central street. Houses were connected at sharing walls for building and space efficiency.
Urban planning in ancient Egypt
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Royal Wadi
60.
Clothing in ancient Egypt
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Egyptian clothing was filled with a variety of colors. Adorned with precious jewels, the fashions of the Ancient Egyptians were made for not only beauty but also comfort. Egyptian fashion was created to keep cool while in the hot desert. In ancient Egypt, linen was by far the most common textile. It helped people to be comfortable in the subtropical heat. Linen is made by spinning the fibers from the stem of the plant. Spinning, sewing were very important techniques for all Egyptian societies. The clothing was usually left in its natural color. Wool was considered impure. Only the wealthy wore animal fibers that were the object of taboos. They were forbidden in temples and sanctuaries. The shenti was worn by all people. Slaves often worked naked. The most common headdress was a striped cloth worn by men. From about 2130 BC during the Old Kingdom, garments were simple.
Clothing in ancient Egypt
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The clothing of men and women of several social levels of ancient Egypt are depicted in this tomb mural from the fifteenth century BC.
61.
Ancient Egyptian cuisine
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The cuisine of ancient Egypt covers a span of over three thousand years, but still retained many consistent traits until well into Greco-Roman times. Depictions of banquets can be found from both the Old Kingdom and New Kingdom. They usually started sometime in the afternoon. Women were separated unless they were married. Professional dancers entertained, accompanied by musicians playing harps, lutes, drums, tambourines, clappers. There were usually abundant quantities of foods; there were whole roast oxen, ducks, geese, pigeons, at times fish. The dishes frequently consisted of stews served with great amounts of bread, fruit. For sweets there were cakes sweetened with honey. The Hathor was often invoked during feasts. Food could be prepared by stewing, baking, boiling, grilling, roasting. Herbs were added for flavor, though the former were expensive imports and therefore confined to the tables of the wealthy. Dates and raisins could be dried for long-term storage. The staples beer were usually prepared in the same locations, as the yeast used for bread was also used for brewing. Any surplus would be sold. Egyptian bread was made exclusively from emmer wheat, more difficult to turn into flour than most other varieties of wheat.
Ancient Egyptian cuisine
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An early Ramesside Period mural painting from Deir el-Medina tomb depicts an Egyptian couple harvesting crops
Ancient Egyptian cuisine
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A depiction of the royal bakery from an engraving in the tomb of Ramesses III in the Valley of the Kings. There are many types of loaves, including ones that are shaped like animals. 20th dynasty.
Ancient Egyptian cuisine
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Hunting game birds and plowing a field. Depiction on a burial chamber from c. 2700 BC. Tomb of Nefermaat I and his wife Itet.
62.
List of ancient Egyptian dynasties
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In Ancient Egyptian history, dynasties are series of rulers sharing a common origin who are usually of the same family. Ancient Egypt's historical period is traditionally divided into pharaonic dynasties. The thirty-first dynasty's name is a later coining. While widely useful, the system does have its shortcomings. Some dynasties only existed concurrently with other dynasties based in other cities. This page lists articles on dynasties of Ancient Egypt. The cities in which power was held during these dynasties follow their names, in parentheses.
List of ancient Egyptian dynasties
63.
Great Royal Wife
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Great Royal Wife, or alternatively Chief King's Wife, is the term, used to refer to the principal wife of the pharaoh of Ancient Egypt. The former is also, in the form of the simplification Great Wife, applied all over modern Africa. While most Ancient Egyptians were monogamous, the pharaoh would have had other, in addition to the Great Royal Wife. This arrangement would allow the pharaoh to enter with the daughters of allies as was the custom of ancient kings. In the past the order of succession in Ancient Egypt was thought to pass through the royal women. This theory, referred to as the Heiress Theory, is now not accepted by Egyptologists. The throne just passed to the eldest living son of the pharaoh. Examples include the mother of Amenhotep III. However, she is only attested in the New Kingdom so the title might be an anachronism. Perhaps the first holder of its title was Nubkhaes of the Second Intermediate Period. A special place in the history of great royal wives was taken by Hatshepsut. She was Great Royal Wife to her half-brother Thutmose II. During this time Hatshepsut also became a God's Wife of Amun. After the death of her husband, she became regent because of the minority of the only male heir, who eventually would become Thutmose III. While he was still very young, however, Hatshepsut was ruled very successfully in her own right for many years.
Great Royal Wife
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Nefertari, the Great Royal Wife of Ramasses II, from the temple he built to her at Abu Simbel, she holds a sistrum and a sacred lotus
Great Royal Wife
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Hatshepsut was Great Royal Wife to Thutmose II, then regent for her stepson Thutmose III (Museum of Fine Arts, Boston)
Great Royal Wife
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Royal titulary
64.
History of ancient Egypt
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The history of Ancient Egypt spans the period from the early prehistoric settlements of the northern Nile valley to the Roman conquest in 30 BC. Note For alternative'revisions' to the chronology of Egypt, see Egyptian chronology. Egypt's history is split according to the ruling dynasty of each pharaoh. The dating of events is still a subject of research. The conservative dates are not supported by any absolute date for a span of about three millennia. The following is the list according to Egyptian chronology. Traces of these early people appear along the terraces of the Nile and in the oases. To the Egyptians the Nile meant the desert meant death, though the desert did provide them protection from invaders. Evidence also indicates human habitation and cattle herding before the 8th millennium BC. Continued desiccation forced them to adopt a more sedentary lifestyle. However, the period from 9th to the 6th millennium BC has left very little in the way of archaeological evidence. The Nile valley of Egypt was basically uninhabitable until the work of irrigating the land along the banks was started. However it appears that this irrigation was largely under way by the 6th millennium. By that time, Nile society was already engaged in the construction of large buildings. At this time, Egyptians in the southwestern corner of Egypt were also constructing large buildings.
History of ancient Egypt
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A Naqada II vase decorated with gazelles, on display at the Louvre.
History of ancient Egypt
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An Osiride statue of Mentuhotep II, the founder of the Middle Kingdom
History of ancient Egypt
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Statuette of Merankhre Mentuhotep VI, a minor king of the 16th Dynasty, reigning over the Theban region c. 1585 BC.
65.
Egyptian language
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The language spoken in ancient Egypt was a branch of the Afroasiatic language family. Egyptian was spoken until the late century in the form of Coptic. Coptic is still used as the liturgical language of the Coptic Orthodox Church of Alexandria. It has today. The Egyptian language belongs to the Afroasiatic family. Of the Afroasiatic branches, Egyptian shows its greatest affinities with Semitic, to a lesser extent Cushitic. In Egyptian, the Proto-Afroasiatic voiced consonants * / z ð / developed into pharyngeal ⟨ ꜥ ⟩ / ʕ /, e.g. Eg. ꜥr.t'portal', Sem. *dalt'door'. Original * / k ḳ / palatalize to ⟨ ṯ j ḏ ⟩ in some environments and are preserved as ⟨ k g q ⟩ in others. Egyptian has perhaps monoradical roots, in contrast to the Semitic preference for triradical roots. Egyptian probably is more archaic in this regard, whereas Semitic likely underwent later regularizations converting roots into the triradical pattern. Scholars group the Egyptian language into six major chronological divisions: Archaic Egyptian language Old Egyptian language Middle Egyptian language, characterizing Middle Kingdom. Late Egyptian language. Demotic Coptic The earliest Egyptian glyphs date back to around 3300 BC. These early texts are generally lumped together under the general term "Archaic Egyptian."
Egyptian language
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Seal impression from the tomb of Seth-Peribsen, containing the oldest known complete sentence in Egyptian
Egyptian language
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Ebers Papyrus detailing treatment of asthma
Egyptian language
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3rd-century Coptic inscription
66.
Ancient Egyptian literature
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Ancient Egyptian literature was written in the Egyptian language from ancient Egypt's pharaonic period until the end of Roman domination. It represents the oldest corpus of Egyptian literature. Along with Sumerian literature, it is considered the world's earliest literature. Writing in ancient Egypt -- both hieratic -- first appeared in the late 4th millennium BC during the late phase of predynastic Egypt. It was not until the early Middle Kingdom that a narrative Egyptian literature was created. This was a "media revolution" which, according to Richard B. However, it is possible that the overall literacy rate was less than one percent of the entire population. The creation of literature was thus the royal court of the ruling pharaoh. However, there is no full consensus among modern scholars concerning the dependence of Egyptian literature on the sociopolitical order of the royal courts. Popular tales included the Story of The Eloquent Peasant, while important teaching texts include the Instructions of Amenemhat and The Loyalist Teaching. Egyptian literature has been preserved on a wide variety of media. This includes papyrus scrolls and packets, limestone or ceramic ostraca, wooden writing boards, coffins. Texts preserved and represent a small fraction of ancient Egyptian literary material. The area of the floodplain of the Nile is under-represented because the environment is unsuitable for the preservation of papyri and ink inscriptions. On the other hand, hidden caches of literature, buried for thousands of years, have been discovered in settlements on the dry desert margins of Egyptian civilization.
Ancient Egyptian literature
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Egyptian hieroglyphs with cartouches for the name " Ramesses II ", from the Luxor Temple, New Kingdom
Ancient Egyptian literature
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The slab stela of the Old Kingdom Egyptian princess Neferetiabet (dated c. 2590–2565 BC), from her tomb at Giza, with hieroglyphs carved and painted on limestone
Ancient Egyptian literature
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Abbott Papyrus, a record written in hieratic script; it describes an inspection of royal tombs in the Theban Necropolis and is dated to the 16th regnal year of Ramesses IX, ca. 1110 BCE.
Ancient Egyptian literature
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An ostracon with hieratic script mentioning officials involved in the inspection and clearing of tombs during the Twenty-first dynasty of Egypt, c. 1070–945 BC
67.
Ancient Egyptian medicine
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The medicine of the ancient Egyptians is some of the oldest documented. Medical thought influenced later traditions, including the Greeks. Until the 19th century, the main sources of information about Egyptian medicine were writings from later in antiquity. The Greek historian Herodotus wrote extensively of his observations of their medicinal practice. Pliny the Elder also wrote favourably of them in historical review. Hippocrates, Herophilos, later Galen studied at the temple of Amenhotep, acknowledged the contribution of ancient Egyptian medicine to Greek medicine. In 1822, the translation of the Rosetta stone finally allowed the translation of papyri, including many related to medical matters. The Edwin Smith Papyrus is a textbook on surgery and details anatomical observations and the "examination, diagnosis, prognosis" of numerous ailments. It is regarded as a copy of several earlier texts. Medical information in it dates from early as 3000 BC. It is thus viewed as a manual. Treatments consisted of ointments made from minerals. The earliest known surgery was performed around 2750 BC. Foul applications meant to turn away disease-causing demons, also includes 877 prescriptions. It may also contain the earliest documented awareness of tumors, if the poorly understood medical terminology has been correctly interpreted.
Ancient Egyptian medicine
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The Edwin Smith Papyrus documents ancient Egyptian medicine, including the diagnosis and treatment of injuries.
Ancient Egyptian medicine
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Ebers Papyrus treatment for cancer: recounting a " tumor against the god Xenus", it recommends "do thou nothing there against"
Ancient Egyptian medicine
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Ancient Egyptian medical instruments depicted in a Ptolemaic period inscription on the Temple of Kom Ombo.
Ancient Egyptian medicine
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This wood and leather prosthetic toe was used by an amputee to facilitate walking
68.
Military of ancient Egypt
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Ancient Egypt was an ancient civilization of eastern North Africa, concentrated along the Northern reaches of the Nile River in Egypt. Its history occurred in a series of stable Kingdoms, separated by periods of relative instability known as Intermediate Periods. Ancient Egypt reached its pinnacle during the New Kingdom, after which it entered a period of slow decline. For most parts of its long history, ancient Egypt was unified under one government. The military concern for the nation was to keep enemies out. Nevertheless, the great expanses of the desert formed a barrier, almost impossible for massive armies to cross. The Egyptians built fortresses and outposts to the south. If a large force was detected a message was sent for the main army corps. Most Egyptian cities lacked other defenses. The history of ancient Egypt is divided into two intermediate periods. During the three Kingdoms Egypt was unified under one government. During the Intermediate periods control was in the hands of the various nomes and various foreigners. The geography of Egypt allowed it to thrive. This circumstance set the stage for many of Egypt's military conquests. They enfeebled their enemies like bows and arrows.
Military of ancient Egypt
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The Hyksos of Ancient Egypt drove chariots
Military of ancient Egypt
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A New Kingdom khopesh
Military of ancient Egypt
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Wooden figures found in the tomb of Mesehti: Egyptian army of the 11th Dynasty
Military of ancient Egypt
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Ancient Egyptian chariot
69.
Music of Egypt
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Music has been an integral part of Egyptian culture since antiquity. The Bible documents the instruments played by the ancient Hebrews, all of which are correlated in Egyptian archaeology. The modern music of Egypt is considered Arabic music as it has been influence on other regional styles. The ancient Egyptians credited the Bat with the invention of music. The cult of Bat was eventually syncretised into that of Hathor because both were depicted as cows. Hathor's music was believed to have been used as part of his effort to civilize the world. The lion-goddess Bastet was also considered a goddess of music. In prehistoric Egypt, chanting were commonly used in magic and rituals. Rhythms during this time were music served to create rhythm. Small shells were used as whistles. During the predynastic period of Egyptian history, funerary chants were accompanied by clappers or a flute. The evidence is for instruments played more securely attested in the Old Kingdom when harps, double clarinets were played. Percussion lutes were added to orchestras by the Middle Kingdom. Cymbals frequently accompanied dance, much as they still do in Egypt today. Typically Egyptian music was composed from the phrygian dominant scale, phrygian scale, double harmonic scale or lydian scale.
Music of Egypt
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Musicians of Amun, Tomb of Nakht, 18th Dynasty, Western Thebes.
Music of Egypt
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Lute and double pipe players from a painting found in the Theban tomb of Nebamun, a nobleman of the 18th Dynasty of the New Kingdom, c. 1350 BC
Music of Egypt
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Broken Egyptian Sistrum
Music of Egypt
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Collection of sistrums at the Louvre
70.
Egyptian mythology
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Egyptian mythology is the collection of myths from ancient Egypt, which describe the actions of the Egyptian gods as a means of understanding the world. The beliefs that these myths express are an important part of Egyptian religion. Myths appear frequently in Egyptian writings and art, particularly in religious material such as hymns, ritual texts, funerary texts, temple decoration. These sources often describe only brief fragments. Myth sets the pattern for the cycles of the present. Present events repeat the events in doing so renew maat, the fundamental order of the universe. Events from the present that might be regarded as myths include Ra's daily journey through its otherworldly counterpart, the Duat. The details of these sacred events differ greatly to another and often seem contradictory. Egyptian myths are primarily metaphorical, translating the behavior of deities into terms that humans can understand. Each variant of a myth represents a symbolic perspective, enriching the Egyptians' understanding of the gods and the world. Mythology profoundly influenced Egyptian culture. It provided the ideological basis for kingship. Symbols from myth appeared in art in tombs, temples, amulets. The development of Egyptian myth is difficult to trace. Egyptologists must make educated guesses based on written sources that appeared much later.
Egyptian mythology
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Nun, the embodiment of the primordial waters, lifts the barque of the sun god Ra into the sky at the moment of creation.
Egyptian mythology
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The sky depicted as a cow goddess supported by other deities. This image combines several coexisting visions of the sky: as a roof, as the surface of a sea, as a cow, and as a goddess in human form.
Egyptian mythology
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Temple decoration at Dendera, depicting the goddesses Isis and Nephthys watching over the corpse of their brother Osiris
Egyptian mythology
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The air god Shu, assisted by other gods, holds up Nut, the sky, as Geb, the earth, lies beneath.
71.
Pharaoh
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The pharaoh ultimately was derived from a compound word represented as pr-3, ꜥꜣ "column". It was used only with specific reference to the buildings of the palace. During the eighteenth dynasty the title pharaoh was employed as a reverential designation of the ruler. From the nineteenth dynasty onward pr-ꜥꜣ on its own was used as regularly as hm.f,'Majesty'. Here, an induction of an individual to the Amun priesthood is dated specifically to the reign of Pharaoh Siamun. This new practice was continued under his successor Psusennes II and the twenty-second dynasty kings. Shoshenq I was the second successor of Siamun. Meanwhile, the old custom of referring to the sovereign as pr-aa continued in Egyptian narratives. By this time, the Egyptian word is reconstructed to have been pronounced * par-ʕoʔ whence Herodotus derove the name of the Egyptian kings, Φερων. In the Bible, the title also occurs as פרעה; from then Late Latin pharaō, both - n stem nouns. The Qur'an likewise spells it فرعون fir'awn with "n". English at first spelt it "Pharao", but the King James Bible revived "Pharaoh" with "h" from the Hebrew. Meanwhile in Egypt itself, *par-ʕoʔ evolved into Sahidic Coptic prro ⲡⲣ̅ⲣⲟ and then rro. Scepters and staves were a general sign of authority in ancient Egypt. One of the earliest royal scepters was discovered in the tomb of Khasekhemwy in Abydos.
Pharaoh
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Den
Pharaoh
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Narmer Palette
Pharaoh
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Nomen and prenomen of Ramesses III
Pharaoh
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Royal titulary
72.
List of pharaohs
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Note that the dates given are approximate. Modern lists of pharaohs are based on historical records: later histories, such as Manetho's Aegyptiaca, as well as archaeological evidence. An additional problem is that ancient king lists are inconsistent with one another and/or selective. The ancient king lists are known: Den seal impressions; found on a cylinder seal in Den's tomb. It lists all 1st dynasty kings by their Horus names. Palermo stone; carved on an olivin-basalt slab. Broken into pieces and thus today incomplete. Giza King List; painted with red, green and black ink on gypsum and cedar wood. Very selective. South Saqqara Stone; carved on a black basalt slab. Very selective. Karnak King List; carved on limestone. Very selective. Abydos King List of Seti I; carved on limestone. Omitting the First Intermediate Period.
List of pharaohs
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Iry-Hor
List of pharaohs
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The Pschent combined the Red Crown of Lower Egypt and the White Crown of Upper Egypt.
List of pharaohs
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Ka
List of pharaohs
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Scorpion II
73.
Ancient Egyptian religion
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Ancient Egyptian religion was a complex system of polytheistic beliefs and rituals which were an integral part of ancient Egyptian society. It centered with many deities who were believed to be present in, in control of, the forces of nature. Rituals such as offerings were efforts to provide for the gods and gain their favor. Religious practice centered on the pharaoh, the king of Egypt, believed to possess a divine power by virtue of his position. The state dedicated enormous resources to the construction of the temples. Individuals could interact with the gods for their own purposes, compelling them to act through magic. These practices were closely linked with, the formal rituals and institutions. The religious tradition grew more prominent in the course of Egyptian history as the status of the Pharaoh declined. Another important aspect was the belief in the funerary practices. The religion lasted for more than 3,000 years. Their intricate relationships shifted. At various times, certain gods became preeminent including the sun god Ra, the creator god Amun, the mother goddess Isis. For a brief period, in the theology promulgated by the Pharaoh Akhenaten, the Aten, replaced the traditional pantheon. Mythology left behind many writings and monuments, along with significant influences on ancient and modern cultures. The rituals now referred to as "ancient Egyptian religion" were integral within every aspect of Egyptian culture.
Ancient Egyptian religion
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The gods Osiris, Anubis, and Horus, in order from left to right
Ancient Egyptian religion
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Amun-Ra kamutef, wearing the plumed headdress of Amun and the sun disk representing Ra
Ancient Egyptian religion
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The air god Shu, assisted by other gods, holds up Nut, the sky, as Geb, the earth, lies beneath.
Ancient Egyptian religion
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Colossal statue of the Pharaoh Ramesses II
74.
List of ancient Egyptian sites
List of ancient Egyptian sites
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The nomes of Ancient Egypt, in lower Egypt
75.
Ancient Egyptian trade
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Epipaleolithic Natufians carried parthenocarpic figs to the southeastern corner of the Fertile Crescent, c. 10,000 BCE. The ancient people of the Sahara imported domesticated animals between 6000 and 4000 BCE. In Nabta Playa by the end of the 7th millennium BCE, prehistoric Egyptians had imported goats and sheep from Southwest Asia. Foreign artifacts dating in the Badarian culture in Egypt indicate contact with distant Syria. By the beginning of the 4th millennium BCE, ancient Egyptians in Maadi were importing pottery as well as construction ideas from Canaan. The donkey and possibly the dromedary had been domesticated. Domestication of the Bactrian use of the horse for transport then followed. Charcoal samples found in the tombs of Nekhen, which were dated to the Naqada I and II periods, have been identified from Lebanon. Predynastic Egyptians of the Naqada period also imported obsidian from Ethiopia, used to shape blades and other objects from flakes. Other artifacts from the Levant that date to the Naqadan era have been found in ancient Egypt. The Indus Valley was also known as the earliest maritime trading partner of the Sumerians and Akkadians in Mesopotamia. The ancient harbor constructed around 2400 BCE is the oldest seafaring harbour known. Ancient cities dating to the First Dynasty of Egypt arose along both its Nile and Red Sea junctions, testifying to the route's ancient popularity. Records exist documenting knowledge of the route among Senusret I, Seti, Ramesses IV and later, the Roman Empire, especially for mining. Later, Ancient Romans would protect the route by lining it with small outposts, some guarding large settlements complete with cultivation.
Ancient Egyptian trade
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Model of a paddling funerary boat from the tomb of Meketre. From the time of the Twelfth dynasty of Egypt, early in the reign of Amenemhat I, circa 1931–1975 BCE.
76.
Writing in Ancient Egypt
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Egyptian hieroglyphs were the formal writing system used in Ancient Egypt. It combined logographic, alphabetic elements, with a total of some 1,000 distinct characters. Cursive hieroglyphs were used for religious literature on papyrus and wood. Demotic Egyptian scripts are derived from hieroglyphic writing; Meroitic was a late derivation from Demotic. The system continued to be used throughout the Late Period, as well as the Persian and Ptolemaic periods. Late survivals of hieroglyphic use are found well into the Roman period, extending into the 4th AD. The decipherment of hieroglyphs would only be solved in the 1820s with the help of the Rosetta Stone. The hieroglyph comes from the Greek adjective ἱερογλυφικός, a compound of ἱερός and γλύφω, supposedly a calque of an Egyptian phrase mdw · w-nṯr "god's words". The glyphs themselves were called τὰ ἱερογλυφικὰ γράμματα "the sacred engraved letters". The hieroglyph has become a noun in English, standing for an individual hieroglyphic character. Hieroglyphic has also become a noun in English, at least in non-academic usage. Hieroglyphs emerged from the artistic traditions of Egypt. For example, symbols on Gerzean pottery from c. 4000 BC have been argued to resemble hieroglyphic writing. There are around 800 hieroglyphs dating back to the Old Kingdom, New Kingdom Eras. By the Greco-Roman period, there are more than 5,000.
Writing in Ancient Egypt
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Hieroglyphs from the Black Schist sarcophagus of Ankhnesneferibre. Twenty-Sixth Dynasty, about 530 BC, Thebes.
Writing in Ancient Egypt
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Demotic script on a replica of the Rosetta Stone.
77.
Giza Necropolis
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The Giza pyramid complex is an archaeological site on the Giza Plateau, on the outskirts of Cairo, Egypt. It is by far the oldest of the ancient Wonders and the only one still in existence. The Great Sphinx lies on the east side of the complex. Current consensus among Egyptologists is that the head of the Great Sphinx is that of Khafre. Along with these major monuments are a number of smaller satellite edifices, known as "queens" pyramids, causeways and valley pyramids. The valley temple was connected to a causeway, largely destroyed when the village was constructed. The causeway led to the Mortuary Temple of Khufu. From this temple the basalt pavement is the only thing that remains. The mortuary temple was connected to the king’s pyramid. The king’s pyramid has three smaller queen’s pyramids associated with it and five boat pits. The boat pits contained a ship, the 2 pits on the south side of the pyramid still contained intact ships. One of these ships has been restored and is on display. Khufu's pyramid still has a limited collection of casing stones at its base. These casing stones were made of fine white limestone quarried from the nearby range. Khafre's complex consists of a valley temple, the Sphinx temple, a causeway, the king's pyramid.
Giza Necropolis
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All of the six pyramids of the Giza pyramid complex
Giza Necropolis
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Views, Objects: Egypt. Gizeh [selected images]. View 05: Sphinx and Pyramids., n.d., New York. Brooklyn Museum Archives
Giza Necropolis
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Pyramids of Ghizeh. 1893. Egypt; heliogravures after original views. Wilbour Library of Egyptology. Brooklyn Museum
Giza Necropolis
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The Great Sphinx partially excavated, photo taken between 1867 and 1899
78.
Egyptology
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A practitioner of the discipline is an "Egyptologist". The first explorers were the ancient Egyptians themselves. Thutmose IV restored the Sphinx and had the dream that inspired his restoration carved on the famous Dream Stele. Less than two centuries later, fourth son of Ramesses II, is famed for restoring historic buildings, temples including the pyramid. The Ptolemies were much interested in the work of the ancient Egyptians, many of the Egyptian monuments, including the pyramids, were restored by them. The Romans too carried out restoration work in this most ancient of lands. A number of their accounts have survived and offer insights as to conditions in their respective time periods. Abdul Latif al-Baghdadi, a teacher at Cairo's Al-Azhar University in the 13th century, wrote detailed descriptions on ancient Egyptian monuments. Similarly, the 15th-century Egyptian historian al-Maqrizi wrote detailed accounts of Egyptian antiquities. The British captured Egypt from the French and gained the Rosetta Stone. Modern Egyptology is generally perceived as beginning about 1822. Egyptology's modern history begins with the invasion of Egypt by Napoleon Bonaparte. The subsequent publication of Description de l'Égypte between 1829 made Egyptian source materials available to Europeans for the first time. Jean-François Champollion, Thomas Young and Ippolito Rosellini were some of the first Egyptologists of wide acclaim. The German Karl Richard Lepsius was an early participant in the investigations of Egypt; mapping, excavating, recording several sites.
Egyptology
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The Great Sphinx of Giza against Khafre's Pyramid at the Giza pyramid complex
Egyptology
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Hieroglyphs and depictions transcribed by Ippolito Rosellini in 1832
Egyptology
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A section of the Papyrus of Ani showing cursive hieroglyphs
79.
List of Egyptologists
List of Egyptologists
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Jan Assmann
List of Egyptologists
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Fernand Bisson de La Roque
List of Egyptologists
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Heinrich Brugsch
List of Egyptologists
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Howard Carter
80.
Ancient Egyptian mathematics
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Ancient Egyptian mathematics is the mathematics, developed and used in Ancient Egypt c.3000 to c.300 BC. Written evidence of the use of mathematics dates back to at least 3000 BC with the ivory labels found in Tomb U-j at Abydos. Some are inscribed with numbers. The lines in the diagram show the use of that unit of measurement. The earliest true mathematical documents date to the 12th dynasty. The Rhind Mathematical Papyrus which dates to the Second Intermediate Period is said to be based on an older mathematical text from the 12th dynasty. The Moscow Mathematical Papyrus and Rhind Mathematical Papyrus are mathematical problem texts. They consist of a collection of problems with solutions. These texts may have been written by a student engaged in solving typical mathematics problems. An interesting feature of Egyptian mathematics is the use of unit fractions. Scribes used tables to help them work with these fractions. The Egyptian Mathematical Leather Roll for instance is a table of unit fractions which are expressed as sums of other unit fractions. Some of the other texts contain 2 n tables. These tables allowed the scribes to rewrite any fraction of the form 1 n as a sum of unit fractions. In the worker's village of Deir several ostraca have been found that record volumes of dirt removed while quarrying the tombs.
Ancient Egyptian mathematics
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Slab stela of Old Kingdom princess Neferetiabet (dated 2590–2565 BC) from her tomb at Giza, painting on limestone, now in the Louvre.
Ancient Egyptian mathematics
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Image of Problem 14 from the Moscow Mathematical Papyrus. The problem includes a diagram indicating the dimensions of the truncated pyramid.