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Seked
Seked (or seqed) is an ancient Egyptian term describing the inclination of the triangular faces of a right pyramid. The system was based on the Egyptians' length measure known as the royal cubit. It was subdivided into seven ''palms'', each of which was sub-divided into four ''digits''. The inclination of measured slopes was therefore expressed as the number of horizontal palms and digits relative to each royal cubit rise. The seked is proportional to the reciprocal of our modern measure of slope or gradient, and to the cotangent of the angle of elevation.Gillings: Mathematics in the Time of the Pharaohs 1982: pp 212 Specifically, if ''s'' is the seked, ''m'' the slope (rise over run), and \phi the angle of elevation from horizontal, then: :s = \frac = 7\cot(\phi). The most famous example of a seked slope is of the Great Pyramid of Giza in Egypt built around 2550 BC. Based on modern surveys, the faces of this monument had a seked of 5½, or 5 palms and 2 digits, in modern terms e ...
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Seked
Seked (or seqed) is an ancient Egyptian term describing the inclination of the triangular faces of a right pyramid. The system was based on the Egyptians' length measure known as the royal cubit. It was subdivided into seven ''palms'', each of which was sub-divided into four ''digits''. The inclination of measured slopes was therefore expressed as the number of horizontal palms and digits relative to each royal cubit rise. The seked is proportional to the reciprocal of our modern measure of slope or gradient, and to the cotangent of the angle of elevation.Gillings: Mathematics in the Time of the Pharaohs 1982: pp 212 Specifically, if ''s'' is the seked, ''m'' the slope (rise over run), and \phi the angle of elevation from horizontal, then: :s = \frac = 7\cot(\phi). The most famous example of a seked slope is of the Great Pyramid of Giza in Egypt built around 2550 BC. Based on modern surveys, the faces of this monument had a seked of 5½, or 5 palms and 2 digits, in modern terms e ...
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Great Pyramid Of Giza
The Great Pyramid of Giza is the biggest Egyptian pyramid and the tomb of Fourth Dynasty pharaoh Khufu. Built in the early 26th century BC during a period of around 27 years, the pyramid is the oldest of the Seven Wonders of the Ancient World, and the only one to remain largely intact. As part of the Giza pyramid complex, it borders present-day Giza in Greater Cairo, Egypt. Initially standing at , the Great Pyramid was the tallest man-made structure in the world for more than 3,800 years. Over time, most of the smooth white limestone casing was removed, which lowered the pyramid's height to the present . What is seen today is the underlying core structure. The base was measured to be about square, giving a volume of roughly , which includes an internal hillock. The dimensions of the pyramid were high, a base length of , with a seked of palms (a slope of 51°50'40"). The Great Pyramid was built by quarrying an estimated 2.3 million large blocks weighing 6 million ton ...
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Rhind Mathematical Papyrus
The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of ancient Egyptian mathematics. It is named after Alexander Henry Rhind, a Scotland, Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt; it was apparently found during illegal excavations in or near the Ramesseum. It dates to around 1550 BC. The British Museum, where the majority of the papyrus is now kept, acquired it in 1865 along with the Egyptian Mathematical Leather Roll, also owned by Henry Rhind. There are a few small fragments held by the Brooklyn Museum in New York City and an central section is missing. 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. The Rhind Mathematical Papyrus dates to the Second Intermediate Period of History of ancient Egypt, Egypt. It was copied by the sc ...
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Cubit
The cubit is an ancient unit of length based on the distance from the elbow to the tip of the middle finger. It was primarily associated with the Sumerians, Egyptians, and Israelites. The term ''cubit'' is found in the Bible regarding Noah's Ark, Ark of the Covenant, Tabernacle, Solomon's Temple. The ''common cubit'' was divided into 6 palms × 4 fingers = 24 digits. ''Royal cubits'' added a palm for 7 palms × 4 fingers = 28 digits. These lengths typically ranged from , with an ancient Roman cubit being as long as . Cubits of various lengths were employed in many parts of the world in antiquity, during the Middle Ages and as recently as early modern times. The term is still used in hedgelaying, the length of the forearm being frequently used to determine the interval between stakes placed within the hedge. Etymology The English word "cubit" comes from the Latin noun "elbow", from the verb "to lie down", from which also comes the adjective " recumbent". Ancie ...
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Slope
In mathematics, the slope or gradient of a line is a number that describes both the ''direction'' and the ''steepness'' of the line. Slope is often denoted by the letter ''m''; there is no clear answer to the question why the letter ''m'' is used for slope, but its earliest use in English appears in O'Brien (1844) who wrote the equation of a straight line as and it can also be found in Todhunter (1888) who wrote it as "''y'' = ''mx'' + ''c''". Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical – as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan. The ''steepness'', incline, or grade of a line is measured by the absolu ...
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Moscow Mathematical Papyrus
The Moscow Mathematical Papyrus, also named the Golenishchev Mathematical Papyrus after its first non-Egyptian owner, Egyptologist Vladimir Golenishchev, is an ancient Egyptian mathematical papyrus containing several problems in arithmetic, geometry, and algebra. 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. Based on the palaeography and orthography of the hieratic text, the text was most likely written down in the 13th Dynasty and based on older material probably dating to the Twelfth Dynasty of Egypt, roughly 1850 BC.Clagett, Marshall. 1999. Ancient Egyptian Science: A Source Book. Volume 3: Ancient Egyptian Mathematics. Memoirs of the American Philosophical Society 232. Philadelphia: American Philosophical Society. Approximately 5½ m (18 ft) long and varying between wide, its format was divided by the Soviet Orientalist Vasily Vasilievich Stru ...
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Flinders Petrie
Sir William Matthew Flinders Petrie ( – ), commonly known as simply Flinders Petrie, was a British Egyptologist and a pioneer of systematic methodology in archaeology and the preservation of artefacts. He held the first chair of Egyptology in the United Kingdom, and excavated many of the most important archaeological sites in Egypt in conjunction with his wife, Hilda Urlin. Some consider his most famous discovery to be that of the Merneptah Stele, an opinion with which Petrie himself concurred. Undoubtedly at least as important is his 1905 discovery and correct identification of the character of the Proto-Sinaitic script, the ancestor of almost all alphabetic scripts. Petrie developed the system of dating layers based on pottery and ceramic findings. He remains controversial for his pro-eugenics views; he was a dedicated believer in the superiority of the Northern peoples over the Latinate and Southern peoples. Early life Petrie was born on 3 June 1853 in Charlto ...
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Meidum
Meidum, Maydum or Maidum ( ar, ميدوم, , ) is an archaeological site in Lower Egypt. It contains a large pyramid and several mudbrick mastabas. The pyramid was Egypt's first straight-sided one, but it partially collapsed in ancient times. The area is located around south of modern Cairo. Pyramid The pyramid at Meidum is thought to be just the second pyramid built after Djoser's and may have been originally built for Huni, the last pharaoh of the Third Dynasty, and continued by Sneferu. Because of its unusual appearance, the pyramid is called ''el-heram el-kaddaab'' – (''False Pyramid'') in Egyptian Arabic. The second extension turned the original step pyramid design into a true pyramid by filling in the steps with limestone encasing. While this approach is consistent with the design of the other true pyramids, Meidum was affected by construction errors. Firstly, the outer layer was founded on sand and not on rock, like the inner layers. Secondly, the inner step pyra ...
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Triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle measurements at known points, rather than measuring distances to the point directly as in trilateration; the use of both angles and distance measurements is referred to as triangulateration. In computer vision Computer stereo vision and optical 3D measuring systems use this principle to determine the spatial dimensions and the geometry of an item. Basically, the configuration consists of two sensors observing the item. One of the sensors is typically a digital camera device, and the other one can also be a camera or a light projector. The projection centers of the sensors and the considered point on the object's surface define a (spatial) triangle. Within this triangle, the distance between the sensors is the base ''b'' and must be kno ...
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Ancient Egyptian Pyramids
The Egyptian pyramids are ancient masonry structures located in Egypt. Sources cite at least 118 identified "Egyptian" pyramids. Approximately 80 pyramids were built within the Kingdom of Kush, now located in the modern country of Sudan. Of those located in modern Egypt, most were built as tombs for the country's pharaohs and their consorts during the Old Kingdom of Egypt, Old and Middle Kingdom of Egypt, Middle Kingdom periods. The earliest known Egyptian pyramids are found at Saqqara, northwest of Memphis, Egypt, Memphis, although at least one step-pyramid-like structure has been found at Saqqara, dating to the First Dynasty of Egypt, First Dynasty: Mastaba 3808, which has been attributed to the reign of Pharaoh Anedjib, with inscriptions, and other archaeological remains of the period, suggesting there may have been others. The otherwise earliest among these is the Pyramid of Djoser built   during the Third dynasty of Egypt, Third Dynasty. This pyramid and its surroun ...
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