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Knotted Cord
A knotted cord was a primitive surveyor's tool for measuring distances. It is a length of cord with knots at regular intervals. They were eventually replaced by surveyor's chains, which being made of metal were less prone to stretching and thus were more accurate and consistent. Knotted cords were used by many ancient cultures. The Greek schoenus is referred to as a rope used to measure land. Ropes generally became cables and chains with Pythagoras making the Greek agros a chain of 10 stadia equal to a nautical mile c 540 BC. The Romans used a waxed cord for measuring distances. A knotted cord 12 lengths long (the units do not matter) closed into a loop can be used to lay out a right angle by forming the loop of cord into a 3–4–5 triangle. This could be used for laying out the corner of a field or a building foundation, for instance. Ancient Egypt Knotted cords were used by rope stretchers, royal surveyors who measured out the sides of fields ( Egyptian ''3ht''). The kno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inca Empire
The Inca Empire (also known as the Incan Empire and the Inka Empire), called ''Tawantinsuyu'' by its subjects, ( Quechua for the "Realm of the Four Parts", "four parts together" ) was the largest empire in pre-Columbian America. The administrative, political and military center of the empire was in the city of Cusco. The Inca civilization arose from the Peruvian highlands sometime in the early 13th century. The Spanish began the conquest of the Inca Empire in 1532 and by 1572, the last Inca state was fully conquered. From 1438 to 1533, the Incas incorporated a large portion of western South America, centered on the Andean Mountains, using conquest and peaceful assimilation, among other methods. At its largest, the empire joined modern-day Peru, what are now western Ecuador, western and south central Bolivia, northwest Argentina, the southwesternmost tip of Colombia and a large portion of modern-day Chile, and into a state comparable to the historical empires o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagoras' Theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides ''a'', ''b'' and the hypotenuse ''c'', often called the Pythagorean equation: :a^2 + b^2 = c^2 , The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rope (unit)
A rope may refer to any of several units of measurement initially determined or formed by ropes or knotted cords. Length The Greco- Roman schoenus, supposedly based on an Egyptian unit derived from a wound reed measuring rope, may also be given in translation as a "rope". According to Strabo, it varied in length between 30 and 120 stadia (roughly 5 to 20 km) depending on local custom. The Byzantine equivalent, the schoinion or "little rope", varied between 60 and 72 Greek feet depending upon the location. The Thai sen of 20 Thai fathoms or 40 m also means and is translated "rope". The Somerset rope was a former English unit used in drainage and hedging. It was 20 feet (now precisely 6.096 m). Area The Romans used the schoenus as an alternative name for the half-jugerum formed by a square with sides of 120 Roman feet. In Somerset, the rope could also double as a measure of area equivalent to 20 feet by 1 foot. Walls in Somerset were formerly sold ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Middle Kingdom Of Egypt
The Middle Kingdom of Egypt (also known as The Period of Reunification) is the period in the history of ancient Egypt following a period of political division known as the First Intermediate Period. The Middle Kingdom lasted from approximately 2040 to 1782 BC, stretching from the reunification of Egypt under the reign of Mentuhotep II in the Eleventh Dynasty to the end of the Twelfth Dynasty. The kings of the Eleventh Dynasty ruled from Thebes and the kings of the Twelfth Dynasty ruled from el-Lisht. The concept of the Middle Kingdom as one of three golden ages was coined in 1845 by German Egyptologist Baron von Bunsen, and its definition evolved significantly throughout the 19th and 20th centuries. Some scholars also include the Thirteenth Dynasty of Egypt wholly into this period, in which case the Middle Kingdom would end around 1650 BC, while others only include it until Merneferre Ay around 1700 BC, last king of this dynasty to be attested in both Upper and Lower Egy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin Papyrus 6619
The Berlin Papyrus 6619, simply called the Berlin Papyrus when the context makes it clear, is one of the primary sources of ancient Egyptian mathematics. One of the two mathematics problems on the Papyrus may suggest that the ancient Egyptians knew the Pythagorean theorem. Description, dating, and provenance The Berlin Papyrus 6619 is an ancient Egyptian papyrus document from the Middle Kingdom, second half of the 12th (c. 1990–1800 BC) or 13th Dynasty (c. 1800 BC – 1649 BC). The two readable fragments were published by Hans Schack-Schackenburg in 1900 and 1902. Connection to the Pythagorean theorem 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 ½ + ¼ the side of the other."Richard J. Gillings, ''Mathematics in the Time of the Pharaohs'', Dover, New York, 1982, 161. The interest in the question may suggest some knowledge of the Pythagorean theorem, though the papyrus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Iside Et Osiride
The ''Moralia'' ( grc, Ἠθικά ''Ethika''; loosely translated as "Morals" or "Matters relating to customs and mores") is a group of manuscripts dating from the 10th–13th centuries, traditionally ascribed to the 1st-century Greek scholar Plutarch of Chaeronea. The eclectic collection contains 78 essays and transcribed speeches. They provide insights into Roman and Greek life, but often are also timeless observations in their own right. Many generations of Europeans have read or imitated them, including Michel de Montaigne and the Renaissance Humanists and Enlightenment philosophers. Contents General structure The ''Moralia'' include ''On the Fortune or the Virtue of Alexander the Great'', an important adjunct to his ''Life'' of the great general; ''On the Worship of Isis and Osiris'', a crucial source of information on Egyptian religious rites; and ''On the Malice of Herodotus'' (which may, like the orations on Alexander's accomplishments, have been a rhetorical exerc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plutarch
Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for his '' Parallel Lives'', a series of biographies of illustrious Greeks and Romans, and '' Moralia'', a collection of essays and speeches. Upon becoming a Roman citizen, he was possibly named Lucius Mestrius Plutarchus (). Life Early life Plutarch was born to a prominent family in the small town of Chaeronea, about east of Delphi, in the Greek region of Boeotia. His family was long established in the town; his father was named Autobulus and his grandfather was named Lamprias. His name is derived from Pluto (πλοῦτον), an epithet of Hades, and Archos (ἀρχός) meaning "Master", the whole name meaning something like "Whose master is Pluto". His brothers, Timon and Lamprias, are frequently mentioned in his essays and dialogue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moritz Cantor
Moritz Benedikt Cantor (23 August 1829 – 10 April 1920) was a German historian of mathematics. Biography Cantor was born at Mannheim. He came from a Sephardi Jewish family that had emigrated to the Netherlands from Portugal, another branch of which had established itself in Russia. In his early youth, Moritz Cantor was not strong enough to go to school, and his parents decided to educate him at home. Later, however, he was admitted to an advanced class of the Gymnasium in Mannheim. From there he went to the University of Heidelberg in 1848, and soon after to the University of Göttingen, where he studied under Gauss and Weber, and where Stern awakened in him a strong interest in historical research. After obtaining his PhD at the University of Heidelberg in 1851, he went to Berlin, where he eagerly followed the lectures of Peter Gustav Lejeune Dirichlet; and upon his return to Heidelberg in 1853, he was appointed privat-docent at the university. In 1863, he was promoted to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pyramid
A pyramid (from el, πυραμίς ') is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilateral, or of any polygon shape. As such, a pyramid has at least three outer triangular surfaces (at least four faces including the base). The square pyramid, with a square base and four triangular outer surfaces, is a common version. A pyramid's design, with the majority of the weight closer to the ground and with the pyramidion at the apex, means that less material higher up on the pyramid will be pushing down from above. This distribution of weight allowed early civilizations to create stable monumental structures. Civilizations in many parts of the world have built pyramids. The largest pyramid by volume is the Great Pyramid of Cholula, in the Mexican state of Puebla. For thousands of years, the largest structures on Earth were py ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics And Architecture
Mathematics and architecture are related, since, as with other arts, architects use mathematics for several reasons. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building; from the Pythagoreans of the sixth century BC onwards, to create forms considered harmonious, and thus to lay out buildings and their surroundings according to mathematical, aesthetic and sometimes religious principles; to decorate buildings with mathematical objects such as tessellations; and to meet environmental goals, such as to minimise wind speeds around the bases of tall buildings. History In ancient Egypt, ancient Greece, India, and the Islamic world, buildings including pyramids, temples, mosques, palaces and mausoleums were laid out with specific proportions for religious reasons. In Islamic architecture, geometric shapes and geometric tiling patterns are used to decorate buildings, both inside and outside. Some Hindu t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surveying
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is called a land surveyor. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designed positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales. Surveyors work with elements of geodesy, geometry, trigonometry, regression analysis, physics, engineering, metrology, programming languages, and the law. They use equipment, such as total stations, robotic total stations, theodolites, GNSS receivers, retroreflectors, 3D scanners, LiDAR sensors, radios, inclinometer, handheld tablets, optical and digital levels, subsurface locat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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