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117-449: NCEES develops and scores the FE, PE and SE exams for engineering licensure. The FE exam is generally the first step in the process to becoming a professional licensed engineer (PE). It is designed for recent graduates and students who are close to finishing an undergraduate engineering degree from an EAC/ABET- accredited program. The PE exam is designed to test for a minimum level of competency in

234-495: A plane table in 1551, but it is thought that the instrument was in use earlier as his description is of a developed instrument. Gunter's chain was introduced in 1620 by English mathematician Edmund Gunter . It enabled plots of land to be accurately surveyed and plotted for legal and commercial purposes. Leonard Digges described a theodolite that measured horizontal angles in his book A geometric practice named Pantometria (1571). Joshua Habermel ( Erasmus Habermehl ) created

351-445: A GPS on large scale surveys makes them popular for major infrastructure or data gathering projects. One-person robotic-guided total stations allow surveyors to measure without extra workers to aim the telescope or record data. A fast but expensive way to measure large areas is with a helicopter, using a GPS to record the location of the helicopter and a laser scanner to measure the ground. To increase precision, surveyors place beacons on

468-439: A base length of 440 cubits (230.6 m; 756.4 ft), with a seked of ⁠5 + 1 / 2 ⁠ palms (a slope of 51°50'40"). The Great Pyramid was built by quarrying an estimated 2.3 million large blocks, weighing 6 million tonnes in total. The majority of the stones are not uniform in size or shape, and are only roughly dressed. The outside layers were bound together by mortar . Primarily local limestone from

585-513: A causeway (one close to the pyramid and one near the Nile); tombs for the immediate family and court of Khufu, including three smaller pyramids for Khufu's wives; an even smaller "satellite pyramid"; and five buried solar barques . The Great Pyramid of Giza was the tomb of pharaoh Khufu, and still contains his granite sarcophagus. It had, like other tombs of Egyptian elites, four main purposes: Make your grave well furnished and prepare thy place in

702-477: A fixed base station and a second roving antenna. The position of the roving antenna can be tracked. The theodolite , total station and RTK GPS survey remain the primary methods in use. Remote sensing and satellite imagery continue to improve and become cheaper, allowing more commonplace use. Prominent new technologies include three-dimensional (3D) scanning and lidar -based topographical surveys. UAV technology along with photogrammetric image processing

819-504: A granite sarcophagus, are above ground, within the pyramid structure. Hemiunu , Khufu's vizier , is believed by some to be the architect of the Great Pyramid. Many varying scientific and alternative hypotheses attempt to explain the exact construction techniques , but, as is the case for other such structures, there is no definite consensus. The funerary complex around the pyramid consisted of two mortuary temples connected by

936-423: A great step forward in the instrument's accuracy. William Gascoigne invented an instrument that used a telescope with an installed crosshair as a target device, in 1640. James Watt developed an optical meter for the measuring of distance in 1771; it measured the parallactic angle from which the distance to a point could be deduced. Dutch mathematician Willebrord Snellius (a.k.a. Snel van Royen) introduced

1053-502: A height above sea level. As the surveying profession grew it created Cartesian coordinate systems to simplify the mathematics for surveys over small parts of the Earth. The simplest coordinate systems assume that the Earth is flat and measure from an arbitrary point, known as a 'datum' (singular form of data). The coordinate system allows easy calculation of the distances and direction between objects over small areas. Large areas distort due to

1170-433: A known size. It was sometimes used before to the invention of EDM where rough ground made chain measurement impractical. Historically, horizontal angles were measured by using a compass to provide a magnetic bearing or azimuth. Later, more precise scribed discs improved angular resolution. Mounting telescopes with reticles atop the disc allowed more precise sighting (see theodolite ). Levels and calibrated circles allowed

1287-434: A loop pattern or link between two prior reference marks so the surveyor can check their measurements. Many surveys do not calculate positions on the surface of the Earth, but instead, measure the relative positions of objects. However, often the surveyed items need to be compared to outside data, such as boundary lines or previous survey's objects. The oldest way of describing a position is via latitude and longitude, and often

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1404-399: A man holding a tablet and a woman holding a mirror. Supposedly, between the statues was a "stone vessel [with] a gold cover". Inside the vessel was "something like pitch ", and when the explorer reached into the vessel "a gold receptacle happened to be inside". The receptacle, when taken from the vessel, was filled with "fresh blood", which quickly dried up. Ibn al-Nadim's work also claims that

1521-413: A misinterpretation of the pyramids as "Joseph's granary" began to gain in popularity. The first textual evidence of this connection is found in the travel narratives of the female Christian pilgrim Egeria , who records that on her visit between 381 and 384 AD, "in the twelve-mile stretch between Memphis and Babylonia [= Old Cairo] are many pyramids, which Joseph made in order to store corn." Ten years later

1638-471: A mixture of comprehensible descriptions, personal descriptions, erroneous reports, and fantastical legends; as a result, many of the speculative errors and confusions about the monument can be traced back to Herodotus and his work. Herodotus writes that the Great Pyramid was built by Khufu (Hellenized as Cheops) who, he erroneously relays, ruled after the Ramesside Period (the 19th dynasty and

1755-618: A multi frequency phase shift of light waves to find a distance. These instruments eliminated the need for days or weeks of chain measurement by measuring between points kilometers apart in one go. Advances in electronics allowed miniaturization of EDM. In the 1970s the first instruments combining angle and distance measurement appeared, becoming known as total stations . Manufacturers added more equipment by degrees, bringing improvements in accuracy and speed of measurement. Major advances include tilt compensators, data recorders and on-board calculation programs. The first satellite positioning system

1872-422: A particular engineering discipline. It is designed for engineers who have gained a minimum of four years of work experience in their chosen engineering discipline. The PE Structural Engineering exam is predominantly developed to test engineers who practice in jurisdictions that license structural engineers separately from other professional engineers. NCEES also prepares examinations for land surveyor licensing in

1989-411: A plan or map, and the points at the ends of the offset lines could be joined to show the feature. Traversing is a common method of surveying smaller areas. The surveyor starts from an old reference mark or known position and places a network of reference marks covering the survey area. They then measure bearings and distances between the reference marks, and to the target features. Most traverses form

2106-406: A point inside a triangle using the angles cast between the vertices at the unknown point. These could be measured more accurately than bearings of the vertices, which depended on a compass. His work established the idea of surveying a primary network of control points, and locating subsidiary points inside the primary network later. Between 1733 and 1740, Jacques Cassini and his son César undertook

2223-478: A profession. They established the basic measurements under which the Roman Empire was divided, such as a tax register of conquered lands (300 AD). Roman surveyors were known as Gromatici . In medieval Europe, beating the bounds maintained the boundaries of a village or parish. This was the practice of gathering a group of residents and walking around the parish or village to establish a communal memory of

2340-428: A reflector or prism to return the light pulses used for distance measurements. They are fully robotic, and can even e-mail point data to a remote computer and connect to satellite positioning systems , such as Global Positioning System . Real Time Kinematic GPS systems have significantly increased the speed of surveying, and they are now horizontally accurate to within 1 cm ± 1 ppm in real-time, while vertically it

2457-476: A star is determined, the bearing can be transferred to a reference point on Earth. The point can then be used as a base for further observations. Survey-accurate astronomic positions were difficult to observe and calculate and so tended to be a base off which many other measurements were made. Since the advent of the GPS system, astronomic observations are rare as GPS allows adequate positions to be determined over most of

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2574-495: A theodolite with a compass and tripod in 1576. Johnathon Sission was the first to incorporate a telescope on a theodolite in 1725. In the 18th century, modern techniques and instruments for surveying began to be used. Jesse Ramsden introduced the first precision theodolite in 1787. It was an instrument for measuring angles in the horizontal and vertical planes. He created his great theodolite using an accurate dividing engine of his own design. Ramsden's theodolite represented

2691-593: A time component. Before EDM (Electronic Distance Measurement) laser devices, distances were measured using a variety of means. In pre-colonial America Natives would use the "bow shot" as a distance reference ("as far as an arrow can slung out of a bow", or "flights of a Cherokee long bow"). Europeans used chains with links of a known length such as a Gunter's chain , or measuring tapes made of steel or invar . To measure horizontal distances, these chains or tapes were pulled taut to reduce sagging and slack. The distance had to be adjusted for heat expansion. Attempts to hold

2808-474: Is a staple of contemporary land surveying. Typically, much if not all of the drafting and some of the designing for plans and plats of the surveyed property is done by the surveyor, and nearly everyone working in the area of drafting today (2021) utilizes CAD software and hardware both on PC, and more and more in newer generation data collectors in the field as well. Other computer platforms and tools commonly used today by surveyors are offered online by

2925-399: Is a term used when referring to moving the level to take an elevation shot from a different location. To "turn" the level, one must first take a reading and record the elevation of the point the rod is located on. While the rod is being kept in exactly the same location, the level is moved to a new location where the rod is still visible. A reading is taken from the new location of the level and

3042-400: Is also appearing. The main surveying instruments in use around the world are the theodolite , measuring tape , total station , 3D scanners , GPS / GNSS , level and rod . Most instruments screw onto a tripod when in use. Tape measures are often used for measurement of smaller distances. 3D scanners and various forms of aerial imagery are also used. The theodolite is an instrument for

3159-412: Is an alternate method of determining the position of objects, and was often used to measure imprecise features such as riverbanks. The surveyor would mark and measure two known positions on the ground roughly parallel to the feature, and mark out a baseline between them. At regular intervals, a distance was measured at right angles from the first line to the feature. The measurements could then be plotted on

3276-505: Is because divergent conditions further away from the base reduce accuracy. Surveying instruments have characteristics that make them suitable for certain uses. Theodolites and levels are often used by constructors rather than surveyors in first world countries. The constructor can perform simple survey tasks using a relatively cheap instrument. Total stations are workhorses for many professional surveyors because they are versatile and reliable in all conditions. The productivity improvements from

3393-585: Is currently about half of that to within 2 cm ± 2 ppm. GPS surveying differs from other GPS uses in the equipment and methods used. Static GPS uses two receivers placed in position for a considerable length of time. The long span of time lets the receiver compare measurements as the satellites orbit. The changes as the satellites orbit also provide the measurement network with well conditioned geometry. This produces an accurate baseline that can be over 20 km long. RTK surveying uses one static antenna and one roving antenna. The static antenna tracks changes in

3510-406: 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. 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 designated positions of structural components for construction or

3627-402: Is thought to be mainly responsible for the 100–300 year offset, since the age of the organic material was determined, not when it was last used. A reanalysis of the data gave a completion date for the pyramid between 2620 and 2484 BC, based on the younger samples. In 1872 Waynman Dixon opened the lower pair of "Air-Shafts", previously closed at both ends, by chiseling holes into the walls of

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3744-432: Is with an altimeter  using air pressure to find the height. When more precise measurements are needed, means like precise levels (also known as differential leveling) are used. When precise leveling, a series of measurements between two points are taken using an instrument and a measuring rod. Differences in height between the measurements are added and subtracted in a series to get the net difference in elevation between

3861-470: The 20th dynasty ). Khufu was a tyrannical king, Herodotus claims, which may explain the Greek's view that such buildings can only come about through cruel exploitation of the people. Herodotus states that gangs of 100,000 labourers worked on the building in three-month shifts, taking 20 years to build. In the first ten years a wide causeway was erected, which, according to Herodotus, was almost as impressive as

3978-498: The Diary of Merer was found at Wadi al-Jarf . It documents the transportation of white limestone blocks from Tura to the Great Pyramid, which is mentioned by its original name Akhet Khufu (with a pyramid determinative ) dozens of times. It details that the stones were accepted at She Akhet-Khufu ("the pool of the pyramid Horizon of Khufu") and Ro-She Khufu ("the entrance to the pool of Khufu"), which were under supervision of Ankhhaf ,

4095-537: The East Field south of the causeway, and the West Field , including the wives, children and grandchildren of Khufu, Hemiunu , Ankhaf and (the funerary cache of) Hetepheres I , mother of Khufu. As Hassan puts it: "From the early dynastic times, it was always the custom for the relatives, friends and courtiers to be buried in the vicinity of the king they had served during life. This was quite in accordance with

4212-579: The Giza Plateau was used for its construction. Other blocks were imported by boat on the Nile : white limestone from Tura for the casing, and blocks of granite from Aswan , weighing up to 80 tonnes, for the "King's Chamber" structure. There are three known chambers inside of the Great Pyramid. The lowest was cut into the bedrock , upon which the pyramid was built, but remained unfinished. The so-called Queen's Chamber and King's Chamber, which contain

4329-713: The Great Pyramid of Giza , built c.  2700 BC , affirm the Egyptians' command of surveying. The groma instrument may have originated in Mesopotamia (early 1st millennium BC). The prehistoric monument at Stonehenge ( c.  2500 BC ) was set out by prehistoric surveyors using peg and rope geometry. The mathematician Liu Hui described ways of measuring distant objects in his work Haidao Suanjing or The Sea Island Mathematical Manual , published in 263 AD. The Romans recognized land surveying as

4446-509: The Principal Triangulation of Britain . The first Ramsden theodolite was built for this survey. The survey was finally completed in 1853. The Great Trigonometric Survey of India began in 1801. The Indian survey had an enormous scientific impact. It was responsible for one of the first accurate measurements of a section of an arc of longitude, and for measurements of the geodesic anomaly. It named and mapped Mount Everest and

4563-538: The Rashidun Caliphate conquered Egypt , ending several centuries of Romano-Byzantine rule. A few centuries later, in 832 AD, the Abbasid caliph al-Ma'mun (786–833) is said to have tunnelled into the side of the structure and discovered the ascending passage and its connecting chambers. Around this time a Coptic legend gained popularity that claimed the antediluvian king Surid Ibn Salhouk had built

4680-621: The Torrens system in South Australia in 1858. Torrens intended to simplify land transactions and provide reliable titles via a centralized register of land. The Torrens system was adopted in several other nations of the English-speaking world. Surveying became increasingly important with the arrival of railroads in the 1800s. Surveying was necessary so that railroads could plan technologically and financially viable routes. At

4797-799: The U.S. Federal Government and other governments' survey agencies, such as the National Geodetic Survey and the CORS network, to get automated corrections and conversions for collected GPS data, and the data coordinate systems themselves. Surveyors determine the position of objects by measuring angles and distances. The factors that can affect the accuracy of their observations are also measured. They then use this data to create vectors, bearings, coordinates, elevations, areas, volumes, plans and maps. Measurements are often split into horizontal and vertical components to simplify calculation. GPS and astronomic measurements also need measurement of

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4914-399: The "granaries of Joseph" ( horrea Ioseph ). This reference from Julius is important, as it indicates that the identification was starting to spread out from pilgrim's travelogues. In 530 AD, Stephanos of Byzantium added more to this idea when he wrote in his Ethnica that the word "pyramid" was connected to the Greek word πυρός ( pyros ), meaning wheat. In the seventh century AD,

5031-586: The 4th. However, after phonetic changes in the Egyptian language and consequently the Greek translation, "Cheops" had transformed into "Souphis" (and similar versions). Greaves , in 1646, reported the great difficulty of ascertaining a date for the pyramid's construction based on the lacking and conflicting historic sources. Because of the differences in spelling, he did not recognize Khufu on Manetho's king list (as transcribed by Africanus and Eusebius ), hence he relied on Herodotus' incorrect account. Summating

5148-668: The Earth's curvature. North is often defined as true north at the datum. Great Pyramid of Giza The Great Pyramid of Giza is the largest Egyptian pyramid . It served as the tomb of pharaoh Khufu , who ruled during the Fourth Dynasty of the Old Kingdom . Built c.  2600 BC , over a period of about 26 years, the pyramid is the oldest of the Seven Wonders of the Ancient World , and

5265-489: The Egyptian idea of the Hereafter." The cemeteries were actively expanded until the 6th dynasty and used less frequently afterwards. The earliest pharaonic name of seal impressions is that of Khufu, the latest of Pepi II . Worker graffiti were written on some of the stones of the tombs as well; for instance, "Mddw" ( Horus name of Khufu) on the mastaba of Chufunacht, probably a grandson of Khufu. Some inscriptions in

5382-531: The Great Pyramid had been attributed to Khufu based on the words of authors of classical antiquity , first and foremost Herodotus and Diodorus Siculus . During the Middle Ages other people were credited with the construction of the pyramid as well, for example Joseph from the Book of Genesis , Nimrod , or the legendary king Saurid ibn Salhouk . In 1837 four additional relieving chambers were found above

5499-424: The Great Pyramid had gained a reputation as a haunted structure. Others feared entering because it was home to animals like bats. A hillock forms the base on which the pyramid stands. It was cut back into steps and only a strip around the perimeter was leveled, which has been measured to be horizontal and flat to within 21 millimetres (0.8 in). The bedrock reaches a height of almost 6 metres (20 ft) above

5616-481: The Great Pyramid. One legend in particular relates how, three hundred years prior to the Great Flood, Surid had a terrifying dream of the world's end, and so he ordered the construction of the pyramids so that they might house all the knowledge of Egypt and survive into the present. The most notable account of this legend was given by al-Masudi (896–956) in his Akbar al-zaman , alongside imaginative tales about

5733-466: The King's Chamber after tunnelling to them. The chambers, previously inaccessible, were covered in hieroglyphs of red paint. The workers who were building the pyramid had marked the blocks with the names of their gangs, which included the pharaoh's name (e.g.: "The gang, The white crown of Khnum-Khufu is powerful"). The names of Khufu were spelled out on the walls over a dozen times. Another of these graffiti

5850-596: The Nile. Herodotus later states that at the Pyramid of Khafre (beside the Great Pyramid) the Nile flows through a built passage to an island in which Khufu is buried. Hawass interprets this to be a reference to the " Osiris Shaft ", which is located at the causeway of Khafre, south of the Great Pyramid. Herodotus described an inscription on the outside of the pyramid, which, according to his translators, indicated

5967-507: The Old Kingdom only kings and queens could have a pyramid tomb. Architectural layout and funeral equipment were also sanctioned, and were, like access to material and workers, at the discretion of the king. The Great Pyramid's internal chambers lack inscriptions and decorations, the norm for Egyptian tombs of the fourth to late fifth dynasty, apart from work-gang graffiti that include Khufu's names. Constructed around 2600 BC, it predates

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6084-574: The Queen's Chamber. One of the objects found within was a cedar plank, which came into possession of James Grant, a friend of Dixon. After inheritance it was donated to the Museum of Aberdeen in 1946; however, it had broken into pieces and was filed incorrectly. Lost in the vast museum collection, it was only rediscovered in 2020, when it was radiocarbon dated to 3341–3094 BC. Being over 500 years older than Khufu's chronological age, Abeer Eladany suggests that

6201-593: The United States. These exams consist of: The NCEES Records program is designed for currently licensed engineers and surveyors who are looking for an easier and faster way to complete the licensure process in multiple jurisdictions, including all 50 states, the District of Columbia, Guam, Puerto Rico, Northern Mariana Islands and the U.S. Virgin Islands. An established NCEES Record will include most—if not all—of

6318-436: The amount of radishes, garlic and onions that the workers would have eaten while working on the pyramid. This could be a note of restoration work that Khaemweset , son of Rameses II , had carried out. Apparently, Herodotus' companions and interpreters could not read the hieroglyphs or deliberately gave him false information. Between 60 and 56 BC, the ancient Greek historian Diodorus Siculus visited Egypt and later dedicated

6435-438: The basis for dividing the western territories into sections to allow the sale of land. The PLSS divided states into township grids which were further divided into sections and fractions of sections. Napoleon Bonaparte founded continental Europe 's first cadastre in 1808. This gathered data on the number of parcels of land, their value, land usage, and names. This system soon spread around Europe. Robert Torrens introduced

6552-457: The bearing from every vertex in a figure, a surveyor can measure around the figure. The final observation will be between the two points first observed, except with a 180° difference. This is called a close . If the first and last bearings are different, this shows the error in the survey, called the angular misclose . The surveyor can use this information to prove that the work meets the expected standards. The simplest method for measuring height

6669-468: The beginning of the century, surveyors had improved the older chains and ropes, but they still faced the problem of accurate measurement of long distances. Trevor Lloyd Wadley developed the Tellurometer during the 1950s. It measures long distances using two microwave transmitter/receivers. During the late 1950s Geodimeter introduced electronic distance measurement (EDM) equipment. EDM units use

6786-480: The boat pits. As the successor and eldest son he would have presumably been responsible for the burial of Khufu. The second boat pit was examined in 1987; excavation work started in 2010. Graffiti on the stones included 4 instances of the name "Khufu", 11 instances of "Djedefre", a year (in reign, season, month and day), measurements of the stone, various signs and marks, and a reference line used in construction, all done in red or black ink. During excavations in 2013

6903-466: The bodies of a man and woman were discovered inside the pyramid in the "best possible state of preservation". The author al-Kaisi, in his work the Tohfat Alalbab, retells the story of al-Ma'mun's entry but with the additional discovery of "an image of a man in green stone", which when opened revealed a body dressed in jewel-encrusted gold armour. Al-Kaisi claims to have seen the case from which

7020-496: The body was taken, and asserts that it was located at the king's palace in Cairo. He also writes that he entered into the pyramid and discovered many preserved bodies. Another attempt to enter the pyramid in search of treasure is recorded during the vizierate of al-Afdal Shahanshah (1094–1121), but it was abandoned after a member of the party was lost in the passages. The Arab polymath Abd al-Latif al-Baghdadi (1163–1231) studied

7137-528: The boundaries. Young boys were included to ensure the memory lasted as long as possible. In England, William the Conqueror commissioned the Domesday Book in 1086. It recorded the names of all the land owners, the area of land they owned, the quality of the land, and specific information of the area's content and inhabitants. It did not include maps showing exact locations. Abel Foullon described

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7254-579: The chapels of the mastabas (like the pyramid, their burial chambers were usually bare of inscriptions) mention Khufu or his pyramid. For instance, an inscription of Mersyankh III states that "Her mother [is the] daughter of the King of Upper and Lower Egypt Khufu." Most often these references are part of a title, for example, Snnw-ka, "Chief of the Settlement and Overseer of the Pyramid City of Akhet-Khufu" or Nykahap, "priest of Khufu who presides over

7371-423: The cladding of the pyramid was still in excellent condition at the time, whereas the uppermost part of the pyramid was formed by a platform 6  cubits (3.1 m; 10.3 ft) high. About the construction of the pyramid he notes that it was built with the help of ramps since no lifting tools had yet been invented. Nothing was left of the ramps, as they were removed after the pyramids were completed. He estimated

7488-451: The coins were planted by Al-Ma'mun to appease his workers, who were likely frustrated that they had found no treasure.) In 987 AD, the Arab bibliographer Ibn al-Nadim relates a fantastical tale in his al-Fihrist about a man who journeyed into the main chamber of a pyramid, which Bayard Dodge argues is the Great Pyramid. According to Ibn al-Nadim, the person in question saw a statue of

7605-422: The construction of the pyramids themselves. It measured nearly 1 kilometre (0.62 mi) long and 20 yards (18.3 m) wide, and elevated to a height of 16 yards (14.6 m), consisting of stone polished and carved with figures. Underground chambers were made on the hill where the pyramids stand. These were intended to be burial places for Khufu himself and were supplied with water by a channel brought in from

7722-537: The custom of inscribing pyramids with text by over 200 years. The pyramid complex of Khufu included two temples that were lavishly decorated and inscribed. The pyramid temple was dedicated to the Sed festival , celebrating Khufu's 30th jubilee. Surviving scenes portray Khufu, officials, priests and other characters performing rituals. The valley temple remains largely unexcavated, but blocks reused by Amenemhat I depict, for instance, nautical scenes and personifications of

7839-405: The development of the human environment since the beginning of recorded history . It is used in the planning and execution of most forms of construction . It is also used in transportation, communications, mapping, and the definition of legal boundaries for land ownership. It is an important tool for research in many other scientific disciplines. The International Federation of Surveyors defines

7956-524: The duration of lines of succession, Greaves concluded 1266 BC to be the beginning of Khufu's reign. Two centuries later, some of the gaps and uncertainties in Manetho's chronology had been cleared by discoveries such as the King Lists of Turin , Abydos , and Karnak . The names of Khufu found within the Great Pyramid's relieving chambers in 1837 helped to make clear that Cheops and Souphis are one and

8073-562: The early days of surveying, this was the primary method of determining accurate positions of objects for topographic maps of large areas. A surveyor first needs to know the horizontal distance between two of the objects, known as the baseline . Then the heights, distances and angular position of other objects can be derived, as long as they are visible from one of the original objects. High-accuracy transits or theodolites were used, and angle measurements were repeated for increased accuracy. See also Triangulation in three dimensions . Offsetting

8190-414: The estates of Khufu (e.g. the estate "Khufu is beautiful"). The mortuary cult of Khufu which operated in these temples for hundreds of years indicates that Khufu was successfully interred in the Great Pyramid. That the funeral was carried out by Khufu's son and successor Djedefre is evidenced by the presence of his cartouches on the blocks that sealed the boat pits next to the pyramid. The Great Pyramid

8307-413: The first book of his Bibliotheca historica to the land, its history, and its monuments, including the Great Pyramid. Diodorus's work was inspired by historians of the past, but he also distanced himself from Herodotus, who Diodorus claims tells marvellous tales and myths. Diodorus presumably drew his knowledge from the lost work of Hecataeus of Abdera , and like Herodotus, he also places the builder of

8424-544: The first prototype satellites of the Global Positioning System (GPS) in 1978. GPS used a larger constellation of satellites and improved signal transmission, thus improving accuracy. Early GPS observations required several hours of observations by a static receiver to reach survey accuracy requirements. Later improvements to both satellites and receivers allowed for Real Time Kinematic (RTK) surveying. RTK surveys provide high-accuracy measurements by using

8541-467: The first triangulation of France. They included a re-surveying of the meridian arc , leading to the publication in 1745 of the first map of France constructed on rigorous principles. By this time triangulation methods were well established for local map-making. It was only towards the end of the 18th century that detailed triangulation network surveys mapped whole countries. In 1784, a team from General William Roy 's Ordnance Survey of Great Britain began

8658-515: The function of surveying as follows: A surveyor is a professional person with the academic qualifications and technical expertise to conduct one, or more, of the following activities; Surveying has occurred since humans built the first large structures. In ancient Egypt , a rope stretcher would use simple geometry to re-establish boundaries after the annual floods of the Nile River . The almost perfect squareness and north–south orientation of

8775-748: The ground (about 20 km (12 mi) apart). This method reaches precisions between 5–40 cm (depending on flight height). Surveyors use ancillary equipment such as tripods and instrument stands; staves and beacons used for sighting purposes; PPE ; vegetation clearing equipment; digging implements for finding survey markers buried over time; hammers for placements of markers in various surfaces and structures; and portable radios for communication over long lines of sight. Land surveyors, construction professionals, geomatics engineers and civil engineers using total station , GPS , 3D scanners, and other collector data use land surveying software to increase efficiency, accuracy, and productivity. Land Surveying Software

8892-509: The ground to large beacons that can be seen from long distances. The surveyors can set up their instruments in this position and measure to nearby objects. Sometimes a tall, distinctive feature such as a steeple or radio aerial has its position calculated as a reference point that angles can be measured against. Triangulation is a method of horizontal location favoured in the days before EDM and GPS measurement. It can determine distances, elevations and directions between distant objects. Since

9009-491: The half brother and vizier of Khufu, and the owner of the largest mastaba of the Giza East Field . The Great Pyramid has been determined to be about 4,600 years old by two principal approaches: indirectly, through its attribution to Khufu and his chronological age, based on archaeological and textual evidence; and directly, via radiocarbon dating of organic material found in the pyramid and included in its mortar. In

9126-400: The height difference is used to find the new elevation of the level gun, which is why this method is referred to as differential levelling . This is repeated until the series of measurements is completed. The level must be horizontal to get a valid measurement. Because of this, if the horizontal crosshair of the instrument is lower than the base of the rod, the surveyor will not be able to sight

9243-623: The horses in Memphis, when he was still young, and stopped at the Sanctuary of Hor-em-akhet (the Sphinx). He spent a time there in going round it, looking at the beauty of the Sanctuary of Khufu and Khafra the revered." In 1954 two boat pits, one containing the Khufu ship , were discovered buried at the south foot of the pyramid. The cartouche of Djedefre was found on many of the blocks that covered

9360-525: The idea that it was a pre-Adamic construction. A few centuries later, the Islamic historian Al-Maqrizi (1364–1442) compiled lore about the Great Pyramid in his Al-Khitat . In addition to reasserting that Al-Ma'mun breached the structure in 820 AD, Al-Maqrizi's work also discusses the sarcophagus in the coffin chambers, explicitly noting that the pyramid was a grave. By the Late Middle Ages ,

9477-417: The level of the river is too low for canals to bring water up to the pyramid. Pliny also recounts how "in the interior of the largest Pyramid there is a well, eighty-six cubits [45.1 m; 147.8 ft] deep, which communicates with the river, it is thought". He also describes a method discovered by Thales of Miletus for ascertaining the pyramid's height by measuring its shadow. During late antiquity ,

9594-547: The lines of succession known from ancient king lists and other texts. The reign lengths from Khufu to known points in the earlier past are summated, bolstered with genealogical data, astronomical observations, and other sources. As such, the historical chronology of Egypt is primarily a political chronology, thus independent from other types of archaeological evidence like stratigraphies , material culture, or radiocarbon dating. The majority of recent chronological estimates date Khufu and his pyramid between 2700 and 2500 BC. Mortar

9711-558: The materials one needs to apply for comity licensure in additional states and territories. NCEES Credentials Evaluations is a service for state licensing boards and applicants. It is designed primarily for candidates who have earned their degrees outside the United States and are pursuing licensure through one of the member licensing boards of NCEES. NCEES exam preparation materials include questions that have been used on past exams and questions written to give examinees extra practice. Land surveyor Surveying or land surveying

9828-464: The measurement of angles. It uses two separate circles , protractors or alidades to measure angles in the horizontal and the vertical plane. A telescope mounted on trunnions is aligned vertically with the target object. The whole upper section rotates for horizontal alignment. The vertical circle measures the angle that the telescope makes against the vertical, known as the zenith angle. The horizontal circle uses an upper and lower plate. When beginning

9945-409: The measurement of vertical angles. Verniers allowed measurement to a fraction of a degree, such as with a turn-of-the-century transit . The plane table provided a graphical method of recording and measuring angles, which reduced the amount of mathematics required. In 1829 Francis Ronalds invented a reflecting instrument for recording angles graphically by modifying the octant . By observing

10062-424: The measuring instrument level would also be made. When measuring up a slope, the surveyor might have to "break" (break chain) the measurement- use an increment less than the total length of the chain. Perambulators , or measuring wheels, were used to measure longer distances but not to a high level of accuracy. Tacheometry is the science of measuring distances by measuring the angle between two ends of an object with

10179-423: The middle of the third millennium BC. The newly developed radiocarbon dating method confirmed that the historic chronology was approximately correct. It is still not a perfectly accurate method due to larger margins of error, calibration uncertainties and the problem of inbuilt age (time between growth and final usage) in plant material, including wood. Astronomical alignments have also been suggested to coincide with

10296-411: The modern systematic use of triangulation . In 1615 he surveyed the distance from Alkmaar to Breda , approximately 72 miles (116 km). He underestimated this distance by 3.5%. The survey was a chain of quadrangles containing 33 triangles in all. Snell showed how planar formulae could be corrected to allow for the curvature of the Earth . He also showed how to resect , or calculate, the position of

10413-428: The names of those who erected such stupendous memorials of their vanity". In pondering how the stones could be transported to such a vast height he gives two explanations: That either vast mounds of nitre and salt were heaped up against the pyramid, which were then melted away with water redirected from the river. Or, that "bridges" were constructed, their bricks afterwards distributed for erecting houses, arguing that

10530-443: The number of workers necessary to erect the Great Pyramid at 360,000 and the construction time at 20 years. Similar to Herodotus, Diodorus also claims that the side of the pyramid is inscribed with writing that "[set] forth [the price of] vegetables and purgatives for the workmen there were paid out over sixteen hundred talents." The Greek geographer, philosopher, and historian Strabo visited Egypt around 25 BC, shortly after Egypt

10647-574: The only wonder that has remained largely intact. It is the most famous monument of the Giza pyramid complex , which is part of the UNESCO World Heritage Site " Memphis and its Necropolis ". It is situated at the northeastern end of the line of the three main pyramids at Giza . Initially standing at 146.6 metres (481 feet), the Great Pyramid was the world's tallest human-made structure for more than 3,800 years. Over time, most of

10764-672: The other Himalayan peaks. Surveying became a professional occupation in high demand at the turn of the 19th century with the onset of the Industrial Revolution . The profession developed more accurate instruments to aid its work. Industrial infrastructure projects used surveyors to lay out canals , roads and rail. In the US, the Land Ordinance of 1785 created the Public Land Survey System . It formed

10881-400: The past the Great Pyramid was dated by its attribution to Khufu alone, putting the construction of the Great Pyramid within his reign, hence dating the pyramid was a matter of dating Khufu and the 4th dynasty. The relative sequence and synchronicity of events is the focal point of this method. Absolute calendar dates are derived from an interlocked network of evidence, the backbone of which are

10998-551: The pyramid Akhet-Khufu". Several tomb owners have a king's name as part of their own name (e.g. Chufudjedef, Chufuseneb, Merichufu). The earliest pharaoh alluded to in that manner at Giza is Snefru (Khufu's father). In 1936 Hassan uncovered a stela of Amenhotep II near the Great Sphinx of Giza , which implies the two larger pyramids were still attributed to Khufu and Khafre in the New Kingdom . It reads: "He yoked

11115-501: The pyramid could be entered at this time. The Roman writer Pliny the Elder , writing in the first century AD, argued that the Great Pyramid had been raised, either "to prevent the lower classes from remaining unoccupied", or as a measure to prevent the pharaoh's riches from falling into the hands of his rivals or successors. Pliny does not speculate as to the pharaoh in question, explicitly noting that "accident [has] consigned to oblivion

11232-578: The pyramid with great care, and in his Account of Egypt , he praises them as works of engineering genius. In addition to measuring the structure, alongside the other pyramids at Giza, al-Baghdadi also writes that the structures were surely tombs, although he thought the Great Pyramid was used for the burial of Agathodaimon or Hermes . Al-Baghdadi ponders whether the pyramid pre-dated the Great Flood as described in Genesis , and even briefly entertained

11349-406: The pyramid, "Chemmis", after Ramses III. According to his report, neither Chemmis ( Khufu ) nor Cephren ( Khafre ) were buried in their pyramids, but rather in secret places, for fear that the people ostensibly forced to build the structures would seek out the bodies for revenge. With this assertion, Diodorus strengthened the connection between pyramid building and slavery. According to Diodorus,

11466-416: The pyramid, such as the story of a man who fell three hours down the pyramid's well and the tale of an expedition that discovered bizarre finds in the structure's inner chambers. Al-zaman also contains a report of al-Ma'mun's entering the pyramid and discovering a vessel containing a thousand coins, which just happened to cover the cost of opening the pyramid. (Some speculate that this story is true, but that

11583-450: The pyramid. In the second book of his work The Histories , he discusses the history of Egypt and the Great Pyramid. This report was created more than 2000 years after the structure was built, meaning that Herodotus obtained his knowledge mainly from a variety of indirect sources, including officials and priests of low rank, local Egyptians, Greek immigrants, and Herodotus's own interpreters. Accordingly, his explanations present themselves as

11700-477: The rod and get a reading. The rod can usually be raised up to 25 feet (7.6 m) high, allowing the level to be set much higher than the base of the rod. The primary way of determining one's position on the Earth's surface when no known positions are nearby is by astronomic observations. Observations to the Sun, Moon and stars could all be made using navigational techniques. Once the instrument's position and bearing to

11817-420: The same. Thus the Great Pyramid was recognized to have been built in the 4th dynasty. The dating among Egyptologists still varied by multiple centuries (around 4000–2000 BC), depending on methodology, preconceived religious notions (such as the biblical deluge ) and which source they thought was more credible. Estimates significantly narrowed in the 20th century, most being within 250 years of each other, around

11934-422: The satellite positions and atmospheric conditions. The surveyor uses the roving antenna to measure the points needed for the survey. The two antennas use a radio link that allows the static antenna to send corrections to the roving antenna. The roving antenna then applies those corrections to the GPS signals it is receiving to calculate its own position. RTK surveying covers smaller distances than static methods. This

12051-466: The smooth white limestone casing was removed, which lowered the pyramid's height to the current 138.5 metres (454.4 ft); what is seen today is the underlying core structure. The base was measured to be about 230.3 metres (755.6 ft) square, giving a volume of roughly 2.6 million cubic metres (92 million cubic feet), which includes an internal hillock. The dimensions of the pyramid were 280 royal cubits (146.7 m; 481.4 ft) high,

12168-678: The surface location of subsurface features, or other purposes required by government or civil law, such as property sales. A professional in land surveying is called a land surveyor . 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 locators, drones, GIS , and surveying software. Surveying has been an element in

12285-423: The surface of the Earth. Few survey positions are derived from the first principles. Instead, most surveys points are measured relative to previously measured points. This forms a reference or control network where each point can be used by a surveyor to determine their own position when beginning a new survey. Survey points are usually marked on the earth's surface by objects ranging from small nails driven into

12402-406: The survey, the surveyor points the instrument in a known direction (bearing), and clamps the lower plate in place. The instrument can then rotate to measure the bearing to other objects. If no bearing is known or direct angle measurement is wanted, the instrument can be set to zero during the initial sight. It will then read the angle between the initial object, the theodolite itself, and the item that

12519-536: The telescope aligns with. The gyrotheodolite is a form of theodolite that uses a gyroscope to orient itself in the absence of reference marks. It is used in underground applications. The total station is a development of the theodolite with an electronic distance measurement device (EDM). A total station can be used for leveling when set to the horizontal plane. Since their introduction, total stations have shifted from optical-mechanical to fully electronic devices. Modern top-of-the-line total stations no longer need

12636-415: The time of construction. Egyptian chronology continues to be refined and data from multiple disciplines have started to be factored in, such as luminescence dating, radiocarbon dating, and dendrochronology. For instance, Ramsey et al. included over 200 radiocarbon samples in their model. The ancient Greek historian Herodotus , writing in the 5th century BC, is one of the first major authors to mention

12753-459: The two endpoints. With the Global Positioning System (GPS), elevation can be measured with satellite receivers. Usually, GPS is somewhat less accurate than traditional precise leveling, but may be similar over long distances. When using an optical level, the endpoint may be out of the effective range of the instrument. There may be obstructions or large changes of elevation between the endpoints. In these situations, extra setups are needed. Turning

12870-523: The usage is confirmed in the anonymous travelogue of seven monks who set out from Jerusalem to visit the famous ascetics in Egypt, wherein they report that they "saw Joseph's granaries, where he stored grain in biblical times". This late 4th-century usage is further confirmed in the geographical treatise Cosmographia , written by Julius Honorius around 376 AD, which explains that the Pyramids were called

12987-420: The west. Look, death counts little for us. Look, life is valued highly by us. The house of the dead (the tomb) is for life. In ancient Egypt, high social status was considered absolutely positive, and the monumental social inequalities were symbolized by gigantic pyramids versus smaller mastabas . The sizes of tombs were regulated officially, with their allowed dimensions written down in royal decrees . In

13104-480: The wood originated from the centre of a long-lived tree or had been recycled for many years prior to being deposited in the pyramid. Circa 450 BC Herodotus attributed the Great Pyramid to Cheops (Hellenization of Khufu), yet erroneously placed his reign following the Ramesside period . Manetho , around 200 years later, composed an extensive list of Egyptian kings, which he divided into dynasties, assigning Khufu to

13221-465: Was annexed by the Romans . In his work Geographica , he argues that the pyramids were the burial place of kings, but he does not mention which king was buried in the structure. Strabo also mentions: "At a moderate height in one of the sides is a stone, which may be taken out; when that is removed, there is an oblique passage to the tomb." This statement has generated much speculation, as it suggests that

13338-417: Was found by Goyon on an exterior block of the 4th layer of the pyramid. The inscriptions are comparable to those found at other sites of Khufu, such as the alabaster quarry at Hatnub or the harbour at Wadi al-Jarf , and are present in pyramids of other pharaohs as well. Throughout the 20th century the cemeteries next to the pyramid were excavated. Family members and high officials of Khufu were buried in

13455-491: Was likely looted as early as the First Intermediate Period and may have been reused afterwards. Arab accounts tell stories of mummies and treasures being found inside the pyramid. For instance, Al-Maqrizi (1364–1442) reports the discovery of three shrouded bodies, a sarcophagus filled with gold, and a corpse in golden armour with a sword of inestimable value and a ruby as large as an egg. Historically

13572-504: Was the US Navy TRANSIT system . The first successful launch took place in 1960. The system's main purpose was to provide position information to Polaris missile submarines. Surveyors found they could use field receivers to determine the location of a point. Sparse satellite cover and large equipment made observations laborious and inaccurate. The main use was establishing benchmarks in remote locations. The US Air Force launched

13689-438: Was used generously in the Great Pyramid's construction. In the mixing process ashes from fires were added to the mortar, organic material that could be extracted and radiocarbon dated . A total of 46 samples of the mortar were taken in 1984 and 1995, making sure they were clearly inherent to the original structure and could not have been incorporated at a later date. The results were calibrated to 2871–2604 BC. The old wood problem

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