Surveying in the context of Point (geometry)

Ancient Greek technology developed during the 5th century BC, continuing up to and including the Roman period, and beyond. Inventions that are credited to the ancient Greeks include the gear, screw, rotary mills, bronze casting techniques, water clock, water organ, the torsion catapult, the use of steam to operate some experimental machines and toys, and a chart to find prime numbers. Many of these inventions occurred late in the Greek period, often inspired by the need to improve weapons and tactics in war. However, peaceful uses are shown by their early development of the watermill, a device which pointed to further exploitation on a large scale under the Romans. They developed surveying and mathematics to an advanced state, and many of their technical advances were published by philosophers, like Archimedes and Heron.

The Geospatial Information Authority of Japan (国土地理院, Kokudo Chiri-in), or GSI, is the national institution responsible for surveying and mapping the national land of Japan. The former name of the organization from 1949 until March 2010 was Geographical Survey Institute; despite the rename, it retains the same initials. It is an extraordinary organ of the Ministry of Land, Infrastructure, Transport and Tourism. Its main offices are situated in Tsukuba City of Ibaraki Prefecture.

It also runs a museum, situated in Tsukuba, the Science Museum of Map and Survey.

Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine.

Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation.

In geodesy, the figure of the Earth is the size and shape used to model planet Earth. The kind of figure depends on application, including the precision needed for the model. A spherical Earth is a well-known historical approximation that is satisfactory for geography, astronomy and many other purposes. Several models with greater accuracy (including ellipsoid) have been developed so that coordinate systems can serve the precise needs of navigation, surveying, cadastre, land use, and various other concerns.

Vector graphics are a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as points, lines, curves and polygons. The associated mechanisms may include vector display and printing hardware, vector data models and file formats, as well as the software based on these data models (especially graphic design software, computer-aided design, and geographic information systems). Vector graphics are an alternative to raster or bitmap graphics, with each having advantages and disadvantages in specific situations.

While vector hardware has largely disappeared in favor of raster-based monitors and printers, vector data and software continue to be widely used, especially when a high degree of geometric precision is required, and when complex information can be decomposed into simple geometric primitives. Thus, it is the preferred model for domains such as engineering, architecture, surveying, 3D rendering, and typography, but is entirely inappropriate for applications such as photography and remote sensing, where raster is more effective and efficient. Some application domains, such as geographic information systems (GIS) and graphic design, use both vector and raster graphics at times, depending on purpose.

The sector, also known as a sector rule, proportional compass, or military compass, is a major calculating instrument that was in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It is used for solving problems in proportion, multiplication and division, geometry, and trigonometry, and for computing various mathematical functions, such as square roots and cube roots. Its several scales permitted easy and direct solutions of problems in gunnery, surveying and navigation. The sector derives its name from the fourth proposition of the sixth book of Euclid, where it is demonstrated that similar triangles have their like sides proportional. Some sectors also incorporated a quadrant, and sometimes a clamp at the end of one leg which allowed the device to be used as a gunner's quadrant.

Gemma Frisius (/ˈfrɪziəs/; born Jemme Reinerszoon; December 9, 1508 – May 25, 1555) was a Dutch physician, mathematician, cartographer, philosopher, and instrument maker. He created important globes, improved the mathematical instruments of his day and applied mathematics in new ways to surveying and navigation. Gemma's rings, an astronomical instrument, are named after him. Along with Gerardus Mercator and Abraham Ortelius, Frisius is often considered one of the founders of the Netherlandish school of cartography, and significantly helped lay the foundations for the school's golden age (approximately 1570s–1670s).

The Science Museum of Map and Survey (地図と測量の科学館, Chizu to Sokuryō no Kagakukan) is a museum in Tsukuba, Ibaraki, Japan that is dedicated to mapping and surveying.

The museum was the first of its kind in Japan when it was opened by the Geographical Survey Institute of Japan in June 1996.

A civil township is a widely used unit of local government in the United States that is subordinate to a county, most often in the northern and midwestern parts of the country. The term town is used in New England, New York, as well as Wisconsin to refer to the equivalent of the civil township in these states; Minnesota uses "town" officially but often uses it and "township" interchangeably. Specific responsibilities and the degree of autonomy vary in each state. Civil townships are distinct from survey townships, but in states that have both, the boundaries often coincide, especially in Indiana, Ohio, and Illinois, and may completely geographically subdivide a county. The U.S. Census Bureau classifies civil townships as minor civil divisions. Currently, there are 20 states with civil townships, including Indiana, Ohio, Illinois, Michigan, Iowa, Minnesota, Wisconsin, Missouri, Kansas, Nebraska, South Dakota, North Dakota, Pennsylvania, and West Virginia (in certain areas).

Township functions are generally overseen by a governing board (the name varies from state to state) and a clerk, trustee, or mayor (in New Jersey and the metro townships of Utah). Township officers frequently include justice of the peace, road commissioner, assessor, and constable, in addition to surveyor. In the 20th century, many townships also added a township administrator or supervisor to the officers as an executive for the board. In some cases, townships run local libraries, senior citizen services, youth services, disabled citizen services, and cemetery services, besides emergency assistance. In some states, a township and a municipality that is coterminous with that township may wholly or partially consolidate their operations.

The Surveyor General of South Australia (also stylised Surveyor-General) is a position originally created for the Surveyor General for the colony of South Australia. The post is held by an official responsible for government surveying.

A surveyor general is an official responsible for government surveying in a specific country or territory. Historically, this would often have been a military appointment, but it is now more likely to be a civilian post.

The following surveyor general positions exist, or have existed historically:

In mathematics, the slope or gradient of a line is a number that describes the direction of the line on a plane. Often denoted by the letter m, slope is calculated as the ratio of the vertical change to the horizontal change ("rise over run") between two distinct points on the line, giving the same A slope is the ratio of the vertical distance (rise) to the horizontal distance (run) between two points, not a direct distance or a direct angle for any choice of points. To explain, a slope is the ratio of the vertical distance (rise) to the horizontal distance (run) between two points, not a direct distance or a direct angleThe line may be physical – as set by a road surveyor, pictorial as in a diagram of a road or roof, or abstract.An application of the mathematical concept is found in the grade or gradient in geography and civil engineering.

The steepness, incline, or grade of a line is the absolute value of its slope: greater absolute value indicates a steeper line. The line trend is defined as follows:

In geodesy, surveying, hydrography and navigation, vertical datum or altimetric datum is a reference coordinate surface used for vertical positions, such as the elevations of Earth-bound features (terrain, bathymetry, water level, and built structures) and altitudes of satellite orbits and in aviation.In planetary science, vertical datums are also known as zero-elevation surface or zero-level reference.

Commonly adopted criteria for a vertical datum include the following approaches:

A geodetic datum or geodetic system (also: geodetic reference datum, geodetic reference system, or geodetic reference frame, or terrestrial reference frame) is a global datum reference or reference frame for unambiguously representing the position of locations on Earth by means of either geodetic coordinates (and related vertical coordinates) or geocentric coordinates. Datums are crucial to any technology or technique based on spatial location, including geodesy, navigation, surveying, geographic information systems, remote sensing, and cartography. A horizontal datum is used to measure a horizontal position, across the Earth's surface, in latitude and longitude or another related coordinate system. A vertical datum is used to measure the elevation or depth relative to a standard origin, such as mean sea level (MSL). A three-dimensional datum enables the expression of both horizontal and vertical position components in a unified form. The concept can be generalized for other celestial bodies as in planetary datums.

Since the rise of the global positioning system (GPS), the ellipsoid and datum WGS 84 it uses has supplanted most others in many applications. The WGS 84 is intended for global use, unlike most earlier datums.Before GPS, there was no precise way to measure the position of a location that was far from reference points used in the realization of local datums, such as from the Prime Meridian at the Greenwich Observatory for longitude, from the Equator for latitude, or from the nearest coast for sea level. Astronomical and chronological methods have limited precision and accuracy, especially over long distances. Even GPS requires a predefined framework on which to base its measurements, so WGS 84 essentially functions as a datum, even though it is different in some particulars from a traditional standard horizontal or vertical datum.

In surveying and geodesy, a marker (also called a mark, monument, or station) is an object firmly installed to indicate points on the Earth's surface with known coordinates. A benchmark is a type of survey marker that indicates elevation (vertical position). Horizontal position markers used for triangulation are also known as triangulation stations. A set of interrelated geodetic markers form a geodetic network. An active station or reference station is occupied permanently with a measurement instrument, such as GPS/GNSS continuously operating reference stations (CORS).Benchmarking or trigpointing is the hobby of searching for these marks.

A sight or sighting device is any device used to assist in precise visual alignment (i.e. aiming) of weapons, surveying instruments, aircraft equipment, optical illumination equipment or larger optical instruments with the intended target. Sights can be a simple set or system of physical markers that serve as visual references for directly aligning the user's line of sight with the target (such as iron sights on firearms), or optical instruments that provide an optically enhanced—often magnified—target image aligned in the same focus with an aiming point (e.g. telescopic, reflector and holographic sights). There are also sights that actively project an illuminated point of aim (a.k.a. "hot spot") onto the target itself so it can be observed by anyone with a direct view, such as laser sights and infrared illuminators on some night vision devices, as well as augmented or even virtual reality-enabled digital cameras ("smart scopes") with software algorithms that produce digitally enhanced target images.

In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object. The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically:

• Absolute bearing refers to the clockwise angle between the magnetic north (magnetic bearing) or true north (true bearing) and an object. For example, an object to due east would have an absolute bearing of 90 degrees. Thus, it is the same as azimuth.
• Relative bearing refers to the angle between the craft's forward direction (heading) and the location of another object. For example, an object relative bearing of 0 degrees would be immediately in front; an object relative bearing 180 degrees would be behind. Bearings can be measured in mils, points, or degrees. Thus, it is the same as an azimuth difference (modulo +/- 360 degrees).