Rikunarita-ORG/Wikinium huggingface dataset:
# Chernihiv Oblast

Chernihiv OblastFlag of Chernihiv OblastCoat of arms of Chernihiv OblastLocation of Chernihiv Oblast in Ukraine
**Chernihiv Oblast** (Ukrainian: Чернігівська область) is an oblast (province) of northern Ukraine. The administrative centre is Chernihiv. The population of Chernihiv Oblast was 1,061,000 in 2014.

In 2022 the Population of **Chernihiv Oblast** is estimated to be 959,000 people
# Geodesy

An old geodetic pillar (1855) at Ostend, Belgium
A Munich archive with lithography plates of maps of Bavaria
**Geodesy**, sometimes called **geodetics**, is a scientific branch of geography which accurately measures the surface of the Earth.

| Geodesy |
| --- |
|  |
| Fundamentals |
| Geodesy **·** Geodynamics Geomatics **·** Cartography |
| Concepts |
| Datum **·** Distance **·** Geoid Figure of the Earth Geodetic system Geog. coord. system Hor. pos. representation Map projection Reference ellipsoid Satellite geodesy Spatial reference system |
| Technologies |
| GNSS **·** GPS **·** GLONASS |
| Standards |
| ED50 **·** ETRS89 **·** NAD83 NAVD88 **·** SAD69 **·** SRID UTM **·** WGS84 |
| History |
| History of geodesy NAVD29 |
| * v
* t
* e
 |

Friedrich Robert Helmert (1843–1917), who started the discipline, talked about measuring and mapping the surface of the earth. This includes its geometric description (the geoid) and the measurement and description of its gravitational field.

Some people involved in the discipline look at geodynamics, the crusts, the tides, or the movement of the geographical poles.

## Related pages

* Cartography
# Geodesic

In mathematics, a **geodesic** is the “straightest” path between 2 points over a curved surface. This can be thought of as a car driving, making sure its wheels are at the same speed, and always sticking to the surface: the geodesic is its path. If a plane flies on a geodesic, its path will almost always not look straight. However the earth is not flat, it has the shape of a sphere. Displayed on a map you would see a curved line only because of the distortion in maps. Paths on a sphere are also called great circles, such that in this case, two points are joined by two distinct geodesics. A **minimal geodesic** (or **segment**) is a particular case where the geodesic joining two distant points has the shortest length.
# Geoid

Flattened sphere (exaggerated)
The **geoid** is a shape like the surface of the Earth. It is a 3-D geometrical shape like an orange. Shapes of this kind are called oblate spheroids, which is a kind of ellipsoid.

The geoid, however, is a very special kind of oblate spheroid. It is defined as follows:

The geoid is the shape that the surface of the oceans would take under the influence of Earth's gravitation and rotation alone, in the absence of other influences such as winds and tides.
It was defined by Gauss, in 1828. It is often described as the true physical shape of the Earth. The study of Earth's measurements and shapes is called geodesy.

For many practical purposes, a simpler shape is used because that makes calculations easier. That shape is called a reference ellipsoid. In basic education, the shape of the Earth is described as being like an orange, a sphere but wider round the equator. This shape is produced by all celestial spinning spheres, such as stars and planets. The details differ somewhat in each individual case.
# Longitude

Map of Earth showing some major latitudes
**Longitude** is a way to say where a place is on the Earth. It is measured starting from an imaginary north–south line called the Prime Meridian. (A meridian is an imaginary line drawn from the North Pole to the South Pole.) Longitude says how far east (positive numbers) or west (negative numbers) of the Prime Meridian any place is.

Longitude is measured using degrees, the same way an angle is. The Prime Meridian is 0° (zero degrees), and the farthest away is +180° eastward and -180° westward. Unlike latitude, which has the equator as a natural starting position, there is no natural starting position for longitude. Other meridians have been used in the past, but most scientists now agree to use the Prime Meridian.

For centuries, navigators at sea were seldom able to know their longitude. Britain created a Board of Longitude to pay a prize to anyone who could solve the problem. The money went to John Harrison and others who made better clocks (chronometers) in the late 18th and early 19th centuries.

Unlike latitude, longitude does not maintain a constant distance between degrees since meridians all come together at the poles and are far apart at the equator. This means people near the North or South Pole can cross many degrees of longitude by travelling a short distance. The time difference between longitudes is 4 minutes per degree. The distance between degrees of longitude is maximum at the equator.

## Related pages

* Latitude

What are the lines latitude and longitude Archived 2021-09-27 at the Wayback Machine
# Map projection

A **map projection** is a way of showing the surface of a three-dimensional sphere on a flat surface. Such projections are necessary to create maps. The problem with projections is that they change the surface in some way; this is called distortion. Depending on the purpose of the map, some distortions may be less bad. This is why cartographers use different mathematical projections for different maps.

Carl Friedrich Gauss showed that is not possible to project the surface of a sphere to a plane, without distorting it. This theorem is known as Theorema egregium today.

To understand the projections, it is easier to imagine a light source, a globe, and another geometric object. The light source shines "a shadow" of each point of the globe onto the geometric object. At the end the surface of the geometric object is unrolled, this yields the map. It is possible to tell the projections apart by the type of helper object used.

* Using a plane gives azimuthal projections.
* Using a cone gives conical projections.
* Using a cylinder gives cylindrical ones.

* Cylindrical projections "put the sphere into a cylinder, and then unroll its surface". Examples of these are Equirectangular projection, Mercator projection
* Psedocylindrincal: Same as cylindrical, but only applies to the main meridian and parallels.
# Reference ellipsoid

Flattened sphere (exaggerated)
A **reference ellipsoid** is an ellipsoid which is used as a frame of reference for geodetic calculations. It is a figure like the shape of the Earth. It is easier to work with than the geoid, which is another shape like that of the Earth.

It is relatively easy to describe the reference ellipsoid using mathematical formulae. Describing the geoid is much more complex, as it results from precise measurements. The first such models were spheres, used since Ancient Greece. In the 17th century, there were doubts that the earth was a sphere. In 1688, Isaac Newton solved a controversy with Giovanni Domenico Cassini by demonstrating mathematically that the rotation of the earth would lead to a flattening around the area of the poles, and not at the equator.

In practice this was shown by Pierre Bouguer and Alexis-Claude Clairaut half a century later. The two had done an expedition to Peru and Lapland (1735-1741). Their measurement of the meridian arc lead to the definition of the metre. This was the ten-millionth part of the idealized distance between the pole and the equator, 1791. Because of different errors in measurement, it turned out to be 0.022% too short, and was redefined twice, in 1793, and 1799. The value of 1799 is still the official definition but it is about 0.197‰ too short.

In 1983, the metre was redefined as the distance, light travels in a certain amount of time, in a vacuum.
# Satellite navigation

A **satellite navigation** or **satnav** system is a way of pinpointing position very exactly.

Satnav uses a system of satellites. The system gives exact positioning. It allows small electronic receivers to find their position (longitude, latitude, and altitude/elevation). The position is given within a few metres using time signals transmitted along a straight line (line of sight) by radio from satellites. The signals also allow the receivers to calculate the current local time to high precision. A satellite navigation system with global coverage may be called a **global navigation satellite system** (**GNSS**). Global Positioning System is the biggest and most used GNSS. GLONASS, owned by Russia, is the second biggest. China, India, and the European Union are working on similar systems of their own.
# GLONASS

**GLONASS** (**Globalnaya Navigatsionnaya Sputnikovaya Sistema**) is a radio-based satellite navigation system. It is operated by the Russian Defence Forces. It provides an alternative to the United States' Global Positioning System (GPS). These are the only two navigational systems with global coverage. Some receivers can use both systems, giving more accurate locations, more quickly.

## Other websites

* Official GLONASS web page Archived 2011-10-20 at the Wayback Machine
# Ordnance Survey National Grid

The **Ordnance Survey National Grid** is a system used to map Great Britain. It is different from using latitude and longitude. The Ordnance Survey (OS) created the system. It is used a lot in their survey data. It is also used in maps based on those surveys.

Squares of the grid system. The red line is the central (2° W) meridian.
The system divides the map into squares. Each square is labelled with two letters. The first letter refers to squares that are 500 km by 500 km. Those squares are outlined in dark grey on the map to the right. Only four of these have a lot of land area in Great Britain: S, T, N and H. The O square contains a tiny area of North Yorkshire. Normally most of this area is submerged at high tide.

For the second letter, each 500 km square is divided into 25 squares that are 100 km by 100 km. Each of those has a letter code from A to Z. (The letter *I* is not used.) The letters start with A in the northwest corner and go to Z in the southeast corner. These squares are outlined in light grey on the map. The ones that have land have letters shown.

The system can also be used to give the location of a smaller area inside a lettered square. This is done by giving the distance east and north from the southwest corner of the square. For example, NH0325 (or NH 03 25) means a one-kilometre square whose southwest corner is 3 km east and 25 km north from the southwest corner of square NH. The system can also specify areas smaller than one kilometre. For example, the grid reference of the 100-metre square containing the summit of Ben Nevis is **NN 166 712**.

* Standing, Peter (2006) *OV0000 a unique grid square at Beast Cliff*, Geograph Project, UK, web article [accessed 11 June 2007]
* "The true origin". *Welcome to OS Net*. Southampton: Ordnance Survey. 4 September 2007. Archived from the original on 5 December 2008. Retrieved 13 August 2009.

## Other websites

* Ordnance Survey Guide to the National Grid
# World Geodetic System

The **World Geodetic System** (**WGS**) is a standard for use in cartography, geodesy, and navigation including GPS.

It comprises a standard coordinate system for the Earth, a standard for raw altitude data, and a geoid that defines the *nominal sea level*. The latest revision is **WGS 84**.
# Spheroid

|  |  |
| --- | --- |
|  |  |
| *oblate spheroid* | *prolate spheroid* |

A **spheroid** is a kind of ellipsoid. It is got by rotating an ellipse about one of its principal axes. This means it is an ellipsoid with two equal semi-diameters.

Spheres are spheroids. Spheroids that are not spheres are either oblate or prolate.

Most celestial objects are oblate spheroids. They usually spin, and as they spin, centrifugal force pulls them into that shape. Few natural objects are prolate spheroids.

## Related pages

* Oblate spheroid
* Ellipsoid
# Elevation

An elevation sign at 8,000 feet (2,400 m) in the San Bernardino Mountains.
When talking about geography, the **elevation** of a certain point is how high it is compared to some reference point. Very often, the reference point is mean sea level, the level of the ocean midway between high and low tide on an average day. Most land has a positive elevation, which means it is above sea level. A few desert places are below sea level, thus have negative elevation.

Sometimes elevation is measured against the center of the earth. The problem there is that the geoid, the shape of the earth, does not really look like a ball, it is slightly squashed (an oblate spheroid). This means, that while still at mean sea level (at the equator), some points are farther away from the center of the earth than others. That way the peak of Chimborazo, a volcano in Ecuador is farther away from the center of the earth than the peak of Mount Everest. Yet, Mount Everest is higher above sea level.

## Related pages

* Altitude
# Ellipsoid

Ellipsoid
An **ellipsoid** is a shape like a sphere, but prolate (longer in one or more directions) like a rugby ball, or like an egg. It is the 3 dimensional analogue of an ellipse.

The Earth is shaped slightly like an ellipsoid. Its shape is called an oblate spheroid. An ellipsoid shaped like the Earth, called a reference ellipsoid, is often preferred to the geoid because it makes calculations simpler.

## Related pages

* Ellipse
* Oblate spheroid
* Geoid
# Coordinate system

Equatorial coordinate system
A **coordinate system** is a system of numbers used to uniquely determine the position of a point. For two-dimensional systems, the numbers (scalars) are in ordered pairs. More dimensions call for more numbers.

For example, (3) is one-dimensional, (1, 4) is two-dimensional, (1, 5, 9) is three-dimensional, (2, 6, 5, 3) is four-dimensional, and (5, 8, 9, 7, 9) is five-dimensional.

## Related pages

* Analytic geometry
* Cartesian coordinate system
* Celestial coordinate system
* Geographic coordinate system
* Polar coordinate system
* Spherical coordinate system
# Map

A map of the Earth made in 1656
A **map** is an image of the Earth or part of the Earth. A map is different from an aerial photograph because it includes interpretation. Many maps are called "charts" such as star charts and nautical charts. Some maps are of distant worlds. Before the late 20th century almost all maps were on paper. Today, many maps are digital, and can be seen on smartphones and computers. However, physical items such as paper maps, charts, or drawings are still used.

The word "map" can **also** be used to talk about or show relationships between ideas, people, events, data, and many other subjects. This is why web developers call a list of web pages on a web site a site map.

A Modern Topographic map of a town (Marburg) in a valley. Map symbols: Green Colour is forest in this map, a blue line is a river. Meaning of a ▲ Triangle: Summit of a mountain or hill with its Elevation in m (meter) and the name of the mountain
Many maps today are made using GIS computer systems. These are database systems that are organized by location instead of named records. People who make maps are cartographers.

If a map is on a piece of paper or a computer screen, it has to be projected. This is because the Earth is round and paper and screens are flat. There are a lot of ways that use mathematics to make map projections. The only kind of map of the Earth that is not projected is one drawn on a sphere. This is called a globe.
# Sphere

A Sphere
A **sphere** is a round, three-dimensional shape.
All points on the edge of the sphere are at the same distance from the center.
The distance from the center is called the radius of the sphere. A real-world sphere is called a *globe* if it is large (such as the Earth), and as a *ball* if it is small, like an association football.

Common things that have the shape of a sphere are basketballs, superballs, and playground balls.
The Earth and the Sun are nearly *spherical*, meaning sphere-shaped.

A sphere is the three-dimensional analog of a circle.

## Calculating measures of a sphere

### Surface area

Using the circumference: WIKINIUM\_MATH\_PH\_0

Using the diameter: WIKINIUM\_MATH\_PH\_2

Using the radius: WIKINIUM\_MATH\_PH\_4

Using the volume: WIKINIUM\_MATH\_PH\_6

### Circumference

Using the surface area: WIKINIUM\_MATH\_PH\_8

Using the diameter: WIKINIUM\_MATH\_PH\_10

Using the radius: WIKINIUM\_MATH\_PH\_12

Using the volume: WIKINIUM\_MATH\_PH\_14

### Diameter

Using the surface area: WIKINIUM\_MATH\_PH\_16

Using the circumference: WIKINIUM\_MATH\_PH\_18

Using the radius: WIKINIUM\_MATH\_PH\_20

Using the volume: WIKINIUM\_MATH\_PH\_22

### Radius

Using the surface area: WIKINIUM\_MATH\_PH\_24

Using the circumference: WIKINIUM\_MATH\_PH\_26

Using the diameter: WIKINIUM\_MATH\_PH\_28

Using the volume: WIKINIUM\_MATH\_PH\_30

### Volume

Using the surface area: WIKINIUM\_MATH\_PH\_32

Using the circumference: WIKINIUM\_MATH\_PH\_34

Using the diameter: WIKINIUM\_MATH\_PH\_36

Using the radius: WIKINIUM\_MATH\_PH\_38

## Equation of a sphere

In Cartesian coordinates, the equation for a sphere with a center at WIKINIUM\_MATH\_PH\_40 is as follows:

 WIKINIUM\_MATH\_PH\_42
where WIKINIUM\_MATH\_PH\_44 is the radius of the sphere.

## Related pages

* Circle
* Pi
* Tau
# Cartesian coordinate system

Two dimensional Cartesian coordinate system. Four points are marked: (2,3) in green, (-3,1) in red, (-1.5,-2.5) in blue and (0,0), the origin, in violet.
In mathematics and geometry, the **Cartesian coordinate system** is a coordinate system used to give the location of points on a plane by using two numbers for each point. It is also called the *rectangular coordinate system*. The numbers are usually called the WIKINIUM\_MATH\_PH\_0 *coordinate* and the WIKINIUM\_MATH\_PH\_2 *coordinate* or sometimes the *abscissa* and *ordinate*. To find the coordinates of a point, two perpendicular lines, called *axes* (singular: *axis*), are drawn. The point where the axes meet is the coordinate **origin**, written (0,0). The WIKINIUM\_MATH\_PH\_4 *coordinate* gives the position of a point measured along the WIKINIUM\_MATH\_PH\_6 axis, and the WIKINIUM\_MATH\_PH\_8 *coordinate* gives the position along the WIKINIUM\_MATH\_PH\_10 axis. The coordinate system stretch's on to infinity in both *axes.*

Cartesian coordinates can be used in three dimensions (3D), by adding a third number, the WIKINIUM\_MATH\_PH\_12 *coordinate*. In four dimensions (4D), a fourth number, the WIKINIUM\_MATH\_PH\_14 *coordinate*, is added. Each coordinate represents a dimension of space.

Using the Cartesian coordinate system, many shapes, like straight lines and parabolas can be described by using algebraic equations. The results of the equations can be seen by plotting (drawing) a point for each solution to the equations. For example, the WIKINIUM\_MATH\_PH\_16 axis is described by the equation WIKINIUM\_MATH\_PH\_18 . A circle having radius WIKINIUM\_MATH\_PH\_20 and centered at the origin can be described with the equation WIKINIUM\_MATH\_PH\_22 (see Figure 2).

The name **Cartesian** comes from the French mathematician and philosopher René Descartes (Latin: *Cartesius*), who worked to merge algebra and Euclidean geometry. This work was important in creating calculus and cartography.

The idea of this system was developed in 1637 in two works by Descartes. In part two of his *Discourse on Method*, Descartes explains plotting the position of a point or object on a surface, using two perpendicular axes as measuring guides. In *La Géométrie* (*Geometry*), he further explores these ideas.

## Related pages

Cartesian coordinate system with the circle of radius 2 centered at the origin marked in red. The equation of the circle is WIKINIUM\_MATH\_PH\_24 .
* Polar coordinate system
# Equator

How the Sun lights the Earth on the day of equinox
Map of Earth showing the equator and other major lines of latitude
The **equator** is a line which is not real drawn around a sphere or planet, such as the Earth. It is one of the lines known as a line of latitude, or circle of latitude. The name "equator" is Latin for "even-maker"; at equator the day and night are exactly the same length around the year.

The equator is halfway between the North Pole and the South Pole. There, the surface of the planet is parallel to the axis of rotation. The equator divides the surface into the northern hemisphere and the southern hemisphere.

## Climate

Unlike the northern hemisphere and the southern hemisphere, countries around the equator do not experience the four seasons, and the climate is usually very humid.

## Related pages

* Northern hemisphere
* Southern hemisphere
* Solstice and equinox
* Tropic of Cancer
* Tropic of Capricorn
* Arctic Circle
* Antarctic Circle
* Celestial equator