Height
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Height is measure of vertical
distance Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two co ...
, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For an example of vertical extent, "This basketball player is 7 foot 1 inches in height." For an example of vertical position, "The height of an airplane in-flight is about 10,000 meters." When the term is used to describe vertical position (of, e.g., an airplane) from
sea level Mean sea level (MSL, often shortened to sea level) is an mean, average surface level of one or more among Earth's coastal Body of water, bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical ...
, height is more often called ''
altitude Altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum (geodesy), datum and a point or object. The exact definition and reference datum varies according to the context (e.g., aviation, geometr ...
''. Furthermore, if the point is attached to the Earth (e.g., a mountain peak), then altitude (height above sea level) is called ''
elevation The elevation of a geographic location (geography), ''location'' is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational equipotenti ...
''. In a two-dimensional Cartesian space, height is measured along the vertical axis (''y'') between a specific point and another that does not have the same ''y''-value. If both points happen to have the same ''y''-value, then their relative height is zero. In the case of
three-dimensional space In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values ('' coordinates'') are required to determine the position of a point. Most commonly, it is the three- ...
, height is measured along the vertical ''z'' axis, describing a distance from (or "above") the ''x-y'' plane.


Etymology

The English-language word ''high'' is derived from
Old English Old English ( or , or ), or Anglo-Saxon, is the earliest recorded form of the English language, spoken in England and southern and eastern Scotland in the Early Middle Ages. It developed from the languages brought to Great Britain by Anglo-S ...
''hēah'', ultimately from Proto-Germanic *''xauxa-z'', from a PIE base ''*keuk-''. The derived noun ''height'', also the obsolete forms ''heighth'' and ''highth'', is from Old English ''híehþo'', later ''héahþu'', as it were from Proto-Germanic ''*xaux-iþa''.


In mathematics

In elementary models of space, height may indicate the third
dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coo ...
, the other two being
length Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most systems of measurement a Base unit (measurement), base unit for length is chosen, ...
and width. Height is normal to the plane formed by the length and width. Height is also used as a name for some more abstract definitions. These include: #The
height Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For an example of vertical extent, "This basketball player is 7 foot 1 inches in height." For an e ...
or altitude of a triangle, which is the length from a vertex of a triangle to the line formed by the opposite side; #The
height Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For an example of vertical extent, "This basketball player is 7 foot 1 inches in height." For an e ...
of a pyramid, which is the smallest distance from the apex to the base; #A measurement in a circular segment of the distance from the midpoint of the arc of the circular segment to the midpoint of the line joining the endpoints of the arc (see diagram in circular segment); #In a rooted tree, the
height Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For an example of vertical extent, "This basketball player is 7 foot 1 inches in height." For an e ...
of a vertex is the length of the longest downward path to a leaf from that vertex; #In algebraic number theory, a " height function" is a measurement related to the minimal polynomial of an algebraic number; among other uses in
commutative algebra Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideal (ring theory), ideals, and module (mathematics), modules over such rings. Both algebraic geometry and algebraic number theo ...
and representation theory; #In ring theory, the
height Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For an example of vertical extent, "This basketball player is 7 foot 1 inches in height." For an e ...
of a prime ideal is the supremum of the lengths of all chains of prime ideals contained in it.


In geosciences

Although height is normally relative to a plane of reference, most measurements of height in the physical world are based upon a zero surface, known as
sea level Mean sea level (MSL, often shortened to sea level) is an mean, average surface level of one or more among Earth's coastal Body of water, bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical ...
. Both altitude and elevation, two synonyms for height, are usually defined as the position of a point above the mean sea level. One can extend the sea-level surface under the continents: naively, one can imagine a lot of narrow canals through the continents. In practice, the sea level under a continent has to be computed from gravity measurements, and slightly different computational methods exist; see Geodesy, heights. In addition to vertical position, the vertical extent of geographic landmarks can be defined in terms of
topographic prominence In topography, prominence or relative height (also referred to as autonomous height, and shoulder drop in US English, and drop in British English) measures the height of a mountain or hill's summit relative to the lowest contour line encircling ...
. For example, the highest mountain (by elevation in reference to sea level) belongs to
Mount Everest Mount Everest (), known locally as Sagarmatha in Nepal and Qomolangma in Tibet, is Earth's highest mountain above sea level. It lies in the Mahalangur Himal sub-range of the Himalayas and marks part of the China–Nepal border at it ...
, located on the border of
Nepal Nepal, officially the Federal Democratic Republic of Nepal, is a landlocked country in South Asia. It is mainly situated in the Himalayas, but also includes parts of the Indo-Gangetic Plain. It borders the Tibet Autonomous Region of China Ch ...
and
Tibet Tibet (; ''Böd''; ), or Greater Tibet, is a region in the western part of East Asia, covering much of the Tibetan Plateau and spanning about . It is the homeland of the Tibetan people. Also resident on the plateau are other ethnic groups s ...
, China; however the tallest mountain, by measurement of apex to base, is Mauna Kea in
Hawaii Hawaii ( ; ) is an island U.S. state, state of the United States, in the Pacific Ocean about southwest of the U.S. mainland. One of the two Non-contiguous United States, non-contiguous U.S. states (along with Alaska), it is the only sta ...
, United States.


In geodesy

Geodesists formalize mean sea level (MSL) by means of the geoid, the equipotential surface that best fits MSL. Then various types of height (normal, dynamic, orthometric, etc.) can be defined, based on the assumption of density of topographic masses necessary in the continuation of MSL under the continents. A purely geometric quantity is the '' ellipsoidal height'', reckoned from the surface of a reference ellipsoid, see Geodetic system, vertical datum.


In aviation

In aviation terminology, the terms ''height'', ''altitude'', and ''elevation'' are not synonyms. Usually, the altitude of an aircraft is measured from sea level, while its height is measured from ground level. Elevation is also measured from sea level, but is most often regarded as a property of the ground. Thus, elevation plus height can equal altitude, but the term ''altitude'' has several meanings in aviation.


In human culture

Human height is one of the areas of study within
anthropometry Anthropometry (, ) refers to the measurement of the human individual. An early tool of biological anthropology, physical anthropology, it has been used for identification, for the purposes of understanding human physical variation, in paleoanthr ...
. While environmental factors have some effect on variations in human height, these influences are insufficient to account for all differences between populations, suggesting that genetic factors are important for explaining variations between human populations. The
United Nations The United Nations (UN) is the Earth, global intergovernmental organization established by the signing of the Charter of the United Nations, UN Charter on 26 June 1945 with the stated purpose of maintaining international peace and internationa ...
uses height (among other
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
) to monitor changes in the
nutrition Nutrition is the biochemistry, biochemical and physiology, physiological process by which an organism uses food and water to support its life. The intake of these substances provides organisms with nutrients (divided into Macronutrient, macro- ...
of developing nations. In human populations, average height can distill down complex data about the group's birth, upbringing, social class, diet, and health care system. In their research, Baten, Stegl and van der Eng came to the conclusion that a change in the average height is a sign for a change in the economic development. With broad data of Indonesia, the researchers state that several incidents in the history of the country has led not only to a change in the economy but also to a change in the population's average height.


See also

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Acrophobia Acrophobia, also known as hypsophobia, is an extreme or irrational fear or phobia of heights, especially when one is not particularly high up. It belongs to a category of specific phobias, called space and motion discomfort, that share similar ...
(fear of heights) *
Centimetre–gram–second system of units The centimetre–gram–second system of units (CGS or cgs) is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unamb ...
*
Chinese units of measurement Chinese units of measurement, known in Chinese as the ''shìzhì'' ("market system"), are the traditional units of measurement of the Han Chinese. Although Chinese numerals have been decimal (base-10) since the Shang dynasty, Shang, several Chine ...
*
Elevation The elevation of a geographic location (geography), ''location'' is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational equipotenti ...
* Height gauge *
Imperial units The imperial system of units, imperial system or imperial units (also known as British Imperial or Exchequer Standards of 1826) is the system of units first defined in the British Weights and Measures Act 1824 and continued to be developed thr ...
*
International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...
*
United States customary units United States customary units form a system of measurement units commonly used in the United States and most U.S. territories since being standardized and adopted in 1832. The United States customary system developed from English units that ...
*
Vertical metre Vertical position or vertical location is a position (mathematics), position along a vertical direction (the plumb line direction) above or below a given vertical datum (a reference level surface, such as mean sea level). Vertical distance or vert ...


References


External links

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