Editing Height

{{Short description|Measure of vertical distance}}
{{About|the measure of vertical distance}}
[[Image:Height demonstration diagram.png|thumb|right|200px|A [[cuboid]] demonstrating the dimensions [[length]], [[width]], and 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 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]], height is more often called ''[[altitude]]''.<ref>{{Cite book |last=Strahler |first=Alan |year=2013 |title=Introducing Physical Geography |url=https://books.google.com/books?id=yTkcAAAAQBAJ&q=altitutde+hieght&pg=PA42 |edition=6th |location=Hoboken, N.J. |publisher=Wiley |page=42 |isbn=9781118396209 |oclc=940600903}}</ref>
Furthermore, if the point is attached to the Earth (e.g., a mountain peak), then altitude (height above sea level) is called ''[[elevation]]''.<ref>{{cite book |quote=Note that altitude usually refers to a height in the air (above sea level) and elevation refers to height on the surface [of the Earth] above (or below) sea level.|last1=Petersen |first1=James F. |last2=Sack |first2=Dorothy |last3=Gabler |first3=Robert E. |title=Physical Geography |date=4 February 2016 |publisher=Cengage Learning |isbn=978-1-305-65264-4 |page=113 |url=https://books.google.com/books?id=ZsmrCwAAQBAJ |language=en}}</ref>

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]], 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]] ''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]], the other two being [[length]] 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 (triangle)|height]] 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 (pyramid)|height]] 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 [[Tree (graph theory)#Rooted tree|rooted tree]], the [[Tree height|height]] 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 (field theory)|minimal polynomial]] of an [[algebraic number]]; among other uses in [[commutative algebra]] and [[representation theory]];
#In [[ring (mathematics)|ring theory]], the [[Krull dimension#height|height]] of a [[prime ideal]] is the supremum of the lengths of all chains of prime ideals contained in it.

==In geosciences==
{{Further|Elevation|Above mean sea level}}
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]]. 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|Geodesy, heights]].

In addition to vertical position, the vertical extent of geographic landmarks can be defined in terms of [[topographic prominence]]. For example, the highest mountain (by elevation in reference to sea level) belongs to [[Mount Everest]], located on the border of [[Nepal]] and [[Tibet]], China; however the [[tallest mountain]], by measurement of apex to base, is [[Mauna Kea]] in [[Hawaii]], United States.

===In geodesy===
{{Main|Geodesy#Heights}}

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|Geodetic system, vertical datum]].

==In aviation==
{{Further|Altitude#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]]. While environmental factors have some effect on variations in human height, these influences are insufficient to account for all differences between populations, suggesting that [[genetics|genetic]] factors are important for explaining variations between human populations.<ref>{{cite journal |last1=Stulp |first1=G |last2=Barrett |first2=L |title=Evolutionary perspectives on human height variation. |journal=Biological Reviews |date=February 2016 |volume=91 |issue=1 |pages=206–34 |doi=10.1111/brv.12165 |pmid=25530478|s2cid=5257723 |url=https://pure.rug.nl/ws/files/62197734/Stulp_et_al_2014_Biological_Reviews.pdf }}</ref>

The [[United Nations]] uses height (among other [[statistics]]) to monitor changes in the [[nutrition]] of [[developing nation]]s. 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.<ref>{{cite journal |last1=van der Eng |first1=Pierre |last2=Baten |first2=Joerg |last3=Stegl |first3=Mojgan |title=Long-Term Economic Growth and the Standard of Living in Indonesia |journal=SSRN Electronic Journal |date=2010 |doi=10.2139/ssrn.1699972|s2cid=127728911 |url=https://www.cbe.anu.edu.au/researchpapers/econ/wp514.pdf }}</ref>

==See also==
{{Div col}}
* [[Acrophobia]] (fear of heights)
* [[Centimetre–gram–second system of units]]
* [[Chinese units of measurement]]
* [[Elevation]]
* [[Height gauge]]
* [[Imperial units]]
* [[International System of Units]]
* [[United States customary units]]
* [[Vertical metre]]
{{Div col end}}

==References==
{{Reflist}}

== External links ==
* {{Commons category-inline}}
* {{Wiktionary inline|height}}
* {{Wiktionary inline|high}}

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[[Category:Height| ]]