Height

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A cuboid demonstrating the dimensions length, width, and height Height demonstration diagram.png
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."

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When the term is used to describe vertical position (of, e.g., an airplane) from sea level, height is more often called altitude . [1] Furthermore, if the point is attached to the Earth (e.g., a mountain peak), then altitude (height above sea level) is called elevation . [2]

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:

  1. The height or altitude of a triangle, which is the length from a vertex of a triangle to the line formed by the opposite side;
  2. The height of a pyramid, which is the smallest distance from the apex to the base;
  3. 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);
  4. In a rooted tree, the height of a vertex is the length of the longest downward path to a leaf from that vertex;
  5. 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 and representation theory;
  6. In ring theory, the height 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. 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. 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

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. 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. [3]

The United Nations uses height (among other statistics) to monitor changes in the nutrition 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. [4]

See also

Related Research Articles

<span class="mw-page-title-main">Geodesy</span> Science of measuring the shape, orientation, and gravity of Earth

Geodesy or geodetics is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems. Geodesy is an earth science and many consider the study of Earth's shape and gravity to be central to that science. It is also a discipline of applied mathematics.

Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system the base unit for length is the metre.

<span class="mw-page-title-main">Altimeter</span> Instrument used to determine the height of an object above a certain point

An altimeter or an altitude meter is an instrument used to measure the altitude of an object above a fixed level. The measurement of altitude is called altimetry, which is related to the term bathymetry, the measurement of depth under water.

Atmospheric pressure, also known as air pressure or barometric pressure, is the pressure within the atmosphere of Earth. The standard atmosphere is a unit of pressure defined as 101,325 Pa (1,013.25 hPa), which is equivalent to 1,013.25 millibars, 760 mm Hg, 29.9212 inches Hg, or 14.696 psi. The atm unit is roughly equivalent to the mean sea-level atmospheric pressure on Earth; that is, the Earth's atmospheric pressure at sea level is approximately 1 atm.

<span class="mw-page-title-main">Altitude</span> Height in relation to a specified reference point

Altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context. Although the term altitude is commonly used to mean the height above sea level of a location, in geography the term elevation is often preferred for this usage.

<span class="mw-page-title-main">Surveying</span> Science of determining the positions of points and the distances and angles between them

Surveying or land surveying 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 the surface location of subsurface features, or other purposes required by government or civil law, such as property sales.

<span class="mw-page-title-main">Sea level</span> Geographical reference point from which various heights are measured

Mean sea level is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datum – a standardised geodetic datum – that is used, for example, as a chart datum in cartography and marine navigation, or, in aviation, as the standard sea level at which atmospheric pressure is measured to calibrate altitude and, consequently, aircraft flight levels. A common and relatively straightforward mean sea-level standard is instead a long-term average of tide gauge readings at a particular reference location.

<span class="mw-page-title-main">Physical geodesy</span> Study of the physical properties of the Earths gravity field

Physical geodesy is the study of the physical properties of Earth's gravity and its potential field, with a view to their application in geodesy.

<span class="mw-page-title-main">Geodetic datum</span> Reference frame for measuring location

A geodetic datum or geodetic system is a global datum reference or reference frame for unambiguously representing the position of locations on Earth by means of either geodetic 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.

In aviation, atmospheric sciences and broadcasting, a height above ground level is a height measured with respect to the underlying ground surface. This is as opposed to height above mean sea level, height above ellipsoid, or height above average terrain. In other words, these expressions indicate where the "zero level" or "reference altitude" – the vertical datum – is located.

In the oil and gas industry, depth in a well is the distance along a well between a point of interest and a reference point or surface. It is the most common method of reference for locations in the well, and therefore, in oil industry speech, "depth" also refers to the location itself.

<span class="mw-page-title-main">National Geodetic Vertical Datum of 1929</span> Vertical datum in the United States

The National Geodetic Vertical Datum of 1929 is the official name since 1973 of the vertical datum established for vertical control surveying in the United States of America by the General Adjustment of 1929. Originally known as Sea Level Datum of 1929, NGVD 29 was determined and published by the United States Coast and Geodetic Survey and used to measure the elevation of a point above and depression below mean sea level (MSL).

<span class="mw-page-title-main">North American Vertical Datum of 1988</span> Vertical datum for orthometric heights

The North American Vertical Datum of 1988 is the vertical datum for orthometric heights established for vertical control surveying in the United States of America based upon the General Adjustment of the North American Datum of 1988.

<span class="mw-page-title-main">Aerial photographic and satellite image interpretation</span>

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<span class="mw-page-title-main">Vertical datum</span> Reference surface for vertical positions

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 and altitudes of satellite orbits and in aviation. In planetary science, vertical datums are also known as zero-elevation surface or zero-level reference.

This glossary of geography terms is a list of definitions of terms and concepts used in geography and related fields, including Earth science, oceanography, cartography, and human geography, as well as those describing spatial dimension, topographical features, natural resources, and the collection, analysis, and visualization of geographic data. It is split across two articles:

<span class="mw-page-title-main">Track geometry</span> Three-dimensional geometry of track layouts and associated measurements

Track geometry is concerned with the properties and relations of points, lines, curves, and surfaces in the three-dimensional positioning of railroad track. The term is also applied to measurements used in design, construction and maintenance of track. Track geometry involves standards, speed limits and other regulations in the areas of track gauge, alignment, elevation, curvature and track surface. Standards are usually separately expressed for horizontal and vertical layouts although track geometry is three-dimensional.

Trees have a wide variety of sizes and shapes and growth habits. Specimens may grow as individual trunks, multitrunk masses, coppices, clonal colonies, or even more exotic tree complexes. Most champion tree programs focus finding and measuring the largest single-trunk example of each species. There are three basic parameters commonly measured to characterize the size of a single trunk tree: tree height measurement, tree girth measurement, and tree crown measurement. Foresters also perform tree volume measurements. A detailed guideline to these basic measurements is provided in The Tree Measuring Guidelines of the Eastern Native Tree Society by Will Blozan.

Vertical position or vertical location is a position along a vertical direction above or below a given vertical datum . Vertical distance or vertical separation is the distance between two vertical positions. Many vertical coordinates exist for expressing vertical position: depth, height, altitude, elevation, etc. Points lying on an equigeopotential surface are said to be on the same vertical level, as in a water level.

Height above mean sea level is a measure of a location's vertical distance in reference to a vertical datum based on a historic mean sea level. In geodesy, it is formalized as orthometric height. The zero level varies in different countries due to different reference points and historic measurement periods. Climate change and other forces can cause sea levels and elevations to vary over time.

References

  1. Strahler, Alan (2013). Introducing Physical Geography (6th ed.). Hoboken, N.J.: Wiley. p. 42. ISBN   9781118396209. OCLC   940600903.
  2. Petersen, James F.; Sack, Dorothy; Gabler, Robert E. (4 February 2016). Physical Geography. Cengage Learning. p. 113. ISBN   978-1-305-65264-4. 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.
  3. Stulp, G; Barrett, L (February 2016). "Evolutionary perspectives on human height variation" (PDF). Biological Reviews. 91 (1): 206–34. doi:10.1111/brv.12165. PMID   25530478. S2CID   5257723.
  4. van der Eng, Pierre; Baten, Joerg; Stegl, Mojgan (2010). "Long-Term Economic Growth and the Standard of Living in Indonesia" (PDF). SSRN Electronic Journal. doi:10.2139/ssrn.1699972. S2CID   127728911.