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Concept
Height
Summary
Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is).
For example, "The height of that building is 50 m" or "The height of an airplane in-flight is about 10,000 m".
For example, "Christopher Columbus is 5 foot 2 inches in vertical height."
When the term is used to describe vertical position (of, e.g., an airplane) from sea level, height is more often called altitude.
Furthermore, if the point is attached to the Earth (e.g., a mountain peak), then altitude (height above sea level) is called elevation.
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.
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 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 altitude of a triangle, which is the length from a vertex of a triangle to the line formed by the opposite side;
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 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 and representation theory;
In ring theory, the height of a prime ideal is the supremum of the lengths of all chains of prime ideals contained in it.
Official source
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