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Height Demonstration Diagram
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") t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Height Demonstration Diagram
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") t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimal Polynomial (field Theory)
In field theory, a branch of mathematics, the minimal polynomial of an element of a field is, roughly speaking, the polynomial of lowest degree having coefficients in the field, such that is a root of the polynomial. If the minimal polynomial of exists, it is unique. The coefficient of the highest-degree term in the polynomial is required to be 1, and the type for the remaining coefficients could be integers, rational numbers, real numbers, or others. More formally, a minimal polynomial is defined relative to a field extension and an element of the extension field . The minimal polynomial of an element, if it exists, is a member of , the ring of polynomials in the variable with coefficients in . Given an element of , let be the set of all polynomials in such that . The element is called a root or zero of each polynomial in . The set is so named because it is an ideal of . The zero polynomial, all of whose coefficients are 0, is in every since for all and . This ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tallest Mountain
This is a list of mountain peaks ordered by their topographic prominence. Terminology The prominence of a peak is the minimum height of climb to the summit on any route from a higher peak, or from sea level if there is no higher peak. The lowest point on that route is the col. For full definitions and explanations of ''topographic prominence'', ''key col'', and ''parent'', see topographic prominence. In particular, the different definitions of the parent of a peak are addressed at length in that article. ''Height'' on the other hand simply means elevation of the summit above sea level. Regarding parents, the ''prominence parent'' of peak A can be found by dividing the island or region in question into territories, by tracing the runoff from the key col (mountain pass) of every peak that is more prominent than peak A. The parent is the peak whose territory peak A resides in. The ''encirclement parent'' is found by tracing the contour below peak A's key col and picking the highe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
China
China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and borders fourteen countries by land, the most of any country in the world, tied with Russia. Covering an area of approximately , it is the world's third largest country by total land area. The country consists of 22 provinces, five autonomous regions, four municipalities, and two Special Administrative Regions (Hong Kong and Macau). The national capital is Beijing, and the most populous city and financial center is Shanghai. Modern Chinese trace their origins to a cradle of civilization in the fertile basin of the Yellow River in the North China Plain. The semi-legendary Xia dynasty in the 21st century BCE and the well-attested Shang and Zhou dynasties developed a bureaucratic political system to serve hereditary monarchies, or dyna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tibet
Tibet (; ''Böd''; ) is a region in East Asia, covering much of the Tibetan Plateau and spanning about . It is the traditional homeland of the Tibetan people. Also resident on the plateau are some other ethnic groups such as Monpa people, Monpa, Tamang people, Tamang, Qiang people, Qiang, Sherpa people, Sherpa and Lhoba peoples and now also considerable numbers of Han Chinese and Hui people, Hui settlers. Since Annexation of Tibet by the People's Republic of China, 1951, the entire plateau has been under the administration of the People's Republic of China, a major portion in the Tibet Autonomous Region, and other portions in the Qinghai and Sichuan provinces. Tibet is the highest region on Earth, with an average elevation of . Located in the Himalayas, the highest elevation in Tibet is Mount Everest, Earth's highest mountain, rising 8,848.86 m (29,032 ft) above sea level. The Tibetan Empire emerged in the 7th century. At its height in the 9th century, the Tibet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nepal
Nepal (; ne, नेपाल ), formerly the Federal Democratic Republic of Nepal ( ne, सङ्घीय लोकतान्त्रिक गणतन्त्र नेपाल ), is a landlocked country in South Asia. It is mainly situated in the Himalayas, but also includes parts of the Indo-Gangetic Plain, bordering the Tibet Autonomous Region of China to the north, and India in the south, east, and west, while it is narrowly separated from Bangladesh by the Siliguri Corridor, and from Bhutan by the Indian state of Sikkim. Nepal has a diverse geography, including fertile plains, subalpine forested hills, and eight of the world's ten tallest mountains, including Mount Everest, the highest point on Earth. Nepal is a multi-ethnic, multi-lingual, multi-religious and multi-cultural state, with Nepali as the official language. Kathmandu is the nation's capital and the largest city. The name "Nepal" is first recorded in texts from the Vedic period of the India ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mount Everest
Mount Everest (; Tibetan: ''Chomolungma'' ; ) is Earth's highest mountain above sea level, located in the Mahalangur Himal sub-range of the Himalayas. The China–Nepal border runs across its summit point. Its elevation (snow height) of was most recently established in 2020 by the Chinese and Nepali authorities. Mount Everest attracts many climbers, including highly experienced mountaineers. There are two main climbing routes, one approaching the summit from the southeast in Nepal (known as the "standard route") and the other from the north in Tibet. While not posing substantial technical climbing challenges on the standard route, Everest presents dangers such as altitude sickness, weather, and wind, as well as hazards from avalanches and the Khumbu Icefall. , over 300 people have died on Everest, many of whose bodies remain on the mountain. The first recorded efforts to reach Everest's summit were made by British mountaineers. As Nepal did not allow foreigners ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topographic Prominence
In topography, prominence (also referred to as autonomous height, relative height, and shoulder drop in US English, and drop or relative height in British English) measures the height of a mountain or hill's summit relative to the lowest contour line encircling it but containing no higher summit within it. It is a measure of the independence of a summit. A peak's ''key col'' (the highest col surrounding the peak) is a unique point on this contour line and the ''parent peak'' is some higher mountain, selected according to various criteria. Definitions The prominence of a peak may be defined as the least drop in height necessary in order to get from the summit to any higher terrain. This can be calculated for a given peak in the following way: for every path connecting the peak to higher terrain, find the lowest point on the path; the ''key col'' (or ''key Saddle point, saddle'', or ''linking col'', or ''link'') is defined as the highest of these points, along all connecting pat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesy
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivalent measurements for other planets (known as '' planetary geodesy''). Geodynamical phenomena, including crustal motion, tides and polar motion, can be studied by designing global and national control networks, applying space geodesy and terrestrial geodetic techniques and relying on datums and coordinate systems. The job title is geodesist or geodetic surveyor. History Definition The word geodesy comes from the Ancient Greek word ''geodaisia'' (literally, "division of Earth"). It is primarily concerned with positioning within the temporally varying gravitational field. Geodesy in the German-speaking world is divided into "higher geodesy" ( or ), which is concerned with measuring Earth on the global scale, and "practical geodes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Ideal
In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the integers are the sets that contain all the multiples of a given prime number, together with the zero ideal. Primitive ideals are prime, and prime ideals are both primary and semiprime. Prime ideals for commutative rings An ideal of a commutative ring is prime if it has the following two properties: * If and are two elements of such that their product is an element of , then is in or is in , * is not the whole ring . This generalizes the following property of prime numbers, known as Euclid's lemma: if is a prime number and if divides a product of two integers, then divides or divides . We can therefore say :A positive integer is a prime number if and only if n\Z is a prime ideal in \Z. Examples * A simple example: In the ring R=\Z, the subset of even numbers is a prime ideal. * Given an integral domain R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Krull Dimension
In commutative algebra, the Krull dimension of a commutative ring ''R'', named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. More generally the Krull dimension can be defined for modules over possibly non-commutative rings as the deviation of the poset of submodules. The Krull dimension was introduced to provide an algebraic definition of the dimension of an algebraic variety: the dimension of the affine variety defined by an ideal ''I'' in a polynomial ring ''R'' is the Krull dimension of ''R''/''I''. A field ''k'' has Krull dimension 0; more generally, ''k'' 'x''1, ..., ''x''''n''has Krull dimension ''n''. A principal ideal domain that is not a field has Krull dimension 1. A local ring has Krull dimension 0 if and only if every element of its maximal ideal is nilpotent. There are several other ways that have been used to define the dimension of a ring. Most of them coinci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ring (mathematics)
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ''ring'' is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. Ring elements may be numbers such as integers or complex numbers, but they may also be non-numerical objects such as polynomials, square matrices, functions, and power series. Formally, a ''ring'' is an abelian group whose operation is called ''addition'', with a second binary operation called ''multiplication'' that is associative, is distributive over the addition operation, and has a multiplicative identity element. (Some authors use the term " " with a missing i to refer to the more general structure that omits this last requirement; see .) Whether a ring is commutative (that is, whether the order in which two elements are multiplied might change the result) has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
