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Topographic Jut
In topography, jut is a measure of the base-to-peak rise and visual impressiveness of a mountain summit or other landform. It describes how sharply or impressively a location rises above surrounding terrain by factoring both height above surroundings and steepness of ascent. Description A mountain with a jut of X can be interpreted to rise as sharply or impressively as a vertical cliff of X. For example, a vertical cliff of height 100 meters, a 45° slope of height 141 meters, and a 30° slope of height 200 meters all measure a jut of 100 meters and can be interpreted to rise equally sharply. Jut can be further decomposed into base-to-peak height and base-to-peak steepness, where jut equals base-to-peak height multiplied by the sine of base-to-peak steepness. Definition Jut J=\max is the maximum ''angle-reduced height'' (symbol ''H), which can be defined as the vector projection, in the line of sight, of the peak's height (or vertical separation), ''H'': :H'=H, \sin, where '' ...
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Topographic Jut
In topography, jut is a measure of the base-to-peak rise and visual impressiveness of a mountain summit or other landform. It describes how sharply or impressively a location rises above surrounding terrain by factoring both height above surroundings and steepness of ascent. Description A mountain with a jut of X can be interpreted to rise as sharply or impressively as a vertical cliff of X. For example, a vertical cliff of height 100 meters, a 45° slope of height 141 meters, and a 30° slope of height 200 meters all measure a jut of 100 meters and can be interpreted to rise equally sharply. Jut can be further decomposed into base-to-peak height and base-to-peak steepness, where jut equals base-to-peak height multiplied by the sine of base-to-peak steepness. Definition Jut J=\max is the maximum ''angle-reduced height'' (symbol ''H), which can be defined as the vector projection, in the line of sight, of the peak's height (or vertical separation), ''H'': :H'=H, \sin, where '' ...
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Topography
Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps. Topography is a field of geoscience and planetary science and is concerned with local detail in general, including not only relief, but also natural, artificial, and cultural features such as roads, land boundaries, and buildings. In the United States, topography often means specifically ''relief'', even though the USGS topographic maps record not just elevation contours, but also roads, populated places, structures, land boundaries, and so on. Topography in a narrow sense involves the recording of relief or terrain, the three-dimensional quality of the surface, and the identification of specific landforms; this is also known as geomorphometry. In modern usage, this involves generation of elevation data in digital form (DEM). It is often considered to include the graphic representation of t ...
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Mountain Summit
A summit is a point on a surface that is higher in elevation than all points immediately adjacent to it. The topographic terms acme, apex, peak (mountain peak), and zenith are synonymous. The term (mountain top) is generally used only for a mountain peak that is located at some distance from the nearest point of higher elevation. For example, a big, massive rock next to the main summit of a mountain is not considered a summit. Summits near a higher peak, with some prominence or isolation, but not reaching a certain cutoff value for the quantities, are often considered ''subsummits'' (or ''subpeaks'') of the higher peak, and are considered part of the same mountain. A pyramidal peak is an exaggerated form produced by ice erosion of a mountain top. Summit may also refer to the highest point along a line, trail, or route. The highest summit in the world is Mount Everest with a height of above sea level. The first official ascent was made by Tenzing Norgay and Sir Edmund Hillary. ...
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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 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 ...
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Steepness
In mathematics, the slope or gradient of a line is a number that describes both the ''direction'' and the ''steepness'' of the line. Slope is often denoted by the letter ''m''; there is no clear answer to the question why the letter ''m'' is used for slope, but its earliest use in English appears in O'Brien (1844) who wrote the equation of a straight line as and it can also be found in Todhunter (1888) who wrote it as "''y'' = ''mx'' + ''c''". Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical – as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan. The ''steepness'', incline, or grade of a line is measured by the absolut ...
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Vector Projection
The vector projection of a vector on (or onto) a nonzero vector , sometimes denoted \operatorname_\mathbf \mathbf (also known as the vector component or vector resolution of in the direction of ), is the orthogonal projection of onto a straight line parallel to . It is a vector parallel to , defined as: \mathbf_1 = a_1\mathbf where a_1 is a scalar, called the scalar projection of onto , and is the unit vector in the direction of . In turn, the scalar projection is defined as: a_1 = \left\, \mathbf\right\, \cos\theta = \mathbf\cdot\mathbf where the operator ⋅ denotes a dot product, ‖a‖ is the length of , and ''θ'' is the angle between and . Which finally gives: \mathbf_1 = \left(\mathbf \cdot \mathbf\right) \mathbf = \frac \frac = \frac = \frac ~ . The scalar projection is equal to the length of the vector projection, with a minus sign if the direction of the projection is opposite to the direction of . The vector component or vector resolute of perpendi ...
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Line Of Sight
The line of sight, also known as visual axis or sightline (also sight line), is an imaginary line between a viewer/observer/spectator's eye(s) and a subject of interest, or their relative direction. The subject may be any definable object taken note of or to be taken note of by the observer, at any distance more than least distance of distinct vision. In optics, refraction of a ray due to use of lenses can cause distortion. Shadows, patterns and movement can also influence line of sight interpretation (as in optical illusions). The term "line" typically presumes that the light by which the observed object is seen travels as a straight ray, which is sometimes not the case as light can take a curved/angulated path when reflected from a mirror, refracted by a lens or density changes in the traversed media, or deflected by a gravitational field. Fields of study feature specific targets, such as vessels in navigation, marker flags or natural features in surveying, celestial object ...
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Elevation Angle
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' measured from a fixed zenith direction, and the ''azimuthal angle'' of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is also called the ''radius'' or ''radial coordinate''. The polar angle may be called ''colatitude'', ''zenith angle'', '' normal angle'', or ''inclination angle''. When radius is fixed, the two angular coordinates make a coordinate system on the sphere sometimes called spherical polar coordinates. The use of symbols and the order of the coordinates differs among sources and disciplines. This article will use ...
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Unit Of Length
A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length. The most common units in modern use are the metric units, used in every country globally. In the United States the U.S. customary units are also in use. British Imperial units are still used for some purposes in the United Kingdom and some other countries. The metric system is sub-divided into SI and non-SI units. Metric system SI The base unit in the International System of Units (SI) is the metre, defined as "the length of the path travelled by light in vacuum during a time interval of seconds." It is approximately equal to . Other SI units are derived from the metre by adding prefixes, as in millimetre or kilometre, thus producing systematic decimal multiples and submultiples of the base unit that span many orders of magnitude. For example, a kilometre is . Non-SI In the centimetre–gram–second system of units, the basic unit of length is the centimetre, or ...
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Topography
Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps. Topography is a field of geoscience and planetary science and is concerned with local detail in general, including not only relief, but also natural, artificial, and cultural features such as roads, land boundaries, and buildings. In the United States, topography often means specifically ''relief'', even though the USGS topographic maps record not just elevation contours, but also roads, populated places, structures, land boundaries, and so on. Topography in a narrow sense involves the recording of relief or terrain, the three-dimensional quality of the surface, and the identification of specific landforms; this is also known as geomorphometry. In modern usage, this involves generation of elevation data in digital form (DEM). It is often considered to include the graphic representation of t ...
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Physical Geography
Physical geography (also known as physiography) is one of the three main branches of geography. Physical geography is the branch of natural science which deals with the processes and patterns in the natural environment such as the atmosphere, hydrosphere, biosphere, and geosphere. This focus is in contrast with the branch of human geography, which focuses on the built environment, and technical geography, which focuses on using, studying, and creating tools to obtain,analyze, interpret, and understand spatial information. The three branches have significant overlap, however. Sub-branches Physical geography can be divided into several branches or related fields, as follows: * Geomorphology is concerned with understanding the surface of the Earth and the processes by which it is shaped, both at the present as well as in the past. Geomorphology as a field has several sub-fields that deal with the specific landforms of various environments e.g. desert geomorphology and fluvi ...
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Geographical Terminology In Mountaineering
Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and phenomena of Earth. The first recorded use of the word γεωγραφία was as a title of a book by Greek scholar Eratosthenes (276–194 BC). Geography is an all-encompassing discipline that seeks an understanding of Earth and its human and natural complexities—not merely where objects are, but also how they have changed and come to be. While geography is specific to Earth, many concepts can be applied more broadly to other celestial bodies in the field of planetary science. One such concept, the first law of geography, proposed by Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things." Geography has been called "the world discipline" and "the bridge between the human and ...
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