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Line Of Greatest Slope
In topography, the line of greatest slope is a curve following the steepest slope. In mountain biking and skiing, the line of greatest slope is sometimes called the fall line.https://rootsrated.com Farlow Gap – Mountain Biking: fall line (2nd paragraph) — "The trail becomes loose and rocky, and becomes fall line into a wide open rock garden..." Definition Mathematically, the line (or path) of greatest slope from a point is determined by the of height, taken as a potential field with respect to an acceleration from the force of gravity. Lines of greatest slope are analogous to |
Surface With Path Of Greatest Slope
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth". The concept of surface has been abstracted and formalized in mathematics, specifically in geometry. Depending on the properties on which the emphasis is given, there are several inequivalent such formalizations that are all called ''surface'', sometimes with a qualifier such as algebraic surface, smooth surface or fractal surface. The concept of surface and its mathematical abstractions are both widely used in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mountain Biking
Mountain biking (MTB) is a sport of riding bicycles off-road, often over rough terrain, usually using specially designed mountain bikes. Mountain bikes share similarities with other bikes but incorporate features designed to enhance durability and performance in rough terrain, such as air or coil-sprung shocks used as suspension, larger and wider wheels and tires, stronger frame materials, and mechanically or hydraulically actuated disc brakes. Mountain biking can generally be broken down into distinct categories: Cross-country cycling, cross country, trail riding#Mountain biking, trail, all mountain, Enduro (mountain biking), enduro, Downhill cycling, downhill and freeride (mountain biking), freeride. About The sport requires endurance, core and back strength, balance, bike handling skills, and self-reliance. Advanced riders pursue both steep technical descents and high-incline climbs. In the case of freeride, downhill, and dirt jumping, aerial maneuvers are performed off bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Topology
In mathematics, geometric topology is the study of manifolds and Map (mathematics)#Maps as functions, maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topology may be said to have originated in the 1935 classification of lens spaces by Reidemeister torsion, which required distinguishing spaces that are homotopy equivalent but not homeomorphic. This was the origin of simple homotopy, ''simple'' homotopy theory. The use of the term geometric topology to describe these seems to have originated rather recently. Differences between low-dimensional and high-dimensional topology Manifolds differ radically in behavior in high and low dimension. High-dimensional topology refers to manifolds of dimension 5 and above, or in relative terms, embeddings in codimension 3 and above. Low-dimensional topology is concerned with questions in dimensions up to 4, or embeddings in codimension up to 2. Dimensio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surfaces
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. Surface or surfaces may also refer to: Mathematics *Surface (mathematics), a generalization of a plane which needs not be flat * Surface (differential geometry), a differentiable two-dimensional manifold *Surface (topology), a two-dimensional manifold *Algebraic surface, an algebraic variety of dimension two * Coordinate surfaces * Fractal surface, generated using a stochastic algorithm * Polyhedral surface *Surface area *Surface integral Arts and entertainment * Surface (band), an American R&B and pop trio ** ''Surface'' (Surface album), 1986 * Surfaces (band), American musical duo * ''Surface'' (Circle album), 1998 * "Surface" (Aero Chord song), 2014 * ''Surface'' (2005 TV series), an American science fiction show, 2005–2006 * ''Surface'' (2022 TV series), an American psychological thriller miniseries that began streaming in 2022 * ''The Surface'' (film), an Americ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topography
Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the landforms 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartography
Cartography (; from , 'papyrus, sheet of paper, map'; and , 'write') is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an imagined reality) can be modeled in ways that communicate spatial information effectively. The fundamental objectives of traditional cartography are to: * Set the map's agenda and select traits of the object to be mapped. This is the concern of map editing. Traits may be physical, such as roads or land masses, or may be abstract, such as toponyms or political boundaries. * Represent the terrain of the mapped object on flat media. This is the concern of map projections. * Eliminate the mapped object's characteristics that are irrelevant to the map's purpose. This is the concern of Cartographic generalization, generalization. * Reduce the complexity of the characteristics that will be mapped. This is also the concern of generalization. * Orchestrate the elements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface (topology)
In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space. Topological surfaces are sometimes equipped with additional information, such as a Riemannian metric or a complex structure, that connects them to other disciplines within mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the physical world. In general In mathematics, a surface is a geometrical shape that resembles a deformed plane. The most familiar examples arise as boundaries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slope
In mathematics, the slope or gradient of a Line (mathematics), line is a number that describes the direction (geometry), direction of the line on a plane (geometry), plane. Often denoted by the letter ''m'', slope is calculated as the ratio of the vertical change to the horizontal change ("rise over run") between two distinct points on the line, giving the same number for any choice of points. The line may be physical – as set by a Surveying, road surveyor, pictorial as in a diagram of a road or roof, or Pure mathematics, abstract. An application of the mathematical concept is found in the grade (slope), grade or gradient in geography and civil engineering. The ''steepness'', incline, or grade of a line is the absolute value of its slope: greater absolute value indicates a steeper line. The line trend is defined as follows: *An "increasing" or "ascending" line goes from left to right and has positive slope: m>0. *A "decreasing" or "descending" line goes from left to right ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abutment
An abutment is the substructure at the ends of a bridge span or dam supporting its superstructure. Single-span bridges have abutments at each end that provide vertical and lateral support for the span, as well as acting as retaining walls to resist lateral movement of the earthen fill of the bridge approach. Multi-span bridges require piers to support ends of spans unsupported by abutments. Dam abutments are generally the sides of a valley or gorge, but may be artificial in order to support arch dams such as Kurobe Dam in Japan. The civil engineering term may also refer to the structure supporting one side of an arch, or masonry used to resist the lateral forces of a vault.Pevsner, N. (1970) ''Cornwall''; 2nd ed. Harmondsworth: Penguin; p. 245 The impost or abacus An abacus ( abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoptio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bridge
A bridge is a structure built to Span (engineering), span a physical obstacle (such as a body of water, valley, road, or railway) without blocking the path underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually something that is otherwise difficult or impossible to cross. There are many different designs of bridges, each serving a particular purpose and applicable to different situations. Designs of bridges vary depending on factors such as the function of the bridge, the nature of the terrain where the bridge is constructed and anchored, the material used to make it, and the funds available to build it. The earliest bridges were likely made with fallen trees and stepping stones. The Neolithic people built boardwalk bridges across marshland. The Arkadiko Bridge, dating from the 13th century BC, in the Peloponnese is one of the oldest arch bridges in existence and use. Etymology The ''Oxford English Dictionary'' traces the origin of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mountaineering
Mountaineering, mountain climbing, or alpinism is a set of outdoor activities that involves ascending mountains. Mountaineering-related activities include traditional outdoor climbing, skiing, and traversing via ferratas that have become mountain sports, sports in their own right. Indoor climbing, sport climbing, and bouldering are also considered variants of mountaineering by some, but are part of a wide group of mountain sports. Unlike most sports, mountaineering lacks widely applied formal rules, regulations, and governance; mountaineers adhere to a large variety of techniques and philosophies (including grade (climbing), grading and climbing guidebook, guidebooks) when climbing mountains. Numerous local alpine clubs support mountaineers by hosting resources and social activities. A federation of alpine clubs, the International Climbing and Mountaineering Federation (UIAA), is the International Olympic Committee-recognized world organization for mountaineering and climbing. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contour Map With An Example Fall Line
Contour may refer to: * Contour (linguistics), a phonetic sound * Pitch contour * Contour (camera system), a 3D digital camera system * Contour Airlines * Contour flying, a form of low level flight * Contour, the KDE Plasma 4 interface for tablet devices * Contour line, a curve along which the function has a constant value * Contour drawing, an artistic technique * A closed path in the mathematical method of contour integration * Boundary (topology) of a set Contours may refer to: * ''Contours'' (album), by Sam Rivers * The Contours, a soul music group Contouring may refer to: * The makeup technique contouring Other uses * CONTOUR, a failed NASA space probe * Contour, Manchester, a residential development under construction in Manchester, England * Contour, a North Wing Apache ultralight aircraft variant * Ford Contour The Ford Mondeo I (first generation) is a mid-size car manufactured and marketed by Ford, beginning on 23 November 1992, with sales beginning on 22 M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
