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Path Of Least Resistance
In physics and mathematics, the path of least resistance is the pathway that provides the least resistance to forward motion by a given object or entity, among a set of alternative paths. The concept is often used to describe why an object or entity takes a given path. Physics In physics, the "path of least resistance" is a heuristic from folk physics that can sometimes, in very simple situations, describe approximately what happens. It is an approximation of the tendency to the least energy state. Other examples are "what goes up must come down" (gravity) and "heat goes from hot to cold" (second law of thermodynamics). But these simple descriptions are not derived from laws of physics and in more complicated cases these heuristics will fail to give even approximately correct results. The path of least resistance applies on a local, not global, reference. For example, water always flows downhill, regardless of whether briefly flowing uphill will help it gain a lower final alt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartoon Mountain Pass Symbolizing Path Of Least Resistance
A cartoon is a type of visual art that is typically drawn, frequently animated, in an unrealistic or semi-realistic style. The specific meaning has evolved, but the modern usage usually refers to either: an image or series of images intended for satire, caricature, or humor; or a motion picture that relies on a sequence of illustrations for its animation. Someone who creates cartoons in the first sense is called a ''cartoonist'', and in the second sense they are usually called an ''animator''. The concept originated in the Middle Ages, and first described a preparatory drawing for a piece of art, such as a painting, fresco, tapestry, or stained glass window. In the 19th century, beginning in '' Punch'' magazine in 1843, cartoon came to refer – ironically at first – to humorous artworks in magazines and newspapers. Then it also was used for political cartoons and comic strips. When the medium developed, in the early 20th century, it began to refer to animated films that rese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metaphor
A metaphor is a figure of speech that, for rhetorical effect, directly refers to one thing by mentioning another. It may provide, or obscure, clarity or identify hidden similarities between two different ideas. Metaphors are usually meant to create a likeness or an Analogy, analogy. Analysts group metaphors with other types of figurative language, such as antithesis, hyperbole, metonymy, and simile. According to Grammarly, "Figurative language examples include similes, metaphors, personification, hyperbole, allusions, and idioms." One of the most commonly cited examples of a metaphor in English literature comes from the "All the world's a stage" monologue from ''As You Like It'': All the world's a stage, And all the men and women merely players; They have their exits and their entrances And one man in his time plays many parts, His Acts being seven ages. At first, the infant... :—William Shakespeare, ''As You Like It'', 2/7 This quotation expresses a metaphor because the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Desire Path
A desire path, also known as desire line in transportation planning and many other names, is an unplanned small trail formed by erosion caused by human or animal traffic. The path usually represents the shortest or the most easily navigated route between an origin and destination, and the width and severity of its surface erosion are often indicators of the traffic level it receives. An early documented example is Broadway_(Manhattan), Broadway in New York City, which follows the Wecquaesgeek, Wecquaesgeek trail which predates American colonization. Desire paths typically emerge as convenient shortcuts where more deliberately constructed paths take a longer or more circuitous route, have gaps, or are non-existent. Once a path has been trodden out through the natural vegetation, subsequent traffic tends to follow that visibly existing route (as it is more convenient than carving out a new path by oneself), and the repeated trampling will further erode away both the remaining grou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Lines Of Drift
Natural lines of drift are those paths across terrain that are the most likely to be used when going from one place to another. These paths are paths of least resistance: those that offer the greatest ease while taking into account obstacles (e.g. rivers, cliffs, dense unbroken woodland, etc.) and modes of transit (e.g. pedestrian, automobile, horses.). Common endpoints or fixed points may include water sources, food sources, and obstacle passages such as fords or bridges. Local paths may be derived from game trails or from artificial paths created by utility lines or political boundaries. Property ownership and land use may also be factors in determining local variation. Improved paths may also be partially defined by the logistics necessary to build roads or railways. See also *Desire path *Footpath *Trail A trail, also known as a path or track, is an unpaved lane or a small paved road (though it can also be a route along a navigable waterways) generally not inten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient Descent
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a trajectory that maximizes that function; the procedure is then known as ''gradient ascent''. It is particularly useful in machine learning for minimizing the cost or loss function. Gradient descent should not be confused with local search algorithms, although both are iterative methods for optimization. Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variational Principle
A variational principle is a mathematical procedure that renders a physical problem solvable by the calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those functions. For example, the problem of determining the shape of a hanging chain suspended at both ends—a catenary—can be solved using variational calculus, and in this case, the variational principle is the following: The solution is a function that minimizes the gravitational potential energy of the chain. History Physics The history of the variational principle in classical mechanics started with Maupertuis's principle in the 18th century. Math Felix Klein's 1872 Erlangen program attempted to identify invariants under a group of transformations. Examples In mathematics * Ekeland's variational principle in mathematical optimization * The finite element method * The variation principle relating topological entropy and Kolmogorov-Sinai entropy. In physics * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Least Action
Action principles lie at the heart of fundamental physics, from classical mechanics through quantum mechanics, particle physics, and general relativity. Action principles start with an energy function called a Lagrangian describing the physical system. The accumulated value of this energy function between two states of the system is called the action. Action principles apply the calculus of variation to the action. The action depends on the energy function, and the energy function depends on the position, motion, and interactions in the system: variation of the action allows the derivation of the equations of motion without vectors or forces. Several distinct action principles differ in the constraints on their initial and final conditions. The names of action principles have evolved over time and differ in details of the endpoints of the paths and the nature of the variation. Quantum action principles generalize and justify the older classical principles by showing they are a di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mountain Pass Theorem
The mountain pass theorem is an existence theorem from the calculus of variations, originally due to Antonio Ambrosetti and Paul Rabinowitz. Given certain conditions on a function, the theorem demonstrates the existence of a saddle point. The theorem is unusual in that there are many other theorems regarding the existence of extremum, extrema, but few regarding saddle points. Statement The assumptions of the theorem are: * I is a functional (mathematics), functional from a Hilbert space ''H'' to the real number, reals, * I\in C^1(H,\mathbb) and I' is Lipschitz continuous on bounded subsets of ''H'', * I satisfies the Palais–Smale compactness condition, * I[0]=0, * there exist positive constants ''r'' and ''a'' such that I[u]\geq a if \Vert u\Vert =r, and * there exists v\in H with \Vert v\Vert >r such that I[v]\leq 0. If we define: :\Gamma=\ and: :c=\inf_\max_ I[\mathbf(t)], then the conclusion of the theorem is that ''c'' is a critical value of ''I''. Visualization The intu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Variations
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of functionals: Map (mathematics), mappings from a set of Function (mathematics), functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as ''geodesics''. A related problem is posed by Fermat's principle: li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Least Effort
The principle of least effort is a broad theory that covers diverse fields from evolutionary biology to webpage design. It postulates that animals, people, and even well-designed machines will naturally choose the path of least resistance or "effort". It is closely related to many other similar principles (see principle of least action or other articles listed below). This is perhaps best known, or at least documented, among researchers in the field of library and information science. Their principle states that an information-seeking client will tend to use the most convenient search method in the least exacting mode available. Information-seeking behavior stops as soon as minimally acceptable results are found. This theory holds true regardless of the user's proficiency as a searcher, or their level of subject expertise. Also, this theory takes into account the user's previous information-seeking experience. The user will use the tools that are most familiar and easy to use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path Of Least Resistance
In physics and mathematics, the path of least resistance is the pathway that provides the least resistance to forward motion by a given object or entity, among a set of alternative paths. The concept is often used to describe why an object or entity takes a given path. Physics In physics, the "path of least resistance" is a heuristic from folk physics that can sometimes, in very simple situations, describe approximately what happens. It is an approximation of the tendency to the least energy state. Other examples are "what goes up must come down" (gravity) and "heat goes from hot to cold" (second law of thermodynamics). But these simple descriptions are not derived from laws of physics and in more complicated cases these heuristics will fail to give even approximately correct results. The path of least resistance applies on a local, not global, reference. For example, water always flows downhill, regardless of whether briefly flowing uphill will help it gain a lower final alt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
