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Artificial intelligence was founded as an academic discipline in 1956, and the field went through multiple cycles of optimism throughout its history, followed by periods of disappointment and loss of funding, known as AI winters. Funding and interest vastly increased after 2012 when deep learning outperformed previous ... | Artificial intelligence | Wikipedia | 420 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
A knowledge base is a body of knowledge represented in a form that can be used by a program. An ontology is the set of objects, relations, concepts, and properties used by a particular domain of knowledge. Knowledge bases need to represent things such as objects, properties, categories, and relations between objects; s... | Artificial intelligence | Wikipedia | 463 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In some problems, the agent's preferences may be uncertain, especially if there are other agents or humans involved. These can be learned (e.g., with inverse reinforcement learning), or the agent can seek information to improve its preferences. Information value theory can be used to weigh the value of exploratory or e... | Artificial intelligence | Wikipedia | 471 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Early work, based on Noam Chomsky's generative grammar and semantic networks, had difficulty with word-sense disambiguation unless restricted to small domains called "micro-worlds" (due to the common sense knowledge problem). Margaret Masterman believed that it was meaning and not grammar that was the key to understand... | Artificial intelligence | Wikipedia | 472 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
State space search
State space search searches through a tree of possible states to try to find a goal state. For example, planning algorithms search through trees of goals and subgoals, attempting to find a path to a target goal, a process called means-ends analysis.
Simple exhaustive searches are rarely sufficient ... | Artificial intelligence | Wikipedia | 490 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Given a problem and a set of premises, problem-solving reduces to searching for a proof tree whose root node is labelled by a solution of the problem and whose leaf nodes are labelled by premises or axioms. In the case of Horn clauses, problem-solving search can be performed by reasoning forwards from the premises or b... | Artificial intelligence | Wikipedia | 450 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Classifiers and statistical learning methods
The simplest AI applications can be divided into two types: classifiers (e.g., "if shiny then diamond"), on one hand, and controllers (e.g., "if diamond then pick up"), on the other hand. Classifiers are functions that use pattern matching to determine the closest match. Th... | Artificial intelligence | Wikipedia | 412 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In feedforward neural networks the signal passes in only one direction. Recurrent neural networks feed the output signal back into the input, which allows short-term memories of previous input events. Long short term memory is the most successful network architecture for recurrent networks. Perceptrons use only a singl... | Artificial intelligence | Wikipedia | 340 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
GPT
Generative pre-trained transformers (GPT) are large language models (LLMs) that generate text based on the semantic relationships between words in sentences. Text-based GPT models are pretrained on a large corpus of text that can be from the Internet. The pretraining consists of predicting the next token (a token b... | Artificial intelligence | Wikipedia | 418 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Applications
AI and machine learning technology is used in most of the essential applications of the 2020s, including: search engines (such as Google Search), targeting online advertisements, recommendation systems (offered by Netflix, YouTube or Amazon), driving internet traffic, targeted advertising (AdSense, Facebo... | Artificial intelligence | Wikipedia | 419 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Applications of AI in this domain include AI-enabled menstruation and fertility trackers that analyze user data to offer prediction, AI-integrated sex toys (e.g., teledildonics), AI-generated sexual education content, and AI agents that simulate sexual and romantic partners (e.g., Replika). AI is also used for the pro... | Artificial intelligence | Wikipedia | 441 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Mathematics
In mathematics, special forms of formal step-by-step reasoning are used. In contrast, LLMs such as GPT-4 Turbo, Gemini Ultra, Claude Opus, LLaMa-2 or Mistral Large are working with probabilistic models, which can produce wrong answers in the form of hallucinations. Therefore, they need not only a large dat... | Artificial intelligence | Wikipedia | 502 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Agents
Artificial intelligent (AI) agents are software entities designed to perceive their environment, make decisions, and take actions autonomously to achieve specific goals. These agents can interact with users, their environment, or other agents. AI agents are used in various applications, including virtual assista... | Artificial intelligence | Wikipedia | 500 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
During the 2024 Indian elections, US$50 millions was spent on authorized AI-generated content, notably by creating deepfakes of allied (including sometimes deceased) politicians to better engage with voters, and by translating speeches to various local languages.
Ethics
AI has potential benefits and potential risks. ... | Artificial intelligence | Wikipedia | 449 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Generative AI is often trained on unlicensed copyrighted works, including in domains such as images or computer code; the output is then used under the rationale of "fair use". Experts disagree about how well and under what circumstances this rationale will hold up in courts of law; relevant factors may include "the pu... | Artificial intelligence | Wikipedia | 333 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Prodigious power consumption by AI is responsible for the growth of fossil fuels use, and might delay closings of obsolete, carbon-emitting coal energy facilities. There is a feverish rise in the construction of data centers throughout the US, making large technology firms (e.g., Microsoft, Meta, Google, Amazon) into v... | Artificial intelligence | Wikipedia | 395 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In September 2024, Microsoft announced an agreement with Constellation Energy to re-open the Three Mile Island nuclear power plant to provide Microsoft with 100% of all electric power produced by the plant for 20 years. Reopening the plant, which suffered a partial nuclear meltdown of its Unit 2 reactor in 1979, will r... | Artificial intelligence | Wikipedia | 497 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
YouTube, Facebook and others use recommender systems to guide users to more content. These AI programs were given the goal of maximizing user engagement (that is, the only goal was to keep people watching). The AI learned that users tended to choose misinformation, conspiracy theories, and extreme partisan content, and... | Artificial intelligence | Wikipedia | 477 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
COMPAS is a commercial program widely used by U.S. courts to assess the likelihood of a defendant becoming a recidivist. In 2016, Julia Angwin at ProPublica discovered that COMPAS exhibited racial bias, despite the fact that the program was not told the races of the defendants. Although the error rate for both whites a... | Artificial intelligence | Wikipedia | 420 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
There are various conflicting definitions and mathematical models of fairness. These notions depend on ethical assumptions, and are influenced by beliefs about society. One broad category is distributive fairness, which focuses on the outcomes, often identifying groups and seeking to compensate for statistical disparit... | Artificial intelligence | Wikipedia | 486 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
People who have been harmed by an algorithm's decision have a right to an explanation. Doctors, for example, are expected to clearly and completely explain to their colleagues the reasoning behind any decision they make. Early drafts of the European Union's General Data Protection Regulation in 2016 included an explici... | Artificial intelligence | Wikipedia | 432 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
AI tools make it easier for authoritarian governments to efficiently control their citizens in several ways. Face and voice recognition allow widespread surveillance. Machine learning, operating this data, can classify potential enemies of the state and prevent them from hiding. Recommendation systems can precisely tar... | Artificial intelligence | Wikipedia | 510 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
From the early days of the development of artificial intelligence, there have been arguments, for example, those put forward by Joseph Weizenbaum, about whether tasks that can be done by computers actually should be done by them, given the difference between computers and humans, and between quantitative calculation an... | Artificial intelligence | Wikipedia | 503 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In May 2023, Geoffrey Hinton announced his resignation from Google in order to be able to "freely speak out about the risks of AI" without "considering how this impacts Google." He notably mentioned risks of an AI takeover, and stressed that in order to avoid the worst outcomes, establishing safety guidelines will requ... | Artificial intelligence | Wikipedia | 474 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Open source
Active organizations in the AI open-source community include Hugging Face, Google, EleutherAI and Meta. Various AI models, such as Llama 2, Mistral or Stable Diffusion, have been made open-weight, meaning that their architecture and trained parameters (the "weights") are publicly available. Open-weight mod... | Artificial intelligence | Wikipedia | 476 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
The regulation of artificial intelligence is the development of public sector policies and laws for promoting and regulating AI; it is therefore related to the broader regulation of algorithms. The regulatory and policy landscape for AI is an emerging issue in jurisdictions globally. According to AI Index at Stanford, ... | Artificial intelligence | Wikipedia | 479 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In November 2023, the first global AI Safety Summit was held in Bletchley Park in the UK to discuss the near and far term risks of AI and the possibility of mandatory and voluntary regulatory frameworks. 28 countries including the United States, China, and the European Union issued a declaration at the start of the sum... | Artificial intelligence | Wikipedia | 353 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Researchers in the 1960s and the 1970s were convinced that their methods would eventually succeed in creating a machine with general intelligence and considered this the goal of their field. In 1965 Herbert Simon predicted, "machines will be capable, within twenty years, of doing any work a man can do". In 1967 Marvin ... | Artificial intelligence | Wikipedia | 508 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
AI gradually restored its reputation in the late 1990s and early 21st century by exploiting formal mathematical methods and by finding specific solutions to specific problems. This "narrow" and "formal" focus allowed researchers to produce verifiable results and collaborate with other fields (such as statistics, econom... | Artificial intelligence | Wikipedia | 319 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In the late teens and early 2020s, AGI companies began to deliver programs that created enormous interest. In 2015, AlphaGo, developed by DeepMind, beat the world champion Go player. The program taught only the game's rules and developed a strategy by itself. GPT-3 is a large language model that was released in 2020 by... | Artificial intelligence | Wikipedia | 447 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Russell and Norvig agree with Turing that intelligence must be defined in terms of external behavior, not internal structure. However, they are critical that the test requires the machine to imitate humans. "Aeronautical engineering texts", they wrote, "do not define the goal of their field as making 'machines that fly... | Artificial intelligence | Wikipedia | 436 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Symbolic AI and its limits
Symbolic AI (or "GOFAI") simulated the high-level conscious reasoning that people use when they solve puzzles, express legal reasoning and do mathematics. They were highly successful at "intelligent" tasks such as algebra or IQ tests. In the 1960s, Newell and Simon proposed the physical symbo... | Artificial intelligence | Wikipedia | 504 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
AI researchers are divided as to whether to pursue the goals of artificial general intelligence and superintelligence directly or to solve as many specific problems as possible (narrow AI) in hopes these solutions will lead indirectly to the field's long-term goals. General intelligence is difficult to define and diffi... | Artificial intelligence | Wikipedia | 492 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Philosopher John Searle characterized this position as "strong AI": "The appropriately programmed computer with the right inputs and outputs would thereby have a mind in exactly the same sense human beings have minds." Searle challenges this claim with his Chinese room argument, which attempts to show that even a compu... | Artificial intelligence | Wikipedia | 479 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Robot designer Hans Moravec, cyberneticist Kevin Warwick and inventor Ray Kurzweil have predicted that humans and machines may merge in the future into cyborgs that are more capable and powerful than either. This idea, called transhumanism, has roots in the writings of Aldous Huxley and Robert Ettinger.
Edward Fredkin... | Artificial intelligence | Wikipedia | 444 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
Several works use AI to force us to confront the fundamental question of what makes us human, showing us artificial beings that have the ability to feel, and thus to suffer. This appears in Karel Čapek's R.U.R., the films A.I. Artificial Intelligence and Ex Machina, as well as the novel Do Androids Dream of Electric Sh... | Artificial intelligence | Wikipedia | 102 | 1164 | https://en.wikipedia.org/wiki/Artificial%20intelligence | Technology | Computing and information technology | null |
In mathematics, a binary relation on a set is antisymmetric if there is no pair of distinct elements of each of which is related by to the other. More formally, is antisymmetric precisely if for all
or equivalently,
The definition of antisymmetry says nothing about whether actually holds or not for any . An an... | Antisymmetric relation | Wikipedia | 493 | 1176 | https://en.wikipedia.org/wiki/Antisymmetric%20relation | Mathematics | Order theory | null |
Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way.
History
The history of astrometry is linked to the history of star catalogues, w... | Astrometry | Wikipedia | 485 | 1181 | https://en.wikipedia.org/wiki/Astrometry | Physical sciences | Astrometry | null |
English astronomer James Bradley first tried to measure stellar parallaxes in 1729. The stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light and the nutation of the Earth's axis. His cataloguing of 3222 stars was refined in 1807 by German astronomer Friedrich Be... | Astrometry | Wikipedia | 266 | 1181 | https://en.wikipedia.org/wiki/Astrometry | Physical sciences | Astrometry | null |
In 1989, the European Space Agency's Hipparcos satellite took astrometry into orbit, where it could be less affected by mechanical forces of the Earth and optical distortions from its atmosphere. Operated from 1989 to 1993, Hipparcos measured large and small angles on the sky with much greater precision than any previo... | Astrometry | Wikipedia | 383 | 1181 | https://en.wikipedia.org/wiki/Astrometry | Physical sciences | Astrometry | null |
Astrometry has also been used to support claims of extrasolar planet detection by measuring the displacement the proposed planets cause in their parent star's apparent position on the sky, due to their mutual orbit around the center of mass of the system. Astrometry is more accurate in space missions that are not affec... | Astrometry | Wikipedia | 470 | 1181 | https://en.wikipedia.org/wiki/Astrometry | Physical sciences | Astrometry | null |
A fundamental aspect of astrometry is error correction. Various factors introduce errors into the measurement of stellar positions, including atmospheric conditions, imperfections in the instruments and errors by the observer or the measuring instruments. Many of these errors can be reduced by various techniques, such ... | Astrometry | Wikipedia | 111 | 1181 | https://en.wikipedia.org/wiki/Astrometry | Physical sciences | Astrometry | null |
An alloy is a mixture of chemical elements of which in most cases at least one is a metallic element, although it is also sometimes used for mixtures of elements; herein only metallic alloys are described. Most alloys are metallic and show good electrical conductivity, ductility, opacity, and luster, and may have prope... | Alloy | Wikipedia | 393 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
An alloy is a mixture of chemical elements, which forms an impure substance (admixture) that retains the characteristics of a metal. An alloy is distinct from an impure metal in that, with an alloy, the added elements are well controlled to produce desirable properties, while impure metals such as wrought iron are less... | Alloy | Wikipedia | 316 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Like oil and water, a molten metal may not always mix with another element. For example, pure iron is almost completely insoluble with copper. Even when the constituents are soluble, each will usually have a saturation point, beyond which no more of the constituent can be added. Iron, for example, can hold a maximum of... | Alloy | Wikipedia | 264 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Some alloys, such as electrum—an alloy of silver and gold—occur naturally. Meteorites are sometimes made of naturally occurring alloys of iron and nickel, but are not native to the Earth. One of the first alloys made by humans was bronze, which is a mixture of the metals tin and copper. Bronze was an extremely useful a... | Alloy | Wikipedia | 512 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Theory
Alloying a metal is done by combining it with one or more other elements. The most common and oldest alloying process is performed by heating the base metal beyond its melting point and then dissolving the solutes into the molten liquid, which may be possible even if the melting point of the solute is far grea... | Alloy | Wikipedia | 325 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
By adding another element to a metal, differences in the size of the atoms create internal stresses in the lattice of the metallic crystals; stresses that often enhance its properties. For example, the combination of carbon with iron produces steel, which is stronger than iron, its primary element. The electrical and t... | Alloy | Wikipedia | 510 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
The base metal iron of the iron-carbon alloy known as steel, undergoes a change in the arrangement (allotropy) of the atoms of its crystal matrix at a certain temperature (usually between and , depending on carbon content). This allows the smaller carbon atoms to enter the interstices of the iron crystal. When this di... | Alloy | Wikipedia | 508 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
In 1906, precipitation hardening alloys were discovered by Alfred Wilm. Precipitation hardening alloys, such as certain alloys of aluminium, titanium, and copper, are heat-treatable alloys that soften when quenched (cooled quickly), and then harden over time. Wilm had been searching for a way to harden aluminium alloys... | Alloy | Wikipedia | 501 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
The use of alloys by humans started with the use of meteoric iron, a naturally occurring alloy of nickel and iron. It is the main constituent of iron meteorites. As no metallurgic processes were used to separate iron from nickel, the alloy was used as it was. Meteoric iron could be forged from a red heat to make object... | Alloy | Wikipedia | 387 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Mercury has been smelted from cinnabar for thousands of years. Mercury dissolves many metals, such as gold, silver, and tin, to form amalgams (an alloy in a soft paste or liquid form at ambient temperature). Amalgams have been used since 200 BC in China for gilding objects such as armor and mirrors with precious metals... | Alloy | Wikipedia | 473 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
The earliest examples of pewter come from ancient Egypt, around 1450 BC. The use of pewter was widespread across Europe, from France to Norway and Britain (where most of the ancient tin was mined) to the Near East. The alloy was also used in China and the Far East, arriving in Japan around 800 AD, where it was used for... | Alloy | Wikipedia | 320 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
While the use of iron started to become more widespread around 1200 BC, mainly because of interruptions in the trade routes for tin, the metal was much softer than bronze. However, very small amounts of steel, (an alloy of iron and around 1% carbon), was always a byproduct of the bloomery process. The ability to modify... | Alloy | Wikipedia | 364 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Steel is an alloy of iron and carbon, but the term alloy steel usually only refers to steels that contain other elements— like vanadium, molybdenum, or cobalt—in amounts sufficient to alter the properties of the base steel. Since ancient times, when steel was used primarily for tools and weapons, the methods of produci... | Alloy | Wikipedia | 403 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Robert Forester Mushet found that by adding tungsten to steel it could produce a very hard edge that would resist losing its hardness at high temperatures. "R. Mushet's special steel" (RMS) became the first high-speed steel. Mushet's steel was quickly replaced by tungsten carbide steel, developed by Taylor and White in... | Alloy | Wikipedia | 445 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
Prior to 1910, research mainly consisted of private individuals tinkering in their own laboratories. However, as the aircraft and automotive industries began growing, research into alloys became an industrial effort in the years following 1910, as new magnesium alloys were developed for pistons and wheels in cars, and ... | Alloy | Wikipedia | 111 | 1187 | https://en.wikipedia.org/wiki/Alloy | Physical sciences | Chemistry | null |
In Euclidean geometry, an angle or plane angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersectio... | Angle | Wikipedia | 452 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Identifying angles
In mathematical expressions, it is common to use Greek letters (α, β, γ, θ, φ, . . . ) as variables denoting the size of some angle (the symbol is typically not used for this purpose to avoid confusion with the constant denoted by that symbol). Lower case Roman letters (a, b, c, . . . ) are also use... | Angle | Wikipedia | 362 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Individual angles
There is some common terminology for angles, whose measure is always non-negative (see ):
An angle equal to 0° or not turned is called a zero angle.
An angle smaller than a right angle (less than 90°) is called an acute angle ("acute" meaning "sharp").
An angle equal to turn (90° or radians) is c... | Angle | Wikipedia | 394 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
An angle that is part of a simple polygon is called an interior angle if it lies on the inside of that simple polygon. A simple concave polygon has at least one interior angle, that is, a reflex angle. In Euclidean geometry, the measures of the interior angles of a triangle add up to radians, 180°, or turn; the mea... | Angle | Wikipedia | 480 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Some authors use the name exterior angle of a simple polygon to mean the explement exterior angle (not supplement!) of the interior angle. This conflicts with the above usage. | Angle | Wikipedia | 37 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Plane-related angles
The angle between two planes (such as two adjacent faces of a polyhedron) is called a dihedral angle. It may be defined as the acute angle between two lines normal to the planes.
The angle between a plane and an intersecting straight line is complementary to the angle between the intersecting lin... | Angle | Wikipedia | 393 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Throughout history, angles have been measured in various units. These are known as angular units, with the most contemporary units being the degree ( ° ), the radian (rad), and the gradian (grad), though many others have been used throughout history. Most units of angular measurement are defined such that one turn (i.e... | Angle | Wikipedia | 454 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
In three-dimensional geometry, "clockwise" and "anticlockwise" have no absolute meaning, so the direction of positive and negative angles must be defined in terms of an orientation, which is typically determined by a normal vector passing through the angle's vertex and perpendicular to the plane in which the rays of th... | Angle | Wikipedia | 391 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Related quantities
For an angular unit, it is definitional that the angle addition postulate holds. Some quantities related to angles where the angle addition postulate does not hold include:
The slope or gradient is equal to the tangent of the angle; a gradient is often expressed as a percentage. For very small value... | Angle | Wikipedia | 504 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
In a complex inner product space, the expression for the cosine above may give non-real values, so it is replaced with
or, more commonly, using the absolute value, with
The latter definition ignores the direction of the vectors. It thus describes the angle between one-dimensional subspaces and spanned by the vector... | Angle | Wikipedia | 502 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Astronomers also measure objects' apparent size as an angular diameter. For example, the full moon has an angular diameter of approximately 0.5° when viewed from Earth. One could say, "The Moon's diameter subtends an angle of half a degree." The small-angle formula can convert such an angular measurement into a distanc... | Angle | Wikipedia | 199 | 1196 | https://en.wikipedia.org/wiki/Angle | Mathematics | Geometry and topology | null |
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an... | Acoustics | Wikipedia | 367 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
In the 6th century BC, the ancient Greek philosopher Pythagoras wanted to know why some combinations of musical sounds seemed more beautiful than others, and he found answers in terms of numerical ratios representing the harmonic overtone series on a string. He is reputed to have observed that when the lengths of vibra... | Acoustics | Wikipedia | 497 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
The physical understanding of acoustical processes advanced rapidly during and after the Scientific Revolution. Mainly Galileo Galilei (1564–1642) but also Marin Mersenne (1588–1648), independently, discovered the complete laws of vibrating strings (completing what Pythagoras and Pythagoreans had started 2000 years ear... | Acoustics | Wikipedia | 499 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Acoustics is defined by ANSI/ASA S1.1-2013 as "(a) Science of sound, including its production, transmission, and effects, including biological and psychological effects. (b) Those qualities of a room that, together, determine its character with respect to auditory effects."
The study of acoustics revolves around the g... | Acoustics | Wikipedia | 492 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Physicists and acoustic engineers tend to discuss sound pressure levels in terms of frequencies, partly because this is how our ears interpret sound. What we experience as "higher pitched" or "lower pitched" sounds are pressure vibrations having a higher or lower number of cycles per second. In a common technique of ac... | Acoustics | Wikipedia | 406 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
The transducers in most common loudspeakers (e.g. woofers and tweeters), are electromagnetic devices that generate waves using a suspended diaphragm driven by an electromagnetic voice coil, sending off pressure waves. Electret microphones and condenser microphones employ electrostatics—as the sound wave strikes the mi... | Acoustics | Wikipedia | 346 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Archaeoacoustics, also known as the archaeology of sound, is one of the only ways to experience the past with senses other than our eyes. Archaeoacoustics is studied by testing the acoustic properties of prehistoric sites, including caves. Iegor Rezkinoff, a sound archaeologist, studies the acoustic properties of caves... | Acoustics | Wikipedia | 504 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Environmental acoustics is the study of noise and vibrations, and their impact on structures, objects, humans, and animals.
The main aim of these studies is to reduce levels of environmental noise and vibration. Typical work and research within environmental acoustics concerns the development of models used in simula... | Acoustics | Wikipedia | 488 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Applications might include: ground vibrations from railways; vibration isolation to reduce vibration in operating theatres; studying how vibration can damage health (vibration white finger); vibration control to protect a building from earthquakes, or measuring how structure-borne sound moves through buildings.
Ultras... | Acoustics | Wikipedia | 425 | 1198 | https://en.wikipedia.org/wiki/Acoustics | Physical sciences | Waves | null |
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned with the way in which electrons are arranged around the nucleus and
the proces... | Atomic physics | Wikipedia | 498 | 1200 | https://en.wikipedia.org/wiki/Atomic%20physics | Physical sciences | Atomic physics | null |
If the electron absorbs a quantity of energy less than the binding energy, it will be transferred to an excited state. After a certain time, the electron in an excited state will "jump" (undergo a transition) to a lower state. In a neutral atom, the system will emit a photon of the difference in energy, since energy is... | Atomic physics | Wikipedia | 502 | 1200 | https://en.wikipedia.org/wiki/Atomic%20physics | Physical sciences | Atomic physics | null |
•Electrons can transition between orbits by absorbing or emitting energy equal to the difference between the energy levels:
\Delta E = E_f - E_i = h\nu,
where:
•h : Planck’s constant.
• \nu : Frequency of emitted/absorbed radiation.
• E_f, E_i : Final and initial energy levels.
History and developments
One of... | Atomic physics | Wikipedia | 410 | 1200 | https://en.wikipedia.org/wiki/Atomic%20physics | Physical sciences | Atomic physics | null |
In quantum mechanics, an atomic orbital () is a function describing the location and wave-like behavior of an electron in an atom. This function describes an electron's charge distribution around the atom's nucleus, and can be used to calculate the probability of finding an electron in a specific region around the nucl... | Atomic orbital | Wikipedia | 509 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Electron properties
With the development of quantum mechanics and experimental findings (such as the two slit diffraction of electrons), it was found that the electrons orbiting a nucleus could not be fully described as particles, but needed to be explained by wave–particle duality. In this sense, electrons have the f... | Atomic orbital | Wikipedia | 396 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
One should remember that these orbital 'states', as described here, are merely eigenstates of an electron in its orbit. An actual electron exists in a superposition of states, which is like a weighted average, but with complex number weights. So, for instance, an electron could be in a pure eigenstate (2, 1, 0), or a... | Atomic orbital | Wikipedia | 492 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
In atomic physics, the atomic spectral lines correspond to transitions (quantum leaps) between quantum states of an atom. These states are labeled by a set of quantum numbers summarized in the term symbol and usually associated with particular electron configurations, i.e., by occupation schemes of atomic orbitals (for... | Atomic orbital | Wikipedia | 311 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Atomic orbitals can be the hydrogen-like "orbitals" which are exact solutions to the Schrödinger equation for a hydrogen-like "atom" (i.e., atom with one electron). Alternatively, atomic orbitals refer to functions that depend on the coordinates of one electron (i.e., orbitals) but are used as starting points for appro... | Atomic orbital | Wikipedia | 405 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
The term orbital was introduced by Robert S. Mulliken in 1932 as short for one-electron orbital wave function. Niels Bohr explained around 1913 that electrons might revolve around a compact nucleus with definite angular momentum. Bohr's model was an improvement on the 1911 explanations of Ernest Rutherford, that of the... | Atomic orbital | Wikipedia | 374 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Bohr atom
In 1909, Ernest Rutherford discovered that the bulk of the atomic mass was tightly condensed into a nucleus, which was also found to be positively charged. It became clear from his analysis in 1911 that the plum pudding model could not explain atomic structure. In 1913, Rutherford's post-doctoral student, Ni... | Atomic orbital | Wikipedia | 382 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
With de Broglie's suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 Schrödinger equation treatment of hydrogen-like atoms, a Bohr electron "wavelength" could be seen to be a function of its momentum; so a Bohr orbiting electron was seen to orbit in a circle at a mul... | Atomic orbital | Wikipedia | 424 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Modern conceptions and connections to the Heisenberg uncertainty principle
Immediately after Heisenberg discovered his uncertainty principle, Bohr noted that the existence of any sort of wave packet implies uncertainty in the wave frequency and wavelength, since a spread of frequencies is needed to create the packet i... | Atomic orbital | Wikipedia | 496 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
For example, the orbital 1s (pronounced as the individual numbers and letters: "'one' 'ess'") is the lowest energy level () and has an angular quantum number of , denoted as s. Orbitals with are denoted as p, d and f respectively.
The set of orbitals for a given n and is called a subshell, denoted
.
The superscrip... | Atomic orbital | Wikipedia | 478 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
The stationary states (quantum states) of a hydrogen-like atom are its atomic orbitals. However, in general, an electron's behavior is not fully described by a single orbital. Electron states are best represented by time-depending "mixtures" (linear combinations) of multiple orbitals. See Linear combination of atomic o... | Atomic orbital | Wikipedia | 509 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
The above results may be summarized in the following table. Each cell represents a subshell, and lists the values of available in that subshell. Empty cells represent subshells that do not exist.
Subshells are usually identified by their - and -values. is represented by its numerical value, but is represented by a ... | Atomic orbital | Wikipedia | 466 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Real spherical harmonics are physically relevant when an atom is embedded in a crystalline solid, in which case there are multiple preferred symmetry axes but no single preferred direction. Real atomic orbitals are also more frequently encountered in introductory chemistry textbooks and shown in common orbital visualiz... | Atomic orbital | Wikipedia | 402 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Simple pictures showing orbital shapes are intended to describe the angular forms of regions in space where the electrons occupying the orbital are likely to be found. The diagrams cannot show the entire region where an electron can be found, since according to quantum mechanics there is a non-zero probability of findi... | Atomic orbital | Wikipedia | 481 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
In general, determines size and energy of the orbital for a given nucleus; as increases, the size of the orbital increases. The higher nuclear charge of heavier elements causes their orbitals to contract by comparison to lighter ones, so that the size of the atom remains very roughly constant, even as the number of ... | Atomic orbital | Wikipedia | 494 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Four of the five d orbitals for look similar, each with four pear-shaped lobes, each lobe tangent at right angles to two others, and the centers of all four lying in one plane. Three of these planes are the xy-, xz-, and yz-planes—the lobes are between the pairs of primary axes—and the fourth has the center along the ... | Atomic orbital | Wikipedia | 496 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Orbitals table
This table shows the real hydrogen-like wave functions for all atomic orbitals up to 7s, and therefore covers the occupied orbitals in the ground state of all elements in the periodic table up to radium and some beyond. "ψ" graphs are shown with − and + wave function phases shown in two different colors... | Atomic orbital | Wikipedia | 271 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
Qualitative understanding of shapes
The shapes of atomic orbitals can be qualitatively understood by considering the analogous case of standing waves on a circular drum. To see the analogy, the mean vibrational displacement of each bit of drum membrane from the equilibrium point over many cycles (a measure of average ... | Atomic orbital | Wikipedia | 503 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
None of the other sets of modes in a drum membrane have a central antinode, and in all of them the center of the drum does not move. These correspond to a node at the nucleus for all non-s orbitals in an atom. These orbitals all have some angular momentum, and in the planetary model, they correspond to particles in orb... | Atomic orbital | Wikipedia | 438 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
In atoms with multiple electrons, the energy of an electron depends not only on its orbital, but also on its interactions with other electrons. These interactions depend on the detail of its spatial probability distribution, and so the energy levels of orbitals depend not only on but also on . Higher values of are as... | Atomic orbital | Wikipedia | 495 | 1206 | https://en.wikipedia.org/wiki/Atomic%20orbital | Physical sciences | Atomic physics | null |
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