query: How large is a cat's brain?

title: Cat intelligence

text: The brain of the domesticated cat is about five centimetres (2.0in) long, and weighs 25–30g (0.88–1.06oz).[1][2] If a typical cat is taken to be 60cm (24in) long with a weight of 3.3kg (7.3lb), then the brain would be at 0.91%[3] of its total body mass, compared to 2.33%[3] of total body mass in the average human. Within the encephalization quotient proposed by Jerison in 1973,[3][4] values above 1 are classified big brained, while values lower than 1 are small brained.[5] The domestic cat is attributed a value of between 1–1.71 relative to human value that is 7.44–7.8.[1][3] The largest brains in the Felidae family are those of the tigers in Java and Bali, of which the largest relative brain size within the panthera is the tigris.[6] It is debated whether there exists a causal relationship between brain size and intelligence in vertebrates. Correlations have been shown between these factors in a number of experiments. However, correlation does not imply causation. Most experiments involving the relevance of brain size to intelligence hinge on the assumption that complex behavior requires a complex (and therefore intelligent) brain; however, this connection has not been consistently demonstrated.[7][8][9][10][11]

title: Homotherium

text:
It had the general appearance of a cat, but some of its physical characteristics are rather unusual for a large cat. The limb proportions of "Homotherium" gave it a hyena-like appearance. The forelegs were elongated, while the hind quarters were rather squat with feet perhaps partially plantigrade, causing the back to slope towards the short tail. Features of the hind limbs indicate that this cat was moderately capable of leaping. The pelvic region, including the sacral vertebrae, was bear-like, as was the short tail composed of 13 vertebrae—about half the number of long-tailed cats'.
The unusually large, square nasal opening, like that of the cheetah ("Acinonyx jubatus"), presumably allowed quicker oxygen intake, which aided in rapid running and in cooling the brain. As in the cheetah, too, the brain's visual cortex was large and complex, emphasizing the scimitar cat's ability to see well and function in the day, rather than the night as do most other cats.

title: Switchin' Kitten

text: During a storm, Tom is trying to find a place to stay after being thrown out of a horse-drawn carriage. In the meantime, Jerry is assisting a mad scientist in a stereotypical old castle. In their experiment, they switch the brains of an orange cat and blue dog. The scientist gives the cat-with-a-dog-brain to Jerry as a companion. While they are sleeping, Tom approaches the castle, capturing Jerry. The cat growls and takes Jerry back, threatening Tom. Tom tries to convince the cat that he is a cat, but fails.

title: Cat intelligence

text: According to researchers at Tufts University School of Veterinary Medicine, the physical structure of the brains of humans and cats is very similar.[14] The human brain and the cat brain both have cerebral cortices[15] with similar lobes.[16]

title: Cat cognitive support diets

text: Cognitive dysfunction syndrome in companion animals is commonly paralleled to Alzheimer’s Disease in humans due to several brain pathologies observed in both senior humans and senior pets. Necropsies and histological studies performed on the brains of humans with Alzheimer’s Disease and those performed on the brains of cats exhibiting signs of CDS both report hyperphosphorylated tau proteins, β-Amyloid aggregates deposited on the cerebral cortex, ‘knotted’ nerve fibers known as neurofibrillary tangles, and neuron loss in several different zones of the brain. The challenges of evaluating and tracking cognitive function in cats has led to very few trials investigating the effect of nutritional intervention on feline cognition, so as a result, many of the nutrients recommended to support cat cognition have been interpreted from human and canine cognitive support supplements.

title: Growing Up in the Universe

text: Dawkins opens by talking how organisms “grow up” to understand the universe around them, which requires certain apparatus, such as a brain. But before brains can become large enough to model the universe they must develop from intermediate forms. Dawkins then discusses the digger wasp and the set of experiments conducted by Nikolaas Tinbergen of how the digger wasp models the local geography around its nest. He then talks about the limitations of the digger wasps’ brain and concludes that only the human brain is sufficiently developed to model large-scale phenomena about the world. He then shows a MRI scan of a human brain (later revealed to be his own brain) and describes how an image develops from the eye onto the visual cortex.

title: Neural circuit

text: Different neuroimaging techniques have been developed to investigate the activity of neural circuits and networks. The use of "brain scanners" or functional neuroimaging to investigate the structure or function of the brain is common, either as simply a way of better assessing brain injury with high resolution pictures, or by examining the relative activations of different brain areas. Such technologies may include functional magnetic resonance imaging (fMRI), brain positron emission tomography (brain PET), and computed axial tomography (CAT) scans. Functional neuroimaging uses specific brain imaging technologies to take scans from the brain, usually when a person is doing a particular task, in an attempt to understand how the activation of particular brain areas is related to the task. In functional neuroimaging, especially fMRI, which measures hemodynamic activity (using BOLD-contrast imaging) which is closely linked to neural activity, PET, and electroencephalography (EEG) is used.

title: Cognitive tuning

text: Their discovery occurred accidentally. In 1962, Hubel and Wiesel were attempting to discover that triggered neurophysiological activity in a cat's brain. The cat they were testing showed no results until they displayed a "crack" to the cat, whereupon the cat's brain starting reacting to the stimulus. This began a long series of discoveries which continues to the present day. Hubel and Wiesel received the Nobel Prize for their discovery.

title: Ten percent of the brain myth

text: Although parts of the brain have broadly understood functions, many mysteries remain about how brain cells (i.e., neurons and glia) work together to produce complex behaviors and disorders. Perhaps the broadest, most mysterious question is how diverse regions of the brain collaborate to form conscious experiences. So far, there is no evidence that there is one site for consciousness, which leads experts to believe that it is truly a collective neural effort. Therefore, as with James's idea that humans have untapped cognitive potential, it may be that a large number of questions about the brain have not been fully answered.

title: Functional integration (neurobiology)

text: Functional integration is the study of how brain regions work together to process information and effect responses. Though functional integration frequently relies on anatomic knowledge of the connections between brain areas, the emphasis is on how large clusters of neurons – numbering in the thousands or millions – fire together under various stimuli. The large datasets required for such a whole-scale picture of brain function have motivated the development of several novel and general methods for the statistical analysis of interdependence, such as dynamic causal modelling and statistical linear parametric mapping. These datasets are typically gathered in human subjects by non-invasive methods such as EEG/MEG, fMRI, or PET. The results can be of clinical value by helping to identify the regions responsible for psychiatric disorders, as well as to assess how different activities or lifestyles affect the functioning of the brain.

title: Michael Gazzaniga

text: Dr. Gazzaniga has led pioneering studies in learning and understanding split brained patients and how their brains work. He has performed numerous studies and done large amounts of research on split brain patients to provide a higher quality understanding into the lives of those affected by this rare phenomenon. He has studied how people who have the two halves of the brain separated function in comparison to those who do not. Dr. Gazzaniga has looked into what bodily functions are controlled by each half of the brain. He has looked at what split brained patients are able to do as a result of their condition such as the ability to draw two different objects with each hand, an ability that a person with a non split brain is unable to do. They study how those with split brain act emotionally and physically in comparison to those who do not have a split brain. Through Gazzaniga’s studies a much greater understanding of the split brain phenomenon has been brought to other physiologists as well as the general population of the world.

title: Wes Burgess

text: Burgess’ studies revealed how the dendrites of brain neurons grow during development. Together with Richard Coss at the University of California, Davis, Burgess was the first to show that sensory stimuli, including social stressors, can cause long-lasting changes in brain cell anatomical structure in just a few minutes. Together with Jaime Villablanca at UCLA, Burgess discovered that early brain injury resembling childhood congenital disorders and adult traumatic brain injury can heal naturally and that rehabilitative exercise improves brain healing. He helped clarify the rôle of the caudate nucleus in aggression and found that, without input from this nucleus, usually aggressive cats are friendly and affiliative. Burgess also contributed to our understanding of how the nervous system responds to morphine, especially during early development.

title: Cat intelligence

text: D.M.Fankhauser Removal and study of the cat brain and Cranial nerves of the cat [Retrieved 2011-12-22] (images and instruction) for an anatomy and physiology class for the dissecting of the brain of a cat

title: Iriomote cat

text: The skull is longer and more narrow than that of a domestic cat. When compared to the leopard cat's skull, the Iriomote cat's is roughly the same size but thicker. Because of this, the Iriomote cat's brain is smaller; a male leopard cat's brain is about 42 grams, whereas a male Iriomote cat's brain is about 30 grams. The occipital bone of the skull and the auditory capsule are not connected. The mandibular symphysis is short.

title: Glass Cat

text: Bungle first appears in "The Patchwork Girl of Oz", the seventh of Baum's fourteen Oz books. The magician Dr. Pipt tests his Powder of Life by animating an ornamental glass cat figurine, for the specific purpose of catching mice for his wife Margolotte. But the Glass Cat turns out to be exceptionally vain, and unwilling to do any work. Margolotte names it Bungle. The Glass Cat is transparent, except for her hard blood-red ruby heart, two large emeralds for eyes, and her bright pink brains, which look rather like a collection of marbles and can be seen working in the cat's head. She has a tail of spun-glass.

title: Brain size

text: Brain size tends to vary according to body size. The relationship is not proportional, however; the brain-to-body mass ratio varies. The largest ratio found is in the shrew. Averaging brain weight across all orders of mammals, it follows a power law, with an exponent of about 0.75. This power law formula applies to the "average" brain of mammals taken as a whole, but each family (cats, rodents, primates, etc.) departs from it to some degree, in a way that generally reflects the overall "sophistication" of behavior. Primates, for a given body size, have brains 5 to 10 times as large as the formula predicts. Predators tend to have relatively larger brains than the animals they prey on; placental mammals (the great majority) have relatively larger brains than marsupials such as the opossum.

title: Quantum mind

text: Another possible conceptual approach is to use quantum mechanics as an analogy to understand a different field of study like consciousness, without expecting that the laws of quantum physics will apply. An example of this approach is the idea of Schrödinger's cat. Erwin Schrödinger described how one could, in principle, create entanglement of a large-scale system by making it dependent on an elementary particle in a superposition. He proposed a scenario with a cat in a locked steel chamber, wherein the cat's life or death depended on the state of a radioactive atom, whether it had decayed and emitted radiation or not. According to Schrödinger, the Copenhagen interpretation implies that "the cat remains both alive and dead" until the state has been observed. Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; on the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics. However, since Schrödinger's time, other interpretations of the mathematics of quantum mechanics have been advanced by physicists, some of which regard the "alive and dead" cat superposition as quite real. Schrödinger's famous thought experiment poses the question, ""when" does a quantum system stop existing as a superposition of states and become one or the other?" In the same way, it is possible to ask whether the brain's act of making a decision is analogous to having a superposition of states of two decision outcomes, so that making a decision means "opening the box" to reduce the brain from a combination of states to one state. But even Schrödinger didn't think this really happened to the cat; he didn't think the cat was literally alive and dead at the same time. This analogy about making a decision uses a formalism that is derived from quantum mechanics, but it doesn't indicate the actual mechanism by which the decision is made. In this way, the idea is similar to quantum cognition. This field clearly distinguishes itself from the quantum mind as it is not reliant on the hypothesis that there is something micro-physical quantum mechanical about the brain. Quantum cognition is based on the quantum-like paradigm, generalized quantum paradigm, or quantum structure paradigm that information processing by complex systems such as the brain can be mathematically described in the framework of quantum information and quantum probability theory. This model uses quantum mechanics only as an analogy, but doesn't propose that quantum mechanics is the physical mechanism by which it operates. For example, quantum cognition proposes that some decisions can be analyzed as if there are interference between two alternatives, but it is not a physical quantum interference effect.

title: Short-beaked echidna

text: A well-developed olfactory system may be used to detect mates and prey. A highly sensitive optic nerve has been shown to have visual discrimination and spatial memory comparable to those of a rat. The brain and central nervous system have been extensively studied for evolutionary comparison with placental mammals, particularly with its fellow monotreme, the platypus. The average brain volume is 25 ml, similar to a cat of approximately the same size; while the platypus has a largely smooth brain, the echidna has a heavily folded and fissured, gyrencephalic brain similar to humans, which is seen as a sign of a highly neurologically advanced animal. The cerebral cortex is thinner, and the brain cells are larger and more densely packed and organised in the echidna than the platypus, suggesting evolutionary divergence must have occurred long ago. Almost half of the sensory area in the brain is devoted to the snout and tongue, and the part devoted to smell is relatively large compared to other animals.

title: Cat intelligence

text: There are a number of reasons for why the cat brain is a goal of computer simulations. Cats are familiar and easily kept animals, so the physiology of cats has been particularly well studied. The physical structures of human brains and cat brains are very similar.[14] Cats, like humans, have binocular vision that gives them depth perception.[97] Moreover, trying to build artificial mammal brains advances the research of both neuroscience and artificial intelligence.[98]

title: Holonomic brain theory

text: Karl Pribram had worked with psychologist Karl Lashley on Lashley's engram experiments, which used lesions to determine the exact location of specific memories in primate brains. Lashley made small lesions in the brains and found that these had little effect on memory. On the other hand, Pribram removed large areas of cortex, leading to multiple serious deficits in memory and cognitive function. Memories were not stored in a single neuron or exact location, but were spread over the entirety of a neural network. Lashley suggested that brain interference patterns could play a role in perception, but was unsure how such patterns might be generated in the brain or how they would lead to brain function.

title: Hanover, Brighton

text: Hanover is home to an unusually large cat population (including one, Pickle) and was featured in the BBC programme Cat Watch 2014: The 21st Century house cat a three-part series that looked at how cats are adapting to a domestic life by the side of people. This led rise to the very active community group Cats of Hanover.

title: Cat intelligence

text: In November 2009, scientists claimed to simulate a cat's brain using a supercomputer[91] containing 24,576 processors.[92][93] This experiment did not simulate the function of the individual neurons in the brain, nor their synaptic patterns. It was intended to demonstrate that the problem of simulating a biological brain could be scaled to very large supercomputer platforms.[94] However, the approach has been criticised as flawed.[95][96]

title: Miodrag Radulovacki

text: Radulovacki reasoned that if the blocking of adenosine receptors produces excitation, then perhaps stimulation of the same receptors could induce sleep. He knew that experiments by John Phillis and his group (Can. J. Physiol. Pharmacol. 57:1289-1312, 1979), which utilized an iontophoretic application of adenosine in the brain, had demonstrated adenosine's depressant effect on the responses of neurons in several brain regions and that the general neurophysiological effects of adenosine were shown to be inhibitory. In addition, the preliminary experiments in dogs by Haulica "et al." (J. Neurochem. 21:,1019–20, 1973) and the administration of adenosine into the brains of rats, cats and fowl suggested that adenosine was able to produce behavioral sleep. The explanation of adenosine's hypnotic effect was through its interaction with serotonin, widely believed to be a sleep inducing agent. However, since there was no suggestion how this adenosine-serotonin link was achieved, experiments highlighting the potential role of adenosine in sleep had largely been forgotten.

title: Large scale brain networks

text: Large scale brain networks are collections of widespread brain regions showing functional connectivity by statistical analysis of the fMRI BOLD signal or other signal fluctuations. An emerging paradigm in neuroscience is that cognitive tasks are performed not by individual brain regions working in isolation, but by networks consisting of several discrete brain regions that are said to be "functionally connected" due to tightly coupled activity. Functional connectivity may be measured as long-range synchronization of the EEG, MEG, or other dynamic brain signals. Synchronized brain regions may also be identified using spatial independent component analysis. The set of identified brain areas that are linked together in a large-scale network varies with cognitive function. When the cognitive state is not explicit (i.e., the subject is at "rest"), the large scale brain network is a resting state network (RSN). As a physical system with graph-like properties, a large scale brain network has both nodes and edges, and cannot be identified simply by the co-activation of brain areas. In recent decades, the analysis of brain networks was made feasible by advances in imaging techniques as well as new tools from graph theory and dynamical systems. Large scale brain networks are identified by their function, and provide a coherent framework for understanding cognition by offering a neural model of how different cognitive functions emerge when different sets of brain regions join together as self-organized coalitions. Disruptions in activity in various networks have been implicated in neuropsychiatric disorders such as depression, Alzheimer's, autism spectrum disorder, schizophrenia and bipolar disorder.

title: Roger Wolcott Sperry

text: Sperry first became interested in "split-brain" research when he was working on the topic of interocular transfer, which occurs when "one learns with one eye how to solve a problem then, with that eye covered and using the other eye, one already knows how to solve the problem". Sperry asked the question: "how can the learning with one eye appear with the use of the other?" Sperry cut nerves in the eyes of cats so the left eye was connected to the left hemisphere and the right eye was connected to the right hemisphere; he also cut the corpus callosum. The cats were then taught to distinguish a triangle from a square with the right eye covered. Then the cats were presented the same problem with the left eye covered; the cats had no idea what they had just learned with the right eye and because of this could be taught to distinguish a square from a triangle. Depending on which eye was covered, the cats would either distinguish a square from a triangle or a triangle from a square, demonstrating that the left and right hemispheres learned and remembered two different events. This led Sperry to believe that the left and right hemispheres function separately when not connected by the corpus callosum.

title: Sean Hill (scientist)

text: Hill has developed a number of large-scale brain models and simulations, including the first large-scale model of the visual thalamocortical system of the cat which accurately replicates multi-scale electrophysiological phenomena during wakefulness and sleep. He has also co-led the Blue Brain's efforts to create digital reconstructions of neocortical microcircuitry.

title: Neuroimaging

text: Computed tomography (CT) or "Computed Axial Tomography" (CAT) scanning uses a series of x-rays of the head taken from many different directions. Typically used for quickly viewing brain injuries, CT scanning uses a computer program that performs a numerical integral calculation (the inverse Radon transform) on the measured x-ray series to estimate how much of an x-ray beam is absorbed in a small volume of the brain. Typically the information is presented as cross-sections of the brain.

title: Spectral bat

text:
The brain is large relative to the body; at 1:67, its brain-to-body mass ratio is higher than that of cats and dogs.
The cerebral hemispheres of the brain are extensively convoluted.
The brain has well-developed olfactory bulbs and its cerebellum is the most ornamented and complex of any member of its subfamily.
McDaniel described its corpus callosum and white matter as "exceptionally thick."

title: Cat intelligence

text: Analyses of cat brains have shown they are divided into many areas with specialized tasks that are extremely interconnected and share sensory information in a kind of hub-and-spoke network, with a large number of specialized hubs and many alternative paths between them. This exchange of sensory information allows the brain to construct a complex perception of the real world and to react to and manipulate its environment.[24]

title: Saber-toothed cat

text: A disputing view of the cat's hunting technique and ability is presented by C. K. Brain in "The Hunters or the Hunted?" in which he attributes the cat's prey-killing abilities to its large neck muscles rather than its jaws. Large cats use both the upper and lower jaw to bite down and bring down the prey. The strong bite of the jaw is accredited to the strong temporalis muscle that attach from the skull to the coronoid process of the jaw. The larger the coronoid process, the larger the muscle that attaches there, so the stronger the bite. As C.K. Brain points out, the saber-toothed cats had a greatly reduced coronoid process and therefore a disadvantageously weak bite. The cat did, however, have an enlarged mastoid process, a muscle attachment at the base of the skull, which attaches to neck muscles. According to C.K. Brain, the saber-tooth would use a "downward thrust of the head, powered by the neck muscles" to drive the large upper canines into the prey. This technique was "more efficient than those of true cats".


query: What does it mean to be an evergreen tree?

title: Evergreen

text: In botany, an evergreen is a plant that has leaves throughout the year, always green. This is true even if the plant retains its foliage only in warm climates, and contrasts with deciduous plants, which completely lose their foliage during the winter or dry season. There are many different kinds of evergreen plants, both trees and shrubs. Evergreens include:

title: Cinnadenia

text: The ecological requirements of the genus are those of fog moisture precipitating almost continuously in a natural habitat, cloud-covered for much of the year. These species are found in tropical forests, subtropical temperate evergreen, or montane evergreen forests, which are a type of rainforest or cloud forest. The ecosystem is characterized by high humidity, no seasonal changes, and a wide variety of botanical and zoological species, but also highly fragile against external aggressions. The temperate evergreen and evergreen forests are typically multispecies with evergreen and hardwood trees, reaching up to 40 m in height. The forests are made up of laurel-leaved evergreen hardwood trees, harbouring a rich biota of understorey plants, invertebrates, birds, and mammals. It is present in tropical and subtropical montane rainforest, laurel forest, in the weed-tree forests in valleys, mixed forests of coniferous and deciduous broad-leaved trees, "Tsuga" forests; from northern Vietnam to the Himalayas.

title: Tamarix

text: Eight species are found in North America. They can be divided into two subgroups:"Tamarix aphylla" (Athel tree), a large evergreen tree, does not sexually reproduce in the local climate and is not considered a seriously invasive species. The Athel tree is commonly used for windbreaks on the edge of agricultural fields and as a shade tree in the deserts of the Southwestern United States.The second subgroup contains the deciduous tamarisks, which are small, shrubby trees, commonly known as "saltcedars". These include "Tamarix pentandra", "Tamarix tetranda", "Tamarix gallica", "Tamarix chinensis", "Tamarix ramosissima", and "Tamarix parvifolia".

title: Evergreen forest

text: An evergreen forest is a forest made up of evergreen trees. They occur across a wide range of climatic zones, and include trees such as conifers, live oak, and holly in cold climates, eucalypts, acacias and banksias in more temperate zones, and rainforest trees in tropical zones.

title: Calodendrum

text: Calodendrum is a genus of medium-sized evergreen trees comprising two species from Africa. "Calodendrum capense" (Cape Chestnut) is a well known tree that is widely cultivated, while "Calodendrum eickii" is a rare forest tree from Tanzania. The botanical name comes from Greek, "kalos" means beautiful and "dendrum" means tree. Both species are harvested for their timber in Africa.

title: Propagation of Christmas trees

text: There are many different species of evergreen trees that are used for Christmas trees. The most common of these species are classified in one of four genera: pines (genus Pinus), spruces (genus Picea), firs (genus Abies), and cypress (genus Cupressa). In addition to these, the Douglas fir (Pseudotsuga Menziesii) is also commonly used as a Christmas tree, but it is not a true fir. The varieties of trees that a nursery chooses to propagate is dependent upon what type of farm is buying the reproduced plant, the climate of the nursery, the climate of the tree farm where the trees are to be grown, and the preferences of the retail customers.

text: The Southeastern Indochina dry evergreen forests are one of three dry broadleaf forest ecoregions with predominantly evergreen trees; trees in dry broadleaf forests typically lose their leaves during the dry season.

title: Kent Bach

text: In his paper, "Content Ex Machina" Bach argues against over-interpreting what he labels the "contextualist platitude" which he defines as: “Generally what a speaker means in uttering a sentence, even if the sentence is devoid of ambiguity, vagueness, or indexicality, goes beyond what the sentence means.” Bach asserts that context does not establish meaning but is merely one of several conversational principles. He states that “context does not determine (in the sense of constitute), but merely enables the hearer to determine (in the sense of ascertain) what the speaker means.” Context provides constraints on what a speaker can reasonably mean and on what a hearer can reasonably interpret a speaker to mean. “contextualist platitude” does not preclude the “older picture of language and communication” and “a fairly standard semantic-pragmatic distinction.” Pragmatic considerations and context do not contribute to the content of what is said. Bach admits that there is meaning in utterances beyond the semantic content of a sentence, but he maintains that context does not determine speaker meaning but rather constrains how a speaker can expect to be understood and helps the hearer understand what is said. “We need the level of locutionary act and, correlatively, a strict, semantic notion of what is said in order to account for (the content of) what a speaker does in uttering a sentence independently of whatever communicative intention (if any) he has in uttering it and regardless of how the content of that intention may depart from the semantic content of the sentence.”

title: Evergreen forest

text: Tropical evergreen forests (or "tropical rainforests") are usually found in areas receiving more than 234 cm of rainfall and having a monthly mean temperature of 20 °C or higher in the coldest months. They occupy about seven percent of the Earth's surface and harbour more than half of the planet's terrestrial plants and animals. Tropical evergreen forests are dense, multi-layered, and harbour many types of plants and animals. These forests are found in the areas receiving heavy rainfall (more than 200  cm annual rainfall). They are very dense. Even the sunlight does not reach the ground. Numerous species of trees are found in these forests. Different types of trees shed their leaves at different times of the year. Therefore, these forests always appear green and are known as evergreen forests. These forests are found in the Andaman and Nicobar Islands, along with the slopes of the Western Ghats and parts of Northeastern states of Assam, West Bengal and Odisha. These areas experience hot and humid climate with the short dry season. The important trees of these forests are rosewood, ebony and mahogany

title: Evergreen (journalism)

text: Within the context of journalism and broadcasting, evergreen content is content that is not time-sensitive. Evergreen content does not rely on current events; thus, an evergreen story can be prepared, then mothballed until it is needed to fill time on a slower news day or on a holiday when fewer journalists are on duty. The term is derived from the evergreen trees.

title: Chocolate

text: Chocolate is made from cocoa beans, the dried and fermented seeds of the cacao tree ("Theobroma cacao"), a small, 4–8 m tall (15–26 ft tall) evergreen tree native to the deep tropical region of the Americas. Recent genetic studies suggest the most common genotype of the plant originated in the Amazon basin and was gradually transported by humans throughout South and Central America. Early forms of another genotype have also been found in what is now Venezuela. The scientific name, "Theobroma", means "food of the gods". The fruit, called a cacao pod, is ovoid, long and wide, ripening yellow to orange, and weighing about when ripe.

title: Narcondam Island

text: Narcondam Island is almost entirely covered with Evergreen and Moist Deciduous forest. Grassy slopes dominate the southern and southeast aspects of the hill (BirdLife International 2001). The island is covered with Tropical Evergreen forest, Semievergreen forest, Moist Deciduous forest, Littoral forest and Mangrove forest (Pande et al. 1991). The island bears old, dead and decaying trees, interlaced with thorny creepers and luxuriantly flowering tall trees (Yahya and Zarri 2002a). The flora on the higher reaches of the hill is mostly evergreen and consists of Dipterocarpus, Sideroxylon and Ficus trees. However, some deciduous species (Bombax insigne) are also present. The vegetation towards the summit is mostly Moist Evergreen with several epiphytes. The lower hills following the shoreline have both deciduous and evergreen trees such as Terminalia catappa, T. bialata and Caryota mitis. The shoreline has some introduced species such as coconut and banana.

title: Marcel Danesi

text: His works typically offer readers an approachable invitation to the use of semiotics to help explain everyday phenomena. For instance, his book "Quest for Meaning: A Guide to Semiotic Theory and Practice" provides readers with a simple three-fold way of considering semiotic inquiry as trying to answer "What does it Mean? How does it convey meaning? And Why does it mean what it means?"

title: Trees in mythology

text: Trees are significant in many of the world's mythologies and religions, and have been given deep and sacred meanings throughout the ages. Human beings, observing the growth and death of trees, and the annual death and revival of their foliage, have often seen them as powerful symbols of growth, death and rebirth. Evergreen trees, which largely stay green throughout these cycles, are sometimes considered symbols of the eternal, immortality or fertility. The image of the Tree of life or world tree occurs in many mythologies.

title: Evergreen tree

text: Evergreen tree may refer to:

title: Beijing

text: The city flowers are the Chinese rose and chrysanthemum. The city trees are the Chinese arborvitae, an evergreen in the cypress family and the Pagoda Tree, also called the Chinese scholar tree, a deciduous tree of the "Fabaceae" family. The oldest scholar tree in the city was planted in what is now Beihai Park during the Tang dynasty, 1,300 years ago.

title: Adam Cost

text:
When asked in 1993 by a "The New York Times" Style reporter what it all meant, Cost said, "If you could give us [Cost and Revs] the meaning of life, I’d give you the meaning of us." At that time the posters included a phone number; those who called heard a woman's recorded voice repeat their questions back to them: "My intuition tells me that you're asking yourselves who are Revs and Cost and what are they doing? What is it? What does it mean? What does it mean? What does it mean?"
Cost and Revs continued to write in New York City with impunity, highly visible examples of the graffiti that Mayor Rudolph Giuliani was determined to eradicate. One letter writer called Cost "probably the worst graffiti vandal in the history of New York."

title: Miracle on Evergreen Terrace

text: When the family comes downstairs to find the tree and presents gone, Bart makes up a story about how he caught a burglar making off with their tree and presents. The police investigate and Kent Brockman does a human interest story on the case.

title: Annabel Port

text:
"Chorus"
Oh what does it mean when the pubs are all packed at five-thirty?
Oh what does it mean when we're all having fish for our tea?
Oh what does it mean when Top of the Pops is on the telly?
Oh yes, the weekend's nearly here;
So sing along with meeee-ee hee hee...

title: Binary search tree

text: A degenerate tree is a tree where for each parent node, there is only one associated child node. It is unbalanced and, in the worst case, performance degrades to that of a linked list. If your add node function does not handle re-balancing, then you can easily construct a degenerate tree by feeding it with data that is already sorted. What this means is that in a performance measurement, the tree will essentially behave like a linked list data structure.

title: Hymenaea

text: Most species of "Hymenaea" are large trees and they are primarily evergreen. They may grow to a height of and emerge above the forest canopy. Some species will grow both as tall forest trees and as smaller shrubby trees depending on their surrounding habitat. The leaves are pinnately bifoliolate, meaning that they have two leaflets attached to the sides of the petiole. The flowers grow in a panicle or corymb type of inflorescence.

title: Ravensara

text:
The genus includes species of evergreen trees, endemic to Madagascar and Comoro Islands. Ravensara species are broad-leaved evergreens, the genus including not only shrubs, but also large trees reaching heights in excess of 30 m at maturity.
They are found commonly both as canopy trees to 30m (sometimes very large to 60 m) and sub-canopy trees in the succession climax species in tropical, lower temperate or subtropical broad-leaved forest. Habitats include evergreen broadleaved forest, mixed coniferous-broadleaved forest, low-elevation evergreen forest and littoral rainforest and feature soils of all types.

title: Evergreen

text: Deciduous trees shed their leaves, usually as an adaptation to a cold or dry/wet season. Evergreen trees do lose leaves, but each tree loses its leaves gradually and not all at once. Most tropical rainforest plants are considered to be evergreens, replacing their leaves gradually throughout the year as the leaves age and fall, whereas species growing in seasonally arid climates may be either evergreen or deciduous. Most warm temperate climate plants are also evergreen. In cool temperate climates, fewer plants are evergreen, with a predominance of conifers, as few evergreen broadleaf plants can tolerate severe cold below about −26°C (−15°F).

text: The Sri Lanka dry-zone dry evergreen forests are made up mostly of evergreen trees, which distinguish them from the deciduous trees that characterize most other tropical dry broadleaf forest ecoregions. The dry-zone dry evergreen forests most closely resemble the East Deccan dry evergreen forests of India's southeast coast.

title: Tropical and subtropical dry broadleaf forests

text: Deciduous trees predominate in most of these forests, and during the drought a leafless period occurs, which varies with species type. Because trees lose moisture through their leaves, the shedding of leaves allows trees such as teak and mountain ebony to conserve water during dry periods. The newly bare trees open up the canopy layer, enabling sunlight to reach ground level and facilitate the growth of thick underbrush. Trees on moister sites and those with access to ground water tend to be evergreen. Infertile sites also tend to support evergreen trees. Three tropical dry broadleaf forest ecoregions, the East Deccan dry evergreen forests, the Sri Lanka dry-zone dry evergreen forests, and the Southeastern Indochina dry evergreen forests, are characterized by evergreen trees.

title: Charter for Trees, Woods and People

text: Creating the Tree Charter: To create this Tree Charter, thousands of tree ‘stories’ were collected from people across the UK about what trees and woods mean to them. A tree story is any expression of what trees and woods mean to people. They can be a sentence or longer phrase, a photo, audio clip or video. The tree stories were collected until the end of February 2017.

title: Allium fistulosum

text: The species is very similar in taste and odor to the related common onion, "Allium cepa", and hybrids between the two (tree onions) exist. "A. fistulosum", however, does not develop bulbs, and possesses hollow leaves ("fistulosum" means "hollow") and scapes. Larger varieties of the "A. fistulosum" resemble the leek, such as the Japanese "negi", whilst smaller varieties resemble chives. "A. fistulosum" can multiply by forming perennial evergreen clumps. It is also grown in a bunch as an ornamental plant.

title: Sierra Juárez, Oaxaca

text:
The Sierra Juárez is one of Oaxaca State's wettest areas and richest in forest diversity, with perhaps 2,000 of the 8,000 or more plant species that are found in the state.
It is mostly covered by montane cloud forest, but includes tropical evergreen forests and forests of pine, pine-oak and oak. The cloud forest forms a band from in height, up to along the northern and eastern slopes. The climate is cool, 14°-20° C (57°-68° F), and has mean annual rainfall that exceeds and is sometimes much higher. The dominant trees are tall and include evergreen and deciduous species, palms, tree ferns, heather shrubs, vines, and moisture-loving herbs.
The tropical evergreen forest is dominated by evergreen trees tall, with abundant lianas and tropical epiphytes. Pine and pine-oak forests, at a height from have evergreen trees tall, with grasses dominating the lower stratum. Oak forests at a height from grow in areas with relatively lower rainfall that have a dry season in summer. The oak forests are found in the western, inland part of the sierra to the Rio Grande Basin.

title: ATA Martial Arts

text: Songahm Taekwondo is the style of martial arts practiced at ATA affiliated schools. Songahm means "Pine Tree and Rock." According to the organization, the term Songahm itself represents "Evergreen strength the year round, long life and a symbol of unchanging human loyalty" as represented by the pine tree and the rock. Soon Ho Lee gave the name, Songahm, and its meaning to his brother, Haeng Ung Lee years before H.U. Lee founded the ATA. In the ATA, the student is compared to a growing pine tree, from a seed (white belt) to a massive tree (black belt).

title: Rapanea melanophloeos

text:
"Rapanea melanophloeos" is a dense, graceful, evergreen tree. Its leaves, stalks and berries often have a purple or maroon color. This tree is usually dioecious (male and female flowers on different trees) and birds are attracted by its tiny, dark purple berries.
The specific name 'melanophloeos' means 'black bark' and resulted from a mistaken identification of the source tree as Swartbas ("Diospyros whyteana").

title: Hedera pastuchovii

text: It is an evergreen woody vine with long climbing stems, growing in mixed forests to 20–30 m high where suitable trees, are available, does not grow well as a groundcover plant. It climbs by means of aerial rootlets which cling to the substrate.


query: When did Degas sculpt his "Little Dancer"?

title: Little Dancer of Fourteen Years

text: The Little Fourteen-Year-Old Dancer (French: La Petite Danseuse de Quatorze Ans) is a sculpture begun c. 1880 by Edgar Degas of a young student of the Paris Opera Ballet dance school, a Belgian named Marie van Goethem.

title: Marie van Goethem

text: With Boyd Gaines as Degas, and Rebecca Luker and New York City Ballet principal dancer Tiler Peck as adult and young Marie, the Kennedy Center for the Performing Arts premiered the Susan Stroman, Lynn Ahrens, and Stephen Flaherty stage musical, "Little Dancer", from October 25 to November 30 2014.

title: Stephen Flaherty

text: Flaherty and Ahrens’ next musical, "Little Dancer", featured direction and choreography by Susan Stroman. Inspired by the famous sculpture, "Little Dancer, Aged 14" by Edgar Degas, the musical had a reading in 2010 at Lincoln Center Theater and a developmental lab production in June 2010. The show premiered at the Kennedy Center’s Eisenhower Theater in October 2014. The cast included Rebecca Luker, Boyd Gaines and Tiler Peck. The musical is inspired by true events,[and] focuses on the relationship between a young ballerina and 19th century French painter and sculptor Edgar Degas. Much of the action is set in the Paris Opera Ballet. A re-working of the show, now titled “Marie” (after the name of the young ballerina), will have its west coast premiere at Seattle’s 5th Avenue Theatre in March 2019.

title: Little Girl in a Blue Armchair

text: By 1877 Cassatt had come into frank conflict with the official French art establishment and had had both her submissions for that year rejected by the Salon. So when Edgar Degas invited her to join the Impressionists the same year, a group similarly disaffected by the "Salon" system, she accepted with alacrity. A planned 1878 exhibition did not take place, because of what Degas judged would be competition from the World's Fair held in Paris that year, but she did hold what amounted to a show of her own at the Spring 1879 Impressionist exhibition, exhibiting a dozen oils and pastels. Exactly which works these all were is not now known with certainty, but it is likely that "Little Girl in a Blue Armchair" was amongst them.

title: Little Dancer of Fourteen Years

text: The sculpture is one-third life size and was originally sculpted in wax, a somewhat unusual choice of medium for the time. It is dressed in a real bodice, tutu and ballet slippers and has a wig of real hair. All but a hair ribbon and the tutu are covered in wax. The 28 bronze repetitions that appear in museums and galleries around the world today were cast after Degas' death. The tutus worn by the bronzes vary from museum to museum.

title: Little Dancer of Fourteen Years

text: Realistic wax figures with real hair and real clothes had also been popular in religious, Folk, and fine arts for centuries before Degas created his Little Dancer.[1][2]

title: Kinetic art

text: Auguste Rodin at first was very impressed by Monet's 'vibrating works' and Degas' unique understanding of spatial relationships. As an artist and an author of art reviews, Rodin published multiple works supporting this style. He claimed that Monet and Degas' work created the illusion "that art captures life through good modeling and movement". In 1881, when Rodin first sculpted and produced his own works of art, he rejected his earlier notions. Sculpting put Rodin into a predicament that he felt no philosopher nor anyone could ever solve; how can artists impart movement and dramatic motions from works so solid as sculptures? After this conundrum occurred to him, he published new articles that didn't attack men such as Manet, Monet, and Degas intentionally, but propagated his own theories that Impressionism is not about communicating movement but presenting it in static form.

title: Little Dancer of Fourteen Years

text: The original wax sculpture was acquired by Paul Mellon in 1956. Beginning in 1985, Mr and Mrs Mellon gave the National Gallery of Art 49 Degas waxes, 10 bronzes and 2 plasters, the largest group of original Degas sculptures. Little Dancer was among the bequests. In 1997, the Airaindor-Valsuani foundry in France began casting a limited edition of Degas bronzes from the pre-1903 Little Dancer plaster. One such Little Dancer bronze is owned by the M.T. Abraham Foundation, which, at times, is lent to other institutions and museums including the State Hermitage Museum in Saint Petersburg, Russia.[15] Like the various states of many of Degas' prints, the Valsuani bronzes record the first version of Degas' Little Dancer, while the Hébrard casts record the second and final state of the sculpture.

title: Rodney Pople

text: Pople won the Glover Prize for landscape painting in March 2012 with a work that included the figure of Martin Bryant, the convicted perpetrator of the Port Arthur Massacre in the foreground of the landscape of Port Arthur. Later in that year, a work entitled "Degas's Night" which included Degas' sculpture "Little Dancer of Fourteen Years" on the background of red-light district in Darlinghurst, New South Wales was also the cause of controversy.

title: Suzanne Manet

text: Édouard Manet and Edgar Degas met by chance at the Louvre in 1862, and after an intense conversation and Manet's demonstration on the art of etching, they became lifelong friends. Sometime in 1868 Degas painted a portrait of Manet and his wife. Manet is reclining on a couch and Suzanne appears to be seated at a piano. The mystery that surrounds the portrait by Degas is the fact that the painting has been slashed from top to bottom and right through the likeness of Suzanne. The supposition is that Manet, for an unknown reason, cut the painting. Manet might have slashed the painting because he did not like the way Suzanne was painted, or because he was feuding at the time with Degas, or he might have been angry with his wife. When Degas saw what had been done to his painting he demanded its return, and he took it back. Degas intended to re-paint the likeness of Suzanne at the piano and he reiterated his intention to Ambroise Vollard in conversation with him around the turn of the century. Degas never got around to fixing the painting and it remains in its slashed state in the Kitakyushu Municipal Museum of Art in Japan.

title: Little Dancer of Fourteen Years

text: Art historian Richard Kendall published a scholarly account of the history of Degas's sculpture, Degas and the Little Dancer, with contributions by Douglas Druick and Arthur Beale.[16] The BBC Two documentary The Private Life of a Masterpiece: Little Dancer Aged Fourteen, produced in 2004, closely examines the sculpture, the model, the circumstances of her life, and the critical reaction to the work. Cathy Marie Buchanan's novel, The Painted Girls, presents a fictionalised account of the life of Marie van Goethem, the model for the sculpture,[17] as does Carolyn Meyer's young adult novel Marie, Dancing[18] and Laurence Anholt's children's picture book Degas and the Little Dancer.[19] In 2014, the Kennedy Center for the Performing Arts in Washington, D.C. premiered the stage musical, Little Dancer, inspired by the story of the young ballerina immortalized by Edgar Degas in his famous sculpture. On September 12, 2016, Dr. Gregory Hedberg presented a paper entitled "Unraveling the Mysteries of Degas’ Little Dancer, Aged Fourteen," at the French Institute, Alliance Français, in New York City.[20]

title: Little Dancer of Fourteen Years

text: After Degas' death, his heirs (brother and sister's children[5]) made the decision to have the bronze repetitions of La Petite Danseuse and other wax and mixed-media sculptures cast. The casting took place at the Hébrard foundry in Paris from 1920 until 1936 when the Hébrard foundry went bankrupt and closed.[6] Thereafter, "Hébrard" Degas Little Dancer bronzes were cast at the Valsuani foundry in Paris until the mid-1970s.[7] Sixty-nine of Degas' wax sculptures survived the casting process. One copy of La Petite Danseuse is currently owned by the creator and owner of Auto Trader, John Madejski. He stated that he bought the sculpture by accident. That copy was sold for £13,257,250 ($19,077,250) at Sotheby's on February, 3rd 2009.[8] Another Hébrard Little Dancer bronze failed to sell at a November 2011 auction at Christie's.[9]

title: Waiting (Degas)

text:
The background is formed from a wide variety of oranges, browns and blacks, while the younger woman is portrayed in pink, blue, and creamy tones which highlight her softness compared to the severity of the older woman. The work is executed with an innovative mixture of subtle (the woman's feet), slashed (the bench) and hatched (the younger woman's dress) strokes.
Degas was taken by the peripheral world of the dancers, the rehearsals and backstage moments, a world to which he did not have access to until 1885; he only became interested in the ballet in 1870, and backstage was strictly limited to long term patrons. His removal from the moment reflected in the image is highlighted by the unusually steep perspective; the viewer seems to be positioned far above the two women; looking down as if seated in a box above the auditorium.
Degas was aware from an early point in his studies of the exhaustion of the girls, and the extent to which they pushed the limits of their bodies for fleeting moments of elegance. He was further conscious of the brevity of a ballerina's career, and the positioning of the older chaperone–more than likely an ex-dancer herself–in this work adds to its poignancy; the younger woman representing what her forlorn looking companion once was. Degas, mindful of this, presents an interesting irony - while the young woman waits to make her entrance the older woman waits for her to leave. The tip of the chaperone's umbrella points in the direction the dancer must take; towards the stage and away from her guardian.

title: Edgar Degas

text:
Degas's style reflects his deep respect for the old masters (he was an enthusiastic copyist well into middle age) and his great admiration for Jean-Auguste-Dominique Ingres and Eugène Delacroix. He was also a collector of Japanese prints, whose compositional principles influenced his work, as did the vigorous realism of popular illustrators such as Daumier and Gavarni. Although famous for horses and dancers, Degas began with conventional historical paintings such as "The Daughter of Jephthah" (c.1859–61) and "The Young Spartans" (c.1860–62), in which his gradual progress toward a less idealized treatment of the figure is already apparent. During his early career, Degas also painted portraits of individuals and groups; an example of the latter is "The Bellelli Family" (c.1858–67), a brilliantly composed and psychologically poignant portrayal of his aunt, her husband, and their children. In this painting, as in "The Young Spartans" and many later works, Degas was drawn to the tensions present between men and women. In his early paintings, Degas already evidenced the mature style that he would later develop more fully by cropping subjects awkwardly and by choosing unusual viewpoints.
By the late 1860s Degas had shifted from his initial forays into history painting to an original observation of contemporary life. Racecourse scenes provided an opportunity to depict horses and their riders in a modern context. He began to paint women at work, milliners and laundresses. "Mlle. Fiocre in the Ballet La Source", exhibited in the Salon of 1868, was his first major work to introduce a subject with which he would become especially identified, dancers.

title: Edgar Degas

text: Degas's paintings, pastels, drawings, and sculptures are on prominent display in many museums, and have been the subject of many museum exhibitions and retrospectives. Recent exhibitions include "Degas: Drawings and Sketchbooks" (The Morgan Library, 2010); "Picasso Looks at Degas" (Museu Picasso de Barcelona, 2010); "Degas and the Nude" (Museum of Fine Arts, Boston, 2011); "Degas' Method" (Ny Carlsberg Glyptotek, 2013); "Degas's Little Dancer" (National Gallery of Art, Washington D.C., 2014) and "Degas: A passion for perfection" (Fitzwilliam Museum, Cambridge, 2017-2018).

title: Rupert Degas

text: Degas was born in London, to film and TV screenwriter Brian Degas and radio and television presenter Maggie Clews, and lived in Little Venice. He was educated at Hill House School in Knightsbridge before spending several years "between parents" in Barcelona, Menorca and New York City. Moving back to London at the age of 12, Degas attended Emanuel School in Wandsworth, where, under the direction of Jeremy Edwards, he appeared in "Twelfth Night" (with a 15 year old Naveen Andrews), "Death of a Salesman", and "Arsenic and Old Lace". Degas also attended Junior Guildhall at the Barbican for several years under the tutelage of Charles Wegner. Degas credits both Edwards and Wegner with "planting theatre into me, and knocking the ego out of me" and was thrilled when years later they came to see his West End debut in "Stones in His Pockets".

title: Edgar Degas

text: Edgar Degas ( or ; born Hilaire-Germain-Edgar De Gas, ; 19 July 1834 – 27 September 1917) was a French artist famous for his paintings, sculptures, prints, and drawings. He is especially identified with the subject of dance; more than half of his works depict dancers. Regarded as one of the founders of Impressionism, he rejected the term, preferring to be called a realist. He was a superb draftsman, and particularly masterly in depicting movement, as can be seen in his rendition of dancers, racecourse subjects and female nudes. His portraits are notable for their psychological complexity and for their portrayal of human isolation.

title: Dharmesh Yelande

text: His inspiration for dance is Remo D’souza, according to his remarks in the DID audition, he says, "Remo Sir is also a mindblowing dancer. Whenever I meet him, it's only dance that we discuss. He's a person with such wonderful dance techniques that one is left simply wondering ‘Ki kya idea hai bhai, yeh step to dhoom macha dega". He himself is a big inspiration to many budding dancers.

title: Edgar Degas

text: Degas's only showing of sculpture during his life took place in 1881 when he exhibited "The Little Dancer of Fourteen Years". A nearly life-size wax figure with real hair and dressed in a cloth tutu, it provoked a strong reaction from critics, most of whom found its realism extraordinary but denounced the dancer as ugly. In a review, J.-K. Huysmans wrote: "The terrible reality of this statuette evidently produces uneasiness in the spectators; all their notions about sculpture, about those cold inanimate whitenesses ... are here overturned. The fact is that with his first attempt Monsieur Degas has revolutionized the traditions of sculpture as he has long since shaken the conventions of painting."

title: Little Dancer of Fourteen Years

text: To construct the statue, Degas used pigmented beeswax, with a metal armature, rope, and paintbrushes covered by clay for structural support.[10]

title: Edgar Degas

text: After Degas's death, his heirs found in his studio 150 wax sculptures, many in disrepair. They consulted foundry owner Adrien Hébrard, who concluded that 74 of the waxes could be cast in bronze. It is assumed that, except for the "Little Dancer Aged Fourteen", all Degas bronzes worldwide are cast from "" (i.e., cast from bronze masters). A "surmoulage" bronze is a bit smaller, and shows less surface detail, than its original bronze mold. The Hébrard Foundry cast the bronzes from 1919 until 1936, and closed down in 1937, shortly before Hébrard's death.

title: Little Dancer of Fourteen Years

text: The Little Dancer wax sculpture we see today is a reworked version of the original sculpture that was shown in 1881. After seeing the wax sculpture in Degas’ living quarters in April 1903, the New York collector Louisine Havemeyer expressed interest in buying the wax. After proposing a bronze or cast wax of the sculpture, which Mrs. Havemeyer refused, Degas took his wax figure upstairs to his working studio and told Vollard he was reworking the sculpture for Havemeyer for 40,000 francs.[11] Degas never sold the sculpture to Mrs. Havemeyer. After Degas died, it was found in a corner of his studio. Paul Lefond, Degas’ biographer, described the Little Dancer wax after Degas’ death as "nothing but a ruin;"[12] and Mary Cassatt telegraphed Mrs. Havemeyer "Statue Bad Condition."[13] However, the wax sculpture we know today is not a ruin. It is Degas' reworked second version of his wax figure. At some point before Degas extensively reworked his sculpture, he allowed a plaster to be cast from the wax figure. This recently re-discovered plaster records the Little Dancer</i>’s original pose, bodice, and hairdo. The plaster is now in a private collection in the United States.[14]

title: Impressionism

text: Edgar Degas was both an avid photographer and a collector of Japanese prints. His "The Dance Class" "(La classe de danse)" of 1874 shows both influences in its asymmetrical composition. The dancers are seemingly caught off guard in various awkward poses, leaving an expanse of empty floor space in the lower right quadrant. He also captured his dancers in sculpture, such as the "Little Dancer of Fourteen Years".

title: Edgar Degas

text: Degas's work was controversial, but was generally admired for its draftsmanship. His "La Petite Danseuse de Quatorze Ans", or "Little Dancer of Fourteen Years", which he displayed at the sixth Impressionist exhibition in 1881, was probably his most controversial piece; some critics decried what they thought its "appalling ugliness" while others saw in it a "blossoming". In part Degas' originality consisted in disregarding the smooth, full surfaces and contours of classical sculpture ... [and] in garnishing his little statue with real hair and clothing made to scale like the accoutrements for a doll. These relatively "real" additions heightened the illusion, but they also posed searching questions, such as what can be referred to as "real" when art is concerned. The suite of pastels depicting nudes that Degas exhibited in the eighth Impressionist Exhibition in 1886 produced "the most concentrated body of critical writing on the artist during his lifetime ... The overall reaction was positive and laudatory".

title: M.T. Abraham Foundation

text: The foundation owns a complete collection of 74 bronze sculptures by the French Impressionist Edgar Degas, including a casting of "The Little Dancer Aged Fourteen." According to a number of experts, Degas, after meeting with criticism for his first sculpture "Little Dancer," had privately accumulated plasters for sculptures that were not found until after his death. They feature dancers, horses, bathers, etc. Apart from the M.T. Abraham Foundation, as of 2010 only four museums worldwide have near-complete collections.

title: Les Choristes

text: Appreciation for the work, as part of those Degas showed in 1877, did not diminish with the passage of time. In 1897, when the work was put on exhibit at the Musée du Luxembourg, Léonce Bénédite called "Les Choristes" part of a group of "acute, ironic and cruel observations ... the work of a firm, sure hand [and] just, sensible eye." He called them "little masterpieces" that a public not generally aware of Degas's genius had done well to acquire.

title: Edgar Degas

text: Degas created a substantial number of other sculptures during a span of four decades, but they remained unseen by the public until a posthumous exhibition in 1918. Neither "The Little Dancer of Fourteen Years" nor any of Degas's other sculptures were cast in bronze during the artist's lifetime. Degas scholars have agreed that the sculptures were not created as aids to painting, although the artist habitually explored ways of linking graphic art and oil painting, drawing and pastel, sculpture and photography. Degas assigned the same significance to sculpture as to drawing: "Drawing is a way of thinking, modelling another".

title: Edgar Degas

text: In the late 1880s, Degas also developed a passion for photography. He photographed many of his friends, often by lamplight, as in his double portrait of Renoir and Mallarmé. Other photographs, depicting dancers and nudes, were used for reference in some of Degas's drawings and paintings.

title: Marie van Goethem

text: Between 1878 and 1881, Degas drew, painted and sculpted Marie in artworks including "Dancer with Fan", "Dancing Lesson", "Dancer Resting", numerous preparatory sketches, and most famously in "Little Dancer of Fourteen Years". He frequently attended ballet performances at the Paris Opera and often observed classes at the dance school. By posing for Degas, Marie likely earned five to six francs per four-hour sitting.

title: Marie van Goethem

text: Marie Geneviève van Goethem (or Goetham or Goeuthen; born 7 June 1865) was a French ballet student and dancer with the Paris Opera Ballet, and the model for Edgar Degas's statue "Little Dancer of Fourteen Years" ("La Petite Danseuse de Quatorze Ans").


query: What is the average menstruation cycle length?

title: Menstrual cycle

text: The first period usually begins between twelve and fifteen years of age, a point in time known as menarche.[5] They may occasionally start as early as eight, and this onset may still be normal.[6] The average age of the first period is generally later in the developing world and earlier in developed world. The typical length of time between the first day of one period and the first day of the next is 21 to 45 days in young women and 21 to 35 days in adults (an average of 28 days[6][7][8]). Menstruation stops occurring after menopause which usually occurs between 45 and 55 years of age.[9] Bleeding usually lasts around 2 to 7 days.[6]

title: Anovulation

text: Anovulation is usually associated with specific symptoms. However, it is important to note that they are not necessarily all displayed simultaneously. Amenorrhea (absence of menstruation) occurs in about 20% of women with ovulatory dysfunction. Infrequent and light menstruation occurs in about 40% of women with ovulatory dysfunction. Another potential symptom is irregular menstruation, where five or more menstrual cycles a year are five or more days shorter or longer than the length of the average cycle. Absence of mastodynia (breast pain or tenderness) occurs in about 20% of women with ovulatory problems. Also possible is increased body mass and facial hair, which is relatively easy to treat, and is often associated with PCOS, or polycystic ovary syndrome.

title: Menstruation

text: Menstruation is the most visible phase of the menstrual cycle and its beginning is used as the marker between cycles. The first day of menstrual bleeding is the date used for the last menstrual period (LMP). The typical length of time between the first day of one period and the first day of the next is 21 to 45 days in young women, and 21 to 31 days in adults (an average of 28 days).[2][3]

title: Flo (app)

text: Flo was initially created as a convenient period tracking application, but later, it developed into an artificial intelligence powered women’s health product. The application covers all phases of a reproductive cycle, including the start of menstruation (teens), cycle tracking, preparation for conception (for women with or without fertility problems), pregnancy, early motherhood, menopause. It is the first menstruation tracking application to use artificial intelligence for accurate cycle predictions.

title: Irregular menstruation

text: Irregular menstruation is a menstrual disorder whose manifestations include irregular cycle lengths as well as metrorrhagia (vaginal bleeding between expected periods).

title: Menstrual Hygiene Day

text: May 28 has symbolic meaning. May is the 5th month of the year and women menstruate an average of 5 days every month. Also, the menstrual cycle averages 28 days.

title: Menstrual cycle

text: Eumenorrhea denotes normal, regular menstruation that lasts for a few days (usually 3 to 5 days, but anywhere from 2 to 7 days is considered normal).[89][96] The average blood loss during menstruation is 35 milliliters with 10–80 ml considered normal.[97] Women who experience Menorrhagia are more susceptible to iron deficiency than the average person.[98] An enzyme called plasmin inhibits clotting in the menstrual fluid.[99]

title: Anovulatory cycle

text:
While the normal menstrual cycle in the human typically lasts 4 weeks (28 days, range 24–35 days) and consists of a follicular phase, ovulation, and a luteal phase, followed by either menstruation or pregnancy, the anovulatory cycle has cycle
lengths of varying degrees. In many circumstances, menstrual intervals are prolonged exceeding 35 days leading to oligomenorrhea (cycle >35 – 180 days interval), or even longer, amenorrhea. In other cases, menstruation may be fairly regular (eumenorrhea), or more frequent (intervals < 21 days), or there may be a loss of menstrual pattern (menorrhagia, dysfunctional uterine bleeding).

title: Erdős–Gyárfás conjecture

text: Weaker results relating the degree of a graph to unavoidable sets of cycle lengths are known: there is a set "S" of lengths, with |"S"| = O("n"), such that every graph with average degree ten or more contains a cycle with its length in "S" , and every graph whose average degree is exponential in the iterated logarithm of "n" necessarily contains a cycle whose length is a power of two . The conjecture is also known to be true for planar claw-free graphs and for graphs that avoid large induced stars and satisfy additional constraints on their degrees .

title: Menstrual disorder

text: "Irregular menstruation" is where there is variation in menstrual cycle length of more than approximately eight days for a woman. The term "metrorrhagia" is often used for irregular menstruation that occurs between the expected menstrual periods.

title: Fertility awareness

text: Use of certain calendar rules to determine the length of the pre-ovulatory infertile phase allows unprotected intercourse during the first few days of the menstrual cycle while maintaining a very low risk of pregnancy. With mucus-only methods, there is a possibility of incorrectly identifying mid-cycle or anovulatory bleeding as menstruation. Keeping a BBT chart enables accurate identification of menstruation, when pre-ovulatory calendar rules may be reliably applied. In temperature-only systems, a calendar rule may be relied on alone to determine pre-ovulatory infertility. In symptothermal systems, the calendar rule is cross-checked by mucus records: observation of fertile cervical mucus overrides any calendar-determined infertility.

title: Calendar-based contraceptive methods

text: It is not known if historical cultures were aware of what part of the menstrual cycle is most fertile. In the year 388, Augustine of Hippo wrote of periodic abstinence. Addressing followers of Manichaeism, his former religion, he said, "Is it not you who used to counsel us to observe as much as possible the time when a woman, after her purification, is most likely to conceive, and to abstain from cohabitation at that time...?" If the Manichaieans practiced something like the Jewish observances of menstruation, then the "time... after her purification" would have indeed been when "a woman... is most likely to conceive." Over a century previously, however, the influential Greek physician Soranus had written that "the time directly before and after menstruation" was the most fertile part of a woman's cycle; this inaccuracy was repeated in the 6th century by the Byzantine physician Aëtius. Similarly, a Chinese sex manual written close to the year 600 stated that only the first five days following menstruation were fertile. Some historians believe that Augustine, too, incorrectly identified the days immediately after menstruation as the time of highest fertility.

title: Solar cycle

text: Until 2009 it was thought that 28 cycles had spanned the 309 years between 1699 and 2008, giving an average length of 11.04 years, but research then showed that the longest of these (1784–1799) seems actually to have been two cycles, so that the average length is only around 10.7 years. Since observations began cycles as short as 9 years and as long as 14 years have been observed, and in the double cycle of 1784–1799 one of the two component cycles had to be less than 8 years in length. Significant amplitude variations also occur.

title: Vagina

text: Non-human primates are optimal models for human biomedical research because humans and non-human primates share physiological characteristics as a result of evolution. While menstruation is heavily associated with human females, and they have the most pronounced menstruation, it is also typical of ape relatives and monkeys. Female macaques menstruate, with a cycle length over the course of a lifetime that is comparable to that of female humans. Estrogens and progestogens in the menstrual cycles and during premenarche and postmenopause are also similar in female humans and macaques; however, only in macaques does keratinization of the epithelium occur during the follicular phase. The vaginal pH of macaques also differs, with near-neutral to slightly alkaline median values and is widely variable, which may be due to its lack of lactobacilli in the vaginal flora. This is one reason why, although macaques are used for studying HIV transmission and testing microbicides, animal models are not often used in the study of sexually transmitted infections, such as trichomoniasis. Another is that such conditions' causes are inextricably bound to humans' genetic makeup, making results from other species difficult to apply to humans.

title: Gestational age

text:
Following are diagrams for estimating gestational age from obstetric ultrasound, by various target parameters:
The fertilization age (also called "embryonic age" and later "fetal age") is the time from the fertilization. It usually occurs within a day of ovulation, which, in turn, occurs on average 14.6 days after the beginning of the preceding menstruation (LMP). There is also considerable variability in this interval, with a 95% prediction interval of the ovulation of 9 to 20 days after menstruation even for an average woman who has a mean LMP-to-ovulation time of 14.6. In a reference group representing all women, the 95% prediction interval of the LMP-to-ovulation is 8.2 to 20.5 days. The actual variability between gestational age as estimated from the beginning of the last menstrual period (without the use of any additional method mentioned in previous section) is substantially larger because of uncertainty which menstrual cycle gave rise to the pregnancy. For example, the menstruation may be scarce enough to give the false appearance that an earlier menstruation gave rise to the pregnancy, potentially giving an estimated gestational age that is approximately one month too large. Also, vaginal bleeding occurs during 15-25% of first trimester pregnancies, and may be mistaken as menstruation, potentially giving an estimated gestational age that is too low.

title: Menstruation

text: Many have questioned the evolution of overt menstruation in humans and related species, speculating on what advantage there could be to losing blood associated with dismantling the endometrium, rather than absorbing it, as most mammals do. Humans do, in fact, reabsorb about two-thirds of the endometrium each cycle. Some work asserts that overt menstruation occurs not because it is beneficial in itself. Rather, the fetal development of these species requires a more developed endometrium, one which is too thick to reabsorb completely. There is a correlation between species that have overt menstruation to those that have a large uterus relative to the adult female body size.[56]

title: Calendar-based contraceptive methods

text: Most menstrual cycles have several days at the beginning that are infertile (pre-ovulatory infertility), a period of fertility, and then several days just before the next menstruation that are infertile (post-ovulatory infertility). The first day of red bleeding is considered day one of the menstrual cycle. To use these methods, a woman is required to know the length of her menstrual cycles.

title: Emergency contraception

text: Temporary disruption of the menstrual cycle is also commonly experienced. If taken before ovulation, the high doses of progestogen in levonorgestrel treatments may induce progestogen withdrawal bleeding a few days after the pills are taken. One study found that about half of women who used levonorgestrel ECPs experienced bleeding within 7 days of taking the pills. If levonorgestrel is taken after ovulation, it may increase the length of the luteal phase, thus delaying menstruation by a few days. Mifepristone, if taken before ovulation, may delay ovulation by 3–4 days (delayed ovulation may result in a delayed menstruation). These disruptions only occur in the cycle in which ECPs were taken; subsequent cycle length is not significantly affected. If a woman's menstrual period is delayed by two weeks or more, it is advised that she take a pregnancy test. (Earlier testing may not give accurate results.)

title: Menstruation

text: The menstrual cycle occurs due to the rise and fall of hormones.[2] This cycle results in the thickening of the lining of the uterus, and the growth of an egg, (which is required for pregnancy).[2] The egg is released from an ovary around day fourteen in the cycle; the thickened lining of the uterus provides nutrients to an embryo after implantation.[2] If pregnancy does not occur, the lining is released in what is known as menstruation.[2]

title: Menstruation (mammal)

text: All female placental mammals have a uterine lining that builds up when the animal is fertile, but is dismantled (menstruated) when the animal is infertile. Some anthropologists have questioned the energy cost of rebuilding the endometrium every fertility cycle. However, anthropologist Beverly Strassmann has proposed that the energy savings of not having to continuously maintain the uterine lining more than offsets energy cost of having to rebuild the lining in the next fertility cycle, even in species such as humans where much of the lining is lost through bleeding (overt menstruation) rather than reabsorbed (covert menstruation).[2][20] However, even in humans, much of it is re-absorbed.

title: Irregular menstruation

text: Irregular cycles or irregular periods is an abnormal variation in length of menstrual cycles. A female usually experiences cycle length variations of up to eight days between the shortest and longest cycle lengths. Lengths ranging between eight and 20 days are considered moderately irregular. Variation of 21 days or more is considered very irregular.

title: Menstruation

text: During pregnancy and for some time after childbirth, menstruation does not occur. The average length of postpartum amenorrhoea is longer when breastfeeding; this is termed lactational amenorrhoea.

title: Menstruation

text: Breastfeeding causes negative feedback to occur on pulse secretion of gonadotropin-releasing hormone (GnRH) and luteinizing hormone (LH). Depending on the strength of the negative feedback, breastfeeding women may experience complete suppression of follicular development, follicular development but no ovulation, or normal menstrual cycles may resume.[38] Suppression of ovulation is more likely when suckling occurs more frequently.[39] The production of prolactin in response to suckling is important to maintaining lactational amenorrhea.[40] On average, women who are fully breastfeeding whose infants suckle frequently experience a return of menstruation at fourteen and a half months postpartum. There is a wide range of response among individual breastfeeding women, however, with some experiencing return of menstruation at two months and others remaining amenorrheic for up to 42 months postpartum.[41]

title: Menstrual synchrony

text: Strassmann argued menstrual synchrony defined as menstruation overlap should be quite common. For example, the expected difference by chance between two women with 28-day cycles—which is approximately the average length of menstrual cycles of women at the age —is 7 days. Considering that the mean duration of menses is 5 days and the range is 2 to 7 days, the probability of menstruation overlap by chance should be high.

title: Menstrual cycle

text: The luteal phase is the final phase of the ovarian cycle and it corresponds to the secretory phase of the uterine cycle. During the luteal phase, the pituitary hormones FSH and LH cause the remaining parts of the dominant follicle to transform into the corpus luteum, which produces progesterone. The increased progesterone in the adrenals starts to induce the production of estrogen. The hormones produced by the corpus luteum also suppress production of the FSH and LH that the corpus luteum needs to maintain itself. Consequently, the level of FSH and LH fall quickly over time, and the corpus luteum subsequently atrophies.[81] Falling levels of progesterone trigger menstruation and the beginning of the next cycle. From the time of ovulation until progesterone withdrawal has caused menstruation to begin, the process typically takes about two weeks, with 14 days considered normal. For an individual woman, the follicular phase often varies in length from cycle to cycle; by contrast, the length of her luteal phase will be fairly consistent from cycle to cycle.[91]

title: Extended cycle combined hormonal contraceptive

text: Although it was evident that the pill could be used to suppress menstruation for arbitrary lengths of time, the original regimen was designed to produce withdrawal bleeding every four weeks to mimic the menstrual cycle.

title: Culture and menstruation

text:
In Buddhism (Theravada or Hinayana) menstruation is viewed as ""a natural physical excretion that women have to go through on a monthly basis, nothing more or less"". However, in certain branches of Japanese Buddhism, menstruating women are banned from attending temples.
In Nichiren Buddhism (Japan) menstruation is not considered a spiritual obstacle to religious practice, although a menstruating woman may choose not to bow, for comfort.
In Hinduism, menstruating women are traditionally advised rules to follow. During menstruation, women are advised not to “enter temple,work in kitchen,wear flowers, have sex, touch other males or females.” Menstruation is seen as unclean, and are often separated from place of worship or any object pertaining to it, for the length of their period.

title: Menstruation

text: Some anthropologists have questioned the energy cost of rebuilding the endometrium every fertility cycle. It has proposed that the energy savings of not having to continuously maintain the uterine lining more than offsets energy cost of having to rebuild the lining in the next fertility cycle, even in species such as humans where much of the lining is lost through bleeding (overt menstruation) rather than reabsorbed (covert menstruation).[56][57]

title: Menstruation (mammal)

text: Females of other species of placental mammal undergo estrous cycles, in which the endometrium is completely reabsorbed by the animal (covert menstruation) at the end of its reproductive cycle. Many zoologists regard this as different from a "true" menstrual cycle. Female domestic animals used for breeding —for example dogs, pigs, cattle, or horses— are monitored for physical signs of an estrous cycle period, which indicates that the animal is ready for insemination.

title: Menstruation (mammal)

text: Average length (days) of estrus and estrous cycles:[23]


query: What is mathematical symmetry?

title: Symmetry in mathematics

text: Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that something does not change under a set of transformations.

title: Inversion transformation

text: In mathematical physics, inversion transformations are a natural extension of Poincaré transformations to include all conformal one-to-one transformations on coordinate space-time. They are less studied in physics because unlike the rotations and translations of Poincaré symmetry an object cannot be physically transformed by the inversion symmetry. Some physical theories are invariant under this symmetry, in these cases it is what is known as a 'hidden symmetry'. Other hidden symmetries of physics include gauge symmetry and general covariance.

title: Symmetry in mathematics

text: A Line symmetry of a system of differential equations is a continuous symmetry of the system of differential equations. Knowledge of a Line symmetry can be used to simplify an ordinary differential equation through reduction of order.[5]

title: Mirror symmetry (string theory)

text: In 1990, Edward Witten introduced topological string theory, a simplified version of string theory, and physicists showed that there is a version of mirror symmetry for topological string theory. This statement about topological string theory is usually taken as the definition of mirror symmetry in the mathematical literature. In an address at the International Congress of Mathematicians in 1994, mathematician Maxim Kontsevich presented a new mathematical conjecture based on the physical idea of mirror symmetry in topological string theory. Known as homological mirror symmetry, this conjecture formalizes mirror symmetry as an equivalence of two mathematical structures: the derived category of coherent sheaves on a Calabi–Yau manifold and the Fukaya category of its mirror.

title: Plane symmetry

text: A plane symmetry is a symmetry of a pattern in the Euclidean plane: that is, a transformation of the plane that carries any directioned lines to lines and preserves many different distances. If one has a pattern in the plane, the set of plane symmetries that preserve the pattern forms a group. The groups that arise in this way are plane symmetry groups and are of considerable mathematical interest. A symmetry plane is a three-dimensional object's symmetry axe.

title: Mathematical formulation of the Standard Model

text: In addition to the accidental (but exact) symmetries described above, the Standard Model exhibits several approximate symmetries. These are the "SU(2) custodial symmetry" and the "SU(2) or SU(3) quark flavor symmetry."

title: Group (mathematics)

text:
"Symmetry groups" are groups consisting of symmetries of given mathematical objects—be they of geometric nature, such as the introductory symmetry group of the square, or of algebraic nature, such as polynomial equations and their solutions. Conceptually, group theory can be thought of as the study of symmetry. Symmetries in mathematics greatly simplify the study of geometrical or analytical objects. A group is said to act on another mathematical object "X" if every group element performs some operation on "X" compatibly to the group law. In the rightmost example below, an element of order 7 of the (2,3,7) triangle group acts on the tiling by permuting the highlighted warped triangles (and the other ones, too). By a group action, the group pattern is connected to the structure of the object being acted on.
In chemical fields, such as crystallography, space groups and point groups describe molecular symmetries and crystal symmetries. These symmetries underlie the chemical and physical behavior of these systems, and group theory enables simplification of quantum mechanical analysis of these properties. For example, group theory is used to show that optical transitions between certain quantum levels cannot occur simply because of the symmetry of the states involved.

title: Platonic solid

text: In mathematics, the concept of symmetry is studied with the notion of a mathematical group. Every polyhedron has an associated symmetry group, which is the set of all transformations (Euclidean isometries) which leave the polyhedron invariant. The order of the symmetry group is the number of symmetries of the polyhedron. One often distinguishes between the "full symmetry group", which includes reflections, and the "proper symmetry group", which includes only rotations.

title: Symmetry (geometry)

text: The types of symmetries that are possible for a geometric object depend on the set of geometric transforms available, and on what object properties should remain unchanged after a transform. Because the composition of two transforms is also a transform and every transform has an inverse transform that undoes it, the set of transforms under which an object is symmetric form a mathematical group, the symmetry group of the object.

title: Group theory

text: Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. They provide a natural framework for analysing the continuous symmetries of differential equations (differential Galois theory), in much the same way as permutation groups are used in Galois theory for analysing the discrete symmetries of algebraic equations. An extension of Galois theory to the case of continuous symmetry groups was one of Lie's principal motivations.

title: String theory

text: Originally, these results of Candelas were justified on physical grounds. However, mathematicians generally prefer rigorous proofs that do not require an appeal to physical intuition. Inspired by physicists' work on mirror symmetry, mathematicians have therefore constructed their own arguments proving the enumerative predictions of mirror symmetry. Today mirror symmetry is an active area of research in mathematics, and mathematicians are working to develop a more complete mathematical understanding of mirror symmetry based on physicists' intuition. Major approaches to mirror symmetry include the homological mirror symmetry program of Maxim Kontsevich and the SYZ conjecture of Andrew Strominger, Shing-Tung Yau, and Eric Zaslow.

title: Symmetry in quantum mechanics

text: Symmetries in quantum mechanics describe features of spacetime and particles which are unchanged under some transformation, in the context of quantum mechanics, relativistic quantum mechanics and quantum field theory, and with applications in the mathematical formulation of the standard model and condensed matter physics. In general, symmetry in physics, invariance, and conservation laws, are fundamentally important constraints for formulating physical theories and models. In practice, they are powerful methods for solving problems and predicting what can happen. While conservation laws do not always give the answer to the problem directly, they form the correct constraints and the first steps to solving a multitude of problems.

title: Mirror symmetry (string theory)

text: In physics, mirror symmetry is justified on physical grounds. However, mathematicians generally require rigorous proofs that do not require an appeal to physical intuition. From a mathematical point of view, the version of mirror symmetry described above is still only a conjecture, but there is another version of mirror symmetry in the context of topological string theory, a simplified version of string theory introduced by Edward Witten, which has been rigorously proven by mathematicians. In the context of topological string theory, mirror symmetry states that two theories called the A-model and B-model are equivalent in the sense that there is a duality relating them. Today mirror symmetry is an active area of research in mathematics, and mathematicians are working to develop a more complete mathematical understanding of mirror symmetry based on physicists' intuition.

title: Group cohomology

text: Group cohomology theory also has a direct application in condensed matter physics. Just like group theory being the mathematical foundation of spontaneous symmetry breaking phases, group cohomology theory is the mathematical foundation of a class of quantum states of matter—short-range entangled states with symmetry. Short-range entangled states with symmetry are also known as symmetry-protected topological states.

title: Continuous symmetry

text: In mathematics, continuous symmetry is an intuitive idea corresponding to the concept of viewing some symmetries as motions, as opposed to discrete symmetry, e.g. reflection symmetry, which is invariant under a kind of flip from one state to another. However, a discrete symmetry can always be reinterpreted as a subset of some higher-dimensional continuous symmetry, e.g. reflection of a 2 dimensional object in 3 dimensional space can be achieved by continuously rotating that object 180 degrees across a non-parallel plane.

title: Symmetry in mathematics

text: In general, every kind of structure in mathematics will have its own kind of symmetry, many of which are listed in the given points mentioned above.

title: Homological mirror symmetry

text: Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory.

title: String theory

text: Group theory is the branch of mathematics that studies the concept of symmetry. For example, one can consider a geometric shape such as an equilateral triangle. There are various operations that one can perform on this triangle without changing its shape. One can rotate it through 120°, 240°, or 360°, or one can reflect in any of the lines labeled , , or in the picture. Each of these operations is called a "symmetry", and the collection of these symmetries satisfies certain technical properties making it into what mathematicians call a group. In this particular example, the group is known as the dihedral group of order 6 because it has six elements. A general group may describe finitely many or infinitely many symmetries; if there are only finitely many symmetries, it is called a finite group.

title: Time translation symmetry

text: Time translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a common interval. Time translation symmetry is the hypothesis that the laws of physics are unchanged, (i.e. invariant) under such a transformation. Time translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history. Time translation symmetry is closely connected, via the Noether theorem, to conservation of energy. In mathematics, the set of all time translations on a given system form a Lie group.

title: Rotation (mathematics)

text: As was stated above, Euclidean rotations are applied to rigid body dynamics. Moreover, most of mathematical formalism in physics (such as the vector calculus) is rotation-invariant; see rotation for more physical aspects. Euclidean rotations and, more generally, Lorentz symmetry described above are thought to be symmetry laws of nature. In contrast, the reflectional symmetry is not a precise symmetry law of nature.

title: Symmetry (physics)

text: The transformations describing physical symmetries typically form a mathematical group. Group theory is an important area of mathematics for physicists.

title: Gauge symmetry (mathematics)

text: In mathematics, any Lagrangian system generally admits gauge symmetries, though it may happen that they are trivial. In theoretical physics, the notion of gauge symmetries depending on parameter functions is a cornerstone of contemporary field theory.

title: Symmetry group

text: In wider contexts, a symmetry group may be any kind of transformation group, or automorphism group. Once we know what kind of mathematical structure we are concerned with, we should be able to pinpoint what mappings preserve the structure. Conversely, specifying the symmetry can define the structure, or at least clarify what we mean by an invariant, geometric language in which to discuss it; this is one way of looking at the Erlangen programme.

title: Symmetry in mathematics

text: In abstract algebra, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object.

title: Symmetry in mathematics

text: Use of symmetry in integration Invariance (mathematics)

title: Symmetry in mathematics

text: The types of symmetry considered in basic geometry (like reflection and rotation symmetry) are described more fully in the main article on symmetry.

title: Mirror symmetry (string theory)

text: Mirror symmetry was originally discovered by physicists. Mathematicians became interested in this relationship around 1990 when Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that it could be used as a tool in enumerative geometry, a branch of mathematics concerned with counting the number of solutions to geometric questions. Candelas and his collaborators showed that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a longstanding problem. Although the original approach to mirror symmetry was based on physical ideas that were not understood in a mathematically precise way, some of its mathematical predictions have since been proven rigorously.

title: Mirror symmetry (string theory)

text: Today, mirror symmetry is a major research topic in pure mathematics, and mathematicians are working to develop a mathematical understanding of the relationship based on physicists' intuition. Mirror symmetry is also a fundamental tool for doing calculations in string theory, and it has been used to understand aspects of quantum field theory, the formalism that physicists use to describe elementary particles. Major approaches to mirror symmetry include the homological mirror symmetry program of Maxim Kontsevich and the SYZ conjecture of Andrew Strominger, Shing-Tung Yau, and Eric Zaslow.

title: Discrete symmetry

text: In mathematics, a discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square's original appearance. Discrete symmetries sometimes involve some type of 'swapping', these swaps usually being called "reflections" or "interchanges". In mathematics and theoretical physics, a discrete symmetry is a symmetry under the transformations of a discrete group—e.g. a topological group with a discrete topology whose elements form a finite or a countable set.

title: Supersymmetric gauge theory

text: A gauge theory is a mathematical framework for analysing gauge symmetries. There are two types of symmetries, viz., global and local. A global symmetry is the symmetry which remains invariant at each point of a manifold (manifold can be either of spacetime coordinates or that of internal quantum numbers). A local symmetry is the symmetry which depends upon the space over which it is defined, and changes with the variation in coordinates. Thus, such symmetry is invariant only locally (i.e., in a neighborhood on the manifold).