title: Indian mathematics

text: It has been hypothesized that the Indian decimal place value system was based on the symbols used on Chinese counting boards from as early as the middle of the first millennium BCE. According to , These counting boards, like the Indian counting pits, ..., had a decimal place value structure ... Indians may well have learned of these decimal place value "rod numerals" from Chinese Buddhist pilgrims or other travelers, or they may have developed the concept independently from their earlier non-place-value system; no documentary evidence survives to confirm either conclusion."


title: Indian mathematics

text: The oldest extant mathematical manuscript in India is the "Bakhshali Manuscript", a birch bark manuscript written in "Buddhist hybrid Sanskrit" in the "Śāradā" script, which was used in the northwestern region of the Indian subcontinent between the 8th and 12th centuries CE. The manuscript was discovered in 1881 by a farmer while digging in a stone enclosure in the village of Bakhshali, near Peshawar (then in British India and now in Pakistan). Of unknown authorship and now preserved in the Bodleian Library in the University of Oxford, the manuscript has been dated recently as 224 AD- 383 AD.


title: Indian mathematics

text: The surviving manuscript has seventy leaves, some of which are in fragments. Its mathematical content consists of rules and examples, written in verse, together with prose commentaries, which include solutions to the examples. The topics treated include arithmetic (fractions, square roots, profit and loss, simple interest, the rule of three, and "regula falsi") and algebra (simultaneous linear equations and quadratic equations), and arithmetic progressions. In addition, there is a handful of geometric problems (including problems about volumes of irregular solids). The Bakhshali manuscript also "employs a decimal place value system with a dot for zero." Many of its problems are of a category known as 'equalisation problems' that lead to systems of linear equations. One example from Fragment III-5-3v is the following:


title: Indian mathematics

text: The prose commentary accompanying the example solves the problem by converting it to three (under-determined) equations in four unknowns and assuming that the prices are all integers.


title: Indian mathematics

text: In 2017, three samples from the manuscript were shown by radiocarbon dating to come from three different centuries: from 224 to 383 AD, 680-779 AD, and 885-993 AD. It is not known how fragments from different centuries came to be packaged together.


title: Indian mathematics

text: This period is often known as the golden age of Indian Mathematics. This period saw mathematicians such as Aryabhata, Varahamihira, Brahmagupta, Bhaskara I, Mahavira, Bhaskara II, Madhava of Sangamagrama and Nilakantha Somayaji give broader and clearer shape to many branches of mathematics. Their contributions would spread to Asia, the Middle East, and eventually to Europe. Unlike Vedic mathematics, their works included both astronomical and mathematical contributions. In fact, mathematics of that period was included in the 'astral science' ("jyotiḥśāstra") and consisted of three sub-disciplines: mathematical sciences ("gaṇita" or "tantra"), horoscope astrology ("horā" or "jātaka") and divination (saṃhitā). This tripartite division is seen in Varāhamihira's 6th century compilation—"Pancasiddhantika" (literally "panca", "five," "siddhānta", "conclusion of deliberation", dated 575 CE)—of five earlier works, Surya Siddhanta, Romaka Siddhanta, Paulisa Siddhanta, Vasishtha Siddhanta and Paitamaha Siddhanta, which were adaptations of still earlier works of Mesopotamian, Greek, Egyptian, Roman and Indian astronomy. As explained earlier, the main texts were composed in Sanskrit verse, and were followed by prose commentaries.


title: Indian mathematics

text: Though its authorship is unknown, the "Surya Siddhanta" (c. 400) contains the roots of modern trigonometry. Because it contains many words of foreign origin, some authors consider that it was written under the influence of Mesopotamia and Greece.


title: Indian mathematics

text: Later Indian mathematicians such as Aryabhata made references to this text, while later Arabic and Latin translations were very influential in Europe and the Middle East.


title: Indian mathematics

text: This Chhedi calendar (594) contains an early use of the modern place-value Hindu–Arabic numeral system now used universally.


title: Indian mathematics

text: Aryabhata (476–550) wrote the "Aryabhatiya." He described the important fundamental principles of mathematics in 332 shlokas. The treatise contained:


title: Indian mathematics

text: Varahamihira (505–587) produced the "Pancha Siddhanta" ("The Five Astronomical Canons"). He made important contributions to trigonometry, including sine and cosine tables to 4 decimal places of accuracy and the following formulas relating sine and cosine functions:


title: Indian mathematics

text: In the 7th century, two separate fields, arithmetic (which included measurement) and algebra, began to emerge in Indian mathematics. The two fields would later be called ' (literally "mathematics of algorithms") and ' (lit. "mathematics of seeds," with "seeds"—like the seeds of plants—representing unknowns with the potential to generate, in this case, the solutions of equations). Brahmagupta, in his astronomical work "" (628 CE), included two chapters (12 and 18) devoted to these fields. Chapter 12, containing 66 Sanskrit verses, was divided into two sections: "basic operations" (including cube roots, fractions, ratio and proportion, and barter) and "practical mathematics" (including mixture, mathematical series, plane figures, stacking bricks, sawing of timber, and piling of grain). In the latter section, he stated his famous theorem on the diagonals of a cyclic quadrilateral:


title: Indian mathematics

text: Brahmagupta's theorem: If a cyclic quadrilateral has diagonals that are perpendicular to each other, then the perpendicular line drawn from the point of intersection of the diagonals to any side of the quadrilateral always bisects the opposite side.


title: Indian mathematics

text: Chapter 12 also included a formula for the area of a cyclic quadrilateral (a generalisation of Heron's formula), as well as a complete description of rational triangles ("i.e." triangles with rational sides and rational areas).


title: Indian mathematics

text: Brahmagupta's formula: The area, "A", of a cyclic quadrilateral with sides of lengths "a", "b", "c", "d", respectively, is given by


title: Indian mathematics

text: Brahmagupta's Theorem on rational triangles: A triangle with rational sides formula_9 and rational area is of the form:


title: Indian mathematics

text: Chapter 18 contained 103 Sanskrit verses which began with rules for arithmetical operations involving zero and negative numbers and is considered the first systematic treatment of the subject. The rules (which included formula_13 and formula_14) were all correct, with one exception: formula_15. Later in the chapter, he gave the first explicit (although still not completely general) solution of the quadratic equation:


title: Indian mathematics

text: Also in chapter 18, Brahmagupta was able to make progress in finding (integral) solutions of Pell's equation,


title: Indian mathematics

text: which was a generalisation of an earlier identity of Diophantus: Brahmagupta used his identity to prove the following lemma:


title: Indian mathematics

text: He then used this lemma to both generate infinitely many (integral) solutions of Pell's equation, given one solution, and state the following theorem:


title: Indian mathematics

text: Theorem (Brahmagupta): If the equation formula_27 has an integer solution for any one of formula_28 then Pell's equation:


title: Indian mathematics

text: Brahmagupta did not actually prove the theorem, but rather worked out examples using his method. The first example he presented was:


title: Indian mathematics

text: In his commentary, Brahmagupta added, "a person solving this problem within a year is a mathematician." The solution he provided was:


title: Indian mathematics

text: Bhaskara I (c. 600–680) expanded the work of Aryabhata in his books titled "Mahabhaskariya", "Aryabhatiya-bhashya" and "Laghu-bhaskariya". He produced:


title: Indian mathematics

text: Virasena (8th century) was a Jain mathematician in the court of Rashtrakuta King Amoghavarsha of Manyakheta, Karnataka. He wrote the "Dhavala", a commentary on Jain mathematics, which:


title: Indian mathematics

text: It is thought that much of the mathematical material in the "Dhavala" can attributed to previous writers, especially Kundakunda, Shamakunda, Tumbulura, Samantabhadra and Bappadeva and date who wrote between 200 and 600 CE.


title: Indian mathematics

text: Mahavira Acharya (c. 800–870) from Karnataka, the last of the notable Jain mathematicians, lived in the 9th century and was patronised by the Rashtrakuta king Amoghavarsha. He wrote a book titled "Ganit Saar Sangraha" on numerical mathematics, and also wrote treatises about a wide range of mathematical topics. These include the mathematics of:


title: Indian mathematics

text: Shridhara (c. 870–930), who lived in Bengal, wrote the books titled "Nav Shatika", "Tri Shatika" and "Pati Ganita". He gave:


title: Indian mathematics

text: The "Pati Ganita" is a work on arithmetic and measurement. It deals with various operations, including:


title: Indian mathematics

text: Aryabhata's differential equations were elaborated in the 10th century by Manjula (also "Munjala"), who realised that the expression


title: Indian mathematics

text: He understood the concept of differentiation after solving the differential equation that resulted from substituting this expression into Aryabhata's differential equation.


title: Indian mathematics

text: Aryabhata II (c. 920–1000) wrote a commentary on Shridhara, and an astronomical treatise "Maha-Siddhanta". The Maha-Siddhanta has 18 chapters, and discusses:


title: Indian mathematics

text: Shripati Mishra (1019–1066) wrote the books "Siddhanta Shekhara", a major work on astronomy in 19 chapters, and "Ganit Tilaka", an incomplete arithmetical treatise in 125 verses based on a work by Shridhara. He worked mainly on:


title: Indian mathematics

text: Bhāskara II (1114–1185) was a mathematician-astronomer who wrote a number of important treatises, namely the "Siddhanta Shiromani", "Lilavati", "Bijaganita", "Gola Addhaya", "Griha Ganitam" and "Karan Kautoohal". A number of his contributions were later transmitted to the Middle East and Europe. His contributions include:


title: Indian mathematics

text: The Kerala school of astronomy and mathematics was founded by Madhava of Sangamagrama in Kerala, South India and included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. It flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri (1559–1632). In attempting to solve astronomical problems, the Kerala school astronomers "independently" created a number of important mathematics concepts. The most important results, series expansion for trigonometric functions, were given in Sanskrit verse in a book by Neelakanta called "Tantrasangraha" and a commentary on this work called "Tantrasangraha-vakhya" of unknown authorship. The theorems were stated without proof, but proofs for the series for "sine", "cosine", and inverse "tangent" were provided a century later in the work "Yuktibhāṣā" (c.1500–c.1610), written in Malayalam, by Jyesthadeva.


title: Indian mathematics

text: Their discovery of these three important series expansions of calculus—several centuries before calculus was developed in Europe by Isaac Newton and Gottfried Leibniz—was an achievement. However, the Kerala School did not invent "calculus", because, while they were able to develop Taylor series expansions for the important trigonometric functions, differentiation, term by term integration, convergence tests, iterative methods for solutions of non-linear equations, and the theory that the area under a curve is its integral, they developed neither a theory of differentiation or integration, nor the fundamental theorem of calculus. The results obtained by the Kerala school include:


title: Indian mathematics

text: The works of the Kerala school were first written up for the Western world by Englishman C.M. Whish in 1835. According to Whish, the Kerala mathematicians had ""laid the foundation for a complete system of fluxions"" and these works abounded ""with fluxional forms and series to be found in no work of foreign countries.""


title: Indian mathematics

text: However, Whish's results were almost completely neglected, until over a century later, when the discoveries of the Kerala school were investigated again by C. Rajagopal and his associates. Their work includes commentaries on the proofs of the arctan series in "Yuktibhāṣā" given in two papers, a commentary on the "Yuktibhāṣā"'s proof of the sine and cosine series and two papers that provide the Sanskrit verses of the "Tantrasangrahavakhya" for the series for arctan, sin, and cosine (with English translation and commentary).


title: Indian mathematics

text: Narayana Pandit is a 14th century mathematician who composed two important mathematical works, an arithmetical treatise, "Ganita Kaumudi", and an algebraic treatise, "Bijganita Vatamsa". Narayana is also thought to be the author of an elaborate commentary of Bhaskara II's Lilavati, titled "Karmapradipika" (or "Karma-Paddhati"). Madhava of Sangamagrama (c. 1340–1425) was the founder of the Kerala School. Although it is possible that he wrote "Karana Paddhati" a work written sometime between 1375 and 1475, all we really know of his work comes from works of later scholars.


title: Indian mathematics

text: Parameshvara (c. 1370–1460) wrote commentaries on the works of Bhaskara I, Aryabhata and Bhaskara II. His "Lilavati Bhasya", a commentary on Bhaskara II's "Lilavati", contains one of his important discoveries: a version of the mean value theorem. Nilakantha Somayaji (1444–1544) composed the "Tantra Samgraha" (which 'spawned' a later anonymous commentary "Tantrasangraha-vyakhya" and a further commentary by the name "Yuktidipaika", written in 1501). He elaborated and extended the contributions of Madhava.


title: Indian mathematics

text: Citrabhanu (c. 1530) was a 16th-century mathematician from Kerala who gave integer solutions to 21 types of systems of two simultaneous algebraic equations in two unknowns. These types are all the possible pairs of equations of the following seven forms:


title: Indian mathematics

text: For each case, Citrabhanu gave an explanation and justification of his rule as well as an example. Some of his explanations are algebraic, while others are geometric. Jyesthadeva (c. 1500–1575) was another member of the Kerala School. His key work was the "Yukti-bhāṣā" (written in Malayalam, a regional language of Kerala). Jyesthadeva presented proofs of most mathematical theorems and infinite series earlier discovered by Madhava and other Kerala School mathematicians.


title: Indian mathematics

text: It has been suggested that Indian contributions to mathematics have not been given due acknowledgement in modern history and that many discoveries and inventions by Indian mathematicians are presently culturally attributed to their Western counterparts, as a result of Eurocentrism. According to G. G. Joseph's take on "Ethnomathematics":


title: Indian mathematics

text: [Their work] takes on board some of the objections raised about the classical Eurocentric trajectory. The awareness [of Indian and Arabic mathematics] is all too likely to be tempered with dismissive rejections of their importance compared to Greek mathematics. The contributions from other civilisations – most notably China and India, are perceived either as borrowers from Greek sources or having made only minor contributions to mainstream mathematical development. An openness to more recent research findings, especially in the case of Indian and Chinese mathematics, is sadly missing"


title: Indian mathematics

text: The historian of mathematics, Florian Cajori, suggested that he and others "suspect that Diophantus got his first glimpse of algebraic knowledge from India." However, he also wrote that "it is certain that portions of Hindu mathematics are of Greek origin".


title: Indian mathematics

text: More recently, as discussed in the above section, the infinite series of calculus for trigonometric functions (rediscovered by Gregory, Taylor, and Maclaurin in the late 17th century) were described in India, by mathematicians of the Kerala school, remarkably some two centuries earlier. Some scholars have recently suggested that knowledge of these results might have been transmitted to Europe through the trade route from Kerala by traders and Jesuit missionaries. Kerala was in continuous contact with China and Arabia, and, from around 1500, with Europe. The existence of communication routes and a suitable chronology certainly make such a transmission a possibility. However, there is no direct evidence by way of relevant manuscripts that such a transmission actually took place. According to David Bressoud, "there is no evidence that the Indian work of series was known beyond India, or even outside of Kerala, until the nineteenth century."


title: Indian mathematics

text: Both Arab and Indian scholars made discoveries before the 17th century that are now considered a part of calculus. However, they did not, as Newton and Leibniz did, "combine many differing ideas under the two unifying themes of the derivative and the integral, show the connection between the two, and turn calculus into the great problem-solving tool we have today." The intellectual careers of both Newton and Leibniz are well-documented and there is no indication of their work not being their own; however, it is not known with certainty whether the immediate "predecessors" of Newton and Leibniz, "including, in particular, Fermat and Roberval, learned of some of the ideas of the Islamic and Indian mathematicians through sources we are not now aware." This is an active area of current research, especially in the manuscript collections of Spain and Maghreb. This research is being pursued, among other places, at the CNRS.


title: Surjective function

text: In mathematics, a surjective function (also known as surjection, or onto function) is a function that every element can be mapped from element so that . In other words, every element of the function's codomain is the image of one element of its domain. It is not required that be unique; the function may map one or more elements of to the same element of .


title: Surjective function

text: The term "surjective" and the related terms "injective" and "bijective" were introduced by Nicolas Bourbaki, a group of mainly French 20th-century mathematicians who, under this pseudonym, wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. The French word "sur" means "over" or "above", and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain.


title: Surjective function

text: Any function induces a surjection by restricting its codomain to the image of its domain. Every surjective function has a right inverse assuming the axiom of choice, and every function with a right inverse is necessarily a surjection. The composition of surjective functions is always surjective. Any function can be decomposed into a surjection and an injection.


title: Surjective function

text: A surjective function is a function whose image is equal to its codomain. Equivalently, a function formula_1 with domain formula_2 and codomain formula_3 is surjective if for every formula_4 in formula_3 there exists at least one formula_6 in formula_2 with formula_8. Surjections are sometimes denoted by a two-headed rightwards arrow (), as in formula_9.


title: Surjective function

text: If (as is often done) a function is identified with its graph, then surjectivity is not a property of the function itself, but rather a property of the mapping. This is, the function together with its codomain. Unlike injectivity, surjectivity cannot be read off of the graph of the function alone.


title: Surjective function

text: The function is said to be a right inverse of the function if "f"("g"("y")) = "y" for every "y" in "Y" ("g" can be undone by "f"). In other words, "g" is a right inverse of "f" if the composition of "g" and "f" in that order is the identity function on the domain "Y" of "g". The function "g" need not be a complete inverse of "f" because the composition in the other order, , may not be the identity function on the domain "X" of "f". In other words, "f" can undo or ""reverse"" "g", but cannot necessarily be reversed by it.


title: Surjective function

text: Every function with a right inverse is necessarily a surjection. The proposition that every surjective function has a right inverse is equivalent to the axiom of choice.


title: Surjective function

text: If is surjective and "B" is a subset of "Y", then "f"("f"("B")) = "B". Thus, "B" can be recovered from its preimage .


title: Surjective function

text: For example, in the first illustration above, there is some function "g" such that "g"("C") = 4. There is also some function "f" such that "f"(4) = "C". It doesn't matter that "g"("C") can also equal 3; it only matters that "f" "reverses" "g".


title: Surjective function

text: A function is surjective if and only if it is right-cancellative: given any functions , whenever "g" "f" = "h" "f", then "g" = "h". This property is formulated in terms of functions and their composition and can be generalized to the more general notion of the morphisms of a category and their composition. Right-cancellative morphisms are called epimorphisms. Specifically, surjective functions are precisely the epimorphisms in the category of sets. The prefix "epi" is derived from the Greek preposition "ἐπί" meaning "over", "above", "on".


title: Surjective function

text: Any morphism with a right inverse is an epimorphism, but the converse is not true in general. A right inverse "g" of a morphism "f" is called a section of "f". A morphism with a right inverse is called a split epimorphism.


title: Surjective function

text: Any function with domain "X" and codomain "Y" can be seen as a left-total and right-unique binary relation between "X" and "Y" by identifying it with its function graph. A surjective function with domain "X" and codomain "Y" is then a binary relation between "X" and "Y" that is right-unique and both left-total and right-total.


title: Surjective function

text: The cardinality of the domain of a surjective function is greater than or equal to the cardinality of its codomain: If is a surjective function, then "X" has at least as many elements as "Y", in the sense of cardinal numbers. (The proof appeals to the axiom of choice to show that a function


title: Surjective function

text: Specifically, if both "X" and "Y" are finite with the same number of elements, then is surjective if and only if "f" is injective.


title: Surjective function

text: Given two sets "X" and "Y", the notation is used to say that either "X" is empty or that there is a surjection from "Y" onto "X". Using the axiom of choice one can show that and together imply that |"Y"| = |"X"|, a variant of the Schröder–Bernstein theorem.


title: Surjective function

text: The composition of surjective functions is always surjective: If "f" and "g" are both surjective, and the codomain of "g" is equal to the domain of "f", then is surjective. Conversely, if is surjective, then "f" is surjective (but "g", the function applied first, need not be). These properties generalize from surjections in the category of sets to any epimorphisms in any category.


title: Surjective function

text: Any function can be decomposed into a surjection and an injection: For any function there exist a surjection and an injection such that "h" = "g" "f". To see this, define "Y" to be the set of preimages where "z" is in . These preimages are disjoint and partition "X". Then "f" carries each "x" to the element of "Y" which contains it, and "g" carries each element of "Y" to the point in "Z" to which "h" sends its points. Then "f" is surjective since it is a projection map, and "g" is injective by definition.


title: Surjective function

text: Any function induces a surjection by restricting its codomain to its range. Any surjective function induces a bijection defined on a quotient of its domain by collapsing all arguments mapping to a given fixed image. More precisely, every surjection can be factored as a projection followed by a bijection as follows. Let "A"/~ be the equivalence classes of "A" under the following equivalence relation: "x" ~ "y" if and only if "f"("x") = "f"("y"). Equivalently, "A"/~ is the set of all preimages under "f". Let "P"(~) : "A" → "A"/~ be the projection map which sends each "x" in "A" to its equivalence class ["x"], and let "f" : "A"/~ → "B" be the well-defined function given by "f"(["x"]) = "f"("x"). Then "f" = "f" o "P"(~).


title: Surjective function

text: Given fixed and , one can form the set of surjections . The cardinality of this set is one of the twelve aspects of Rota's Twelvefold way, and is given by formula_13, where formula_14 denotes a Stirling number of the second kind.


title: Breathing

text: Breathing (or ventilation) is the process of moving air into and from the lungs to facilitate gas exchange with the internal environment, mostly to flush out carbon dioxide and bring in oxygen.


title: Breathing

text: All aerobic creatures need oxygen for cellular respiration, which extracts energy from the reaction of oxygen with molecules derived from food and produces carbon dioxide as a waste product. Breathing, or "external respiration", brings air into the lungs where gas exchange takes place in the alveoli through diffusion. The body's circulatory system transports these gases to and from the cells, where "cellular respiration" takes place.


title: Breathing

text: The breathing of all vertebrates with lungs consists of repetitive cycles of inhalation and exhalation through a highly branched system of tubes or airways which lead from the nose to the alveoli. The number of respiratory cycles per minute is the breathing or respiratory rate, and is one of the four primary vital signs of life. Under normal conditions the breathing depth and rate is automatically, and unconsciously, controlled by several homeostatic mechanisms which keep the partial pressures of carbon dioxide and oxygen in the arterial blood constant. Keeping the partial pressure of carbon dioxide in the arterial blood unchanged under a wide variety of physiological circumstances, contributes significantly to tight control of the pH of the extracellular fluids (ECF). Over-breathing (hyperventilation) and under-breathing (hypoventilation), which decrease and increase the arterial partial pressure of carbon dioxide respectively, cause a rise in the pH of ECF in the first case, and a lowering of the pH in the second. Both cause distressing symptoms.


title: Breathing

text: Breathing has other important functions. It provides a mechanism for speech, laughter and similar expressions of the emotions. It is also used for reflexes such as yawning, coughing and sneezing. Animals that cannot thermoregulate by perspiration, because they lack sufficient sweat glands, may lose heat by evaporation through panting.


title: Breathing

text: The lungs are not capable of inflating themselves, and will expand only when there is an increase in the volume of the thoracic cavity. In humans, as in the other mammals, this is achieved primarily through the contraction of the diaphragm, but also by the contraction of the intercostal muscles which pull the rib cage upwards and outwards as shown in the diagrams on the right. During forceful inhalation (Figure on the right) the accessory muscles of inhalation, which connect the ribs and sternum to the cervical vertebrae and base of the skull, in many cases through an intermediary attachment to the clavicles, exaggerate the pump handle and bucket handle movements (see illustrations on the left), bringing about a greater change in the volume of the chest cavity. During exhalation (breathing out), at rest, all the muscles of inhalation relax, returning the chest and abdomen to a position called the "resting position", which is determined by their anatomical elasticity. At this point the lungs contain the functional residual capacity of air, which, in the adult human, has a volume of about 2.5–3.0 liters.


title: Breathing

text: During heavy breathing (hyperpnea) as, for instance, during exercise, exhalation is brought about by relaxation of all the muscles of inhalation, (in the same way as at rest), but, in addition, the abdominal muscles, instead of being passive, now contract strongly causing the rib cage to be pulled downwards (front and sides). This not only decreases the size of the rib cage but also pushes the abdominal organs upwards against the diaphragm which consequently bulges deeply into the thorax. The end-exhalatory lung volume is now less air than the resting "functional residual capacity". However, in a normal mammal, the lungs cannot be emptied completely. In an adult human, there is always still at least one liter of residual air left in the lungs after maximum exhalation.


title: Breathing

text: Diaphragmatic breathing causes the abdomen to rhythmically bulge out and fall back. It is, therefore, often referred to as "abdominal breathing". These terms are often used interchangeably because they describe the same action.


title: Breathing

text: When the accessory muscles of inhalation are activated, especially during labored breathing, the clavicles are pulled upwards, as explained above. This external manifestation of the use of the accessory muscles of inhalation is sometimes referred to as clavicular breathing, seen especially during asthma attacks and in people with chronic obstructive pulmonary disease.


title: Breathing

text: Ideally, air is breathed first out and secondly in through the nose. The nasal cavities (between the nostrils and the pharynx) are quite narrow, firstly by being divided in two by the nasal septum, and secondly by lateral walls that have several longitudinal folds, or shelves, called


title: Breathing

text: nasal conchae, thus exposing a large area of nasal mucous membrane to the air as it is inhaled (and exhaled). This causes the inhaled air to take up moisture from the wet mucus, and warmth from the underlying blood vessels, so that the air is very nearly saturated with water vapor and is at almost body temperature by the time it reaches the larynx. Part of this moisture and heat is recaptured as the exhaled air moves out over the partially dried-out, cooled mucus in the nasal passages, during exhalation. The sticky mucus also traps much of the particulate matter that is breathed in, preventing it from reaching the lungs.


title: Breathing

text: The anatomy of a typical mammalian respiratory system, below the structures normally listed among the "upper airways" (the nasal cavities, the pharynx, and larynx), is often described as a respiratory tree or tracheobronchial tree (figure on the left). Larger airways give rise to branches that are slightly narrower, but more numerous than the "trunk" airway that gives rise to the branches. The human respiratory tree may consist of, on average, 23 such branchings into progressively smaller airways, while the respiratory tree of the mouse has up to 13 such branchings. Proximal divisions (those closest to the top of the tree, such as the trachea and bronchi) function mainly to transmit air to the lower airways. Later divisions such as the respiratory bronchioles, alveolar ducts and alveoli are specialized for gas exchange.


title: Breathing

text: The trachea and the first portions of the main bronchi are outside the lungs. The rest of the "tree" branches within the lungs, and ultimately extends to every part of the lungs.


title: Breathing

text: The alveoli are the blind-ended terminals of the "tree", meaning that any air that enters them has to exit the same way it came. A system such as this creates dead space, a term for the volume of air that fills the airways at the end of inhalation, and is breathed out, unchanged, during the next exhalation, never having reached the alveoli. Similarly, the dead space is filled with alveolar air at the end of exhalation, which is the first air to breathed back into the alveoli during inhalation, before any fresh air which follows after it. The dead space volume of a typical adult human is about 150 ml.


title: Breathing

text: The primary purpose of breathing is to refresh air in the alveoli so that gas exchange can take place in the blood. The equilibration of the partial pressures of the gases in the alveolar blood and the alveolar air occurs by diffusion. After exhaling, adult human lungs still contain 2.5–3 L of air, their functional residual capacity or FRC. On inhalation, only about 350 mL of new, warm, moistened atmospheric air is brought in and is well mixed with the FRC. Consequently, the gas composition of the FRC changes very little during the breathing cycle. This means that the pulmonary, capillary blood always equilibrates with a relatively constant air composition in the lungs and the diffusion rate with arterial blood gases remains equally constant with each breath. Body tissues are therefore not exposed to large swings in oxygen and carbon dioxide tensions in the blood caused by the breathing cycle, and the peripheral and central chemoreceptors measure only gradual changes in dissolved gases. Thus the homeostatic control of the breathing rate depends only on the partial pressures of oxygen and carbon dioxide in the arterial blood, which then also maintains a constant pH of the blood.


title: Breathing

text: The rate and depth of breathing is automatically controlled by the respiratory centers that receive information from the peripheral and central chemoreceptors. These chemoreceptors continuously monitor the partial pressures of carbon dioxide and oxygen in the arterial blood. The first of these sensors are the central chemoreceptors on the surface of the medulla oblongata of the brain stem which are particularly sensitive to pH as well as the partial pressure of carbon dioxide in the blood and cerebrospinal fluid. The second group of sensors measure the partial pressure of oxygen in the arterial blood. Together the latter are known as the peripheral chemoreceptors, and are situated in the aortic and carotid bodies. Information from all of these chemoreceptors is conveyed to the respiratory centers in the pons and medulla oblongata, which responds to fluctuations in the partial pressures of carbon dioxide and oxygen in the arterial blood by adjusting the rate and depth of breathing, in such a way as to restore the partial pressure of carbon dioxide to 5.3 kPa (40 mm Hg), the pH to 7.4 and, to a lesser extent, the partial pressure of oxygen to 13 kPa (100 mm Hg). For example, exercise increases the production of carbon dioxide by the active muscles. This carbon dioxide diffuses into the venous blood and ultimately raises the partial pressure of carbon dioxide in the arterial blood. This is immediately sensed by the carbon dioxide chemoreceptors on the brain stem. The respiratory centers respond to this information by causing the rate and depth of breathing to increase to such an extent that the partial pressures of carbon dioxide and oxygen in the arterial blood return almost immediately to the same levels as at rest. The respiratory centers communicate with the muscles of breathing via motor nerves, of which the phrenic nerves, which innervate the diaphragm, are probably the most important.


title: Breathing

text: Automatic breathing can be overridden to a limited extent by simple choice, or to facilitate swimming, speech, singing or other vocal training. It is impossible to suppress the urge to breathe to the point of hypoxia but training can increase the ability to hold one's breath. Conscious breathing practices have been shown to promote relaxation and stress relief but have not been proven to have any other health benefits.


title: Breathing

text: Other automatic breathing control reflexes also exist. Submersion, particularly of the face, in cold water, triggers a response called the diving reflex. This has the initial result of shutting down the airways against the influx of water. The metabolic rate slows right down. This is coupled with intense vasoconstriction of the arteries to the limbs and abdominal viscera, reserving the oxygen that is in blood and lungs at the beginning of the dive almost exclusively for the heart and the brain. The diving reflex is an often-used response in animals that routinely need to dive, such as penguins, seals and whales. It is also more effective in very young infants and children than in adults.


title: Breathing

text: Inhaled air is by volume 78% nitrogen, 20.95% oxygen and small amounts of other gases including argon, carbon dioxide, neon, helium, and hydrogen.


title: Breathing

text: The gas exhaled is 4% to 5% by volume of carbon dioxide, about a 100 fold increase over the inhaled amount. The volume of oxygen is reduced by a small amount, 4% to 5%, compared to the oxygen inhaled. The typical composition is:


title: Breathing

text: In addition to air, underwater divers practicing technical diving may breathe oxygen-rich, oxygen-depleted or helium-rich breathing gas mixtures. Oxygen and analgesic gases are sometimes given to patients under medical care. The atmosphere in space suits is pure oxygen. However, this is kept at around 20% of Earthbound atmospheric pressure to regulate the rate of inspiration.


title: Breathing

text: Atmospheric pressure decreases with the height above sea level (altitude) and since the alveoli are open to the outside air through the open airways, the pressure in the lungs also decreases at the same rate with altitude. At altitude, a pressure differential is still required to drive air into and out of the lungs as it is at sea level. The mechanism for breathing at altitude is essentially identical to breathing at sea level but with the following differences:


title: Breathing

text: The atmospheric pressure decreases exponentially with altitude, roughly halving with every rise in altitude. The composition of atmospheric air is, however, almost constant below 80 km, as a result of the continuous mixing effect of the weather. The concentration of oxygen in the air (mmols O per liter of air) therefore decreases at the same rate as the atmospheric pressure. At sea level, where the ambient pressure is about 100 kPa, oxygen constitutes 21% of the atmosphere and the partial pressure of oxygen () is 21 kPa (i.e. 21% of 100 kPa). At the summit of Mount Everest, , where the total atmospheric pressure is 33.7 kPa, oxygen still constitutes 21% of the atmosphere but its partial pressure is only 7.1 kPa (i.e. 21% of 33.7 kPa = 7.1 kPa). Therefore, a greater volume of air must be inhaled at altitude than at sea level in order to breathe in the same amount of oxygen in a given period.


title: Breathing

text: During inhalation, air is warmed and saturated with water vapor as it passes through the nose and pharynx before it enters the alveoli. The "saturated" vapor pressure of water is dependent only on temperature; at a body core temperature of 37 °C it is 6.3 kPa (47.0 mmHg), regardless of any other influences, including altitude. Consequently, at sea level, the "tracheal" air (immediately before the inhaled air enters the alveoli) consists of: water vapor ( = 6.3 kPa), nitrogen ( = 74.0 kPa), oxygen ( = 19.7 kPa) and trace amounts of carbon dioxide and other gases, a total of 100 kPa. In dry air, the at sea level is 21.0 kPa, compared to a of 19.7 kPa in the tracheal air (21% of [100 – 6.3] = 19.7 kPa). At the summit of Mount Everest tracheal air has a total pressure of 33.7 kPa, of which 6.3 kPa is water vapor, reducing the in the tracheal air to 5.8 kPa (21% of [33.7 – 6.3] = 5.8 kPa), beyond what is accounted for by a reduction of atmospheric pressure alone (7.1 kPa).


title: Breathing

text: The pressure gradient forcing air into the lungs during inhalation is also reduced by altitude. Doubling the volume of the lungs halves the pressure in the lungs at any altitude. Having the sea level air pressure (100 kPa) results in a pressure gradient of 50 kPa but doing the same at 5500 m, where the atmospheric pressure is 50 kPa, a doubling of the volume of the lungs results in a pressure gradient of the only 25 kPa. In practice, because we breathe in a gentle, cyclical manner that generates pressure gradients of only 2–3 kPa, this has little effect on the actual rate of inflow into the lungs and is easily compensated for by breathing slightly deeper. The lower viscosity of air at altitude allows air to flow more easily and this also helps compensate for any loss of pressure gradient.


title: Breathing

text: All of the above effects of low atmospheric pressure on breathing are normally accommodated by increasing the respiratory minute volume (the volume of air breathed in — "or" out — per minute), and the mechanism for doing this is automatic. The exact increase required is determined by the respiratory gases homeostatic mechanism, which regulates the arterial and . This homeostatic mechanism prioritizes the regulation of the arterial over that of oxygen at sea level. That is to say, at sea level the arterial is maintained at very close to 5.3 kPa (or 40 mmHg) under a wide range of circumstances, at the expense of the arterial , which is allowed to vary within a very wide range of values, before eliciting a corrective ventilatory response. However, when the atmospheric pressure (and therefore the atmospheric ) falls to below 75% of its value at sea level, oxygen homeostasis is given priority over carbon dioxide homeostasis. This switch-over occurs at an elevation of about . If this switch occurs relatively abruptly, the hyperventilation at high altitude will cause a severe fall in the arterial with a consequent rise in the pH of the arterial plasma leading to respiratory alkalosis. This is one contributor to high altitude sickness. On the other hand, if the switch to oxygen homeostasis is incomplete, then hypoxia may complicate the clinical picture with potentially fatal results.


title: Breathing

text: Pressure increases with the depth of water at the rate of about one atmosphere — slightly more than 100 kPa, or one bar, for every 10 meters. Air breathed underwater by divers is at the ambient pressure of the surrounding water and this has a complex range of physiological and biochemical implications. If not properly managed, breathing compressed gasses underwater may lead to several diving disorders which include pulmonary barotrauma, decompression sickness, nitrogen narcosis, and oxygen toxicity. The effects of breathing gasses under pressure are further complicated by the use of one or more special gas mixtures.


title: Breathing

text: Air is provided by a diving regulator, which reduces the high pressure in a diving cylinder to the ambient pressure. The breathing performance of regulators is a factor when choosing a suitable regulator for the type of diving to be undertaken. It is desirable that breathing from a regulator requires low effort even when supplying large amounts of air. It is also recommended that it supplies air smoothly without any sudden changes in resistance while inhaling or exhaling. In the graph, right, note the initial spike in pressure on exhaling to open the exhaust valve and that the initial drop in pressure on inhaling is soon overcome as the Venturi effect designed into the regulator to allow an easy draw of air. Many regulators have an adjustment to change the ease of inhaling so that breathing is effortless.


title: Breathing

text: Abnormal breathing patterns include Kussmaul breathing, Biot's respiration and Cheyne–Stokes respiration.


title: Breathing

text: Other breathing disorders include shortness of breath (dyspnea), stridor, apnea, sleep apnea (most commonly obstructive sleep apnea), mouth breathing, and snoring. Many conditions are associated with obstructed airways. Chronic mouth breathing may be associated with illness. Hypopnea refers to overly shallow breathing; hyperpnea refers to fast and deep breathing brought on by a demand for more oxygen, as for example by exercise. The terms hypoventilation and hyperventilation also refer to shallow breathing and fast and deep breathing respectively, but under inappropriate circumstances or disease. However, this distinction (between, for instance, hyperpnea and hyperventilation) is not always adhered to, so that these terms are frequently used interchangeably.


title: Breathing

text: The word "spirit" comes from the Latin "spiritus", meaning breath. Historically, breath has often been considered in terms of the concept of life force. The Hebrew Bible refers to God breathing the breath of life into clay to make Adam a living soul (nephesh). It also refers to the breath as returning to God when a mortal dies. The terms spirit, prana, the Polynesian mana, the Hebrew ruach and the psyche in psychology are related to the concept of breath.


title: Breathing

text: In T'ai chi, aerobic exercise is combined with breathing exercises to strengthen the diaphragm muscles, improve posture and make better use of the body's qi. Different forms of meditation, and yoga advocate various breathing methods. A form of Buddhist meditation called anapanasati meaning mindfulness of breath was first introduced by Buddha. Breathing disciplines are incorporated into meditation, certain forms of yoga such as pranayama, and the Buteyko method as a treatment for asthma and other conditions.


title: Breathing

text: In music, some wind instrument players use a technique called circular breathing. Singers also rely on breath control.


title: Breathing

text: Common cultural expressions related to breathing include: "to catch my breath", "took my breath away", "inspiration", "to expire", "get my breath back".


title: Breathing

text: Certain breathing patterns have a tendency to occur with certain moods. Due to this relationship, practitioners of various disciplines consider that they can encourage the occurrence of a particular mood by adopting the breathing pattern that it most commonly occurs in conjunction with. For instance, and perhaps the most common recommendation is that deeper breathing which utilizes the diaphragm and abdomen more can encourage relaxation. Practitioners of different disciplines often interpret the importance of breathing regulation and its perceived influence on mood in different ways. Buddhists may consider that it helps precipitate a sense of inner-peace, holistic healers that it encourages an overall state of health and business advisers that it provides relief from work-based stress.


title: Breathing

text: During physical exercise, a deeper breathing pattern is adapted to facilitate greater oxygen absorption. An additional reason for the adoption of a deeper breathing pattern is to strengthen the body's core. During the process of deep breathing, the thoracic diaphragm adopts a lower position in the core and this helps to generate intra-abdominal pressure which strengthens the lumbar spine. Typically, this allows for more powerful physical movements to be performed. As such, it is frequently recommended when lifting heavy weights to take a deep breath or adopt a deeper breathing pattern.


title: The X-Files (season 11)

text: The eleventh and final season of the American science fiction television series "The X-Files" premiered on January 3, 2018, on Fox. The season consists of ten episodes and concluded on March 21, 2018. It follows newly re-instated Federal Bureau of Investigation (FBI) agents Fox Mulder (David Duchovny) and Dana Scully (Gillian Anderson). The season's storyline picks up directly after last season's finale and the search for Mulder and Scully's son William is the main story arc of the season.


title: The X-Files (season 11)

text: Dana Scully (Gillian Anderson) wakes up in the hospital after having a seizure, now realizing the events of "My Struggle II" were a vision and haven't actually happened yet. Mulder initially presumes Scully’s ramblings are a product of her illness but leaves the hospital to investigate. Agent Jeffrey Spender later appears at Scully’s bedside, revealing that someone is looking for William. He first balks at telling her the location of her son, revealing only the name of the family that adopted him—Van De Kamp. Mulder tails a henchman who he believes will take him to The Smoking Man, but he arrives somewhere else with mysterious conspirators; Mr. Y (A.C. Peterson) and Erika Price (Barbara Hershey). They try to negotiate with Mulder into turning over his son but Mulder refuses. Walter Skinner (Mitch Pileggi) tries to meet with Scully, but can't find her. As he goes to his car, he is met inside by The Smoking Man and Reyes. Meanwhile, Scully tries to leave the hospital but her seizures return causing her to crash her car. She is rescued by Agent Einstein and Agent Miller, and is readmitted to the hospital. Both agents leave the room. An assassin sent by Mr. Y and Erika enters and tries to suffocate Scully, but Mulder steps in and saves her by slicing the assassin's neck. As Skinner comes in, Mulder confronts him since he smells like smoke. In a flashback to when Skinner was in the car with the Smoking Man, the latter reveals (in a further flashback to 17 years, "En Ami") that "he", not Mulder, artificially impregnated Scully.


title: The X-Files (season 11)

text: Scully opens her eyes in the dark, laying on her side on a bed in a mysterious house. She explores the mysterious house and ends up in an endless pattern of the same room. Mulder theorizes that the experience is a type of sleep paralysis. She goes back to her memories of her sleep paralysis, where she grabs a snow globe with a model of the boat in it. Mulder and Scully get to the dock, meeting with Detective Costa (Louis Ferreira). Later, Scully’s attention is drawn to a man that observes them intently from one of the portable walkways. Costa informs them that the victims asked if they found Ghouli. When Scully turns to check if the mystery guy is there, he’s gone. Both agents investigate the two teenagers about the slashing. Both of them go on about the experience and their boyfriend, Jackson Van De Kamp. The agents arrive at the Van De Kamp household, the same house Scully saw in her dream. Two gunshots are heard with a third coming from upstairs. Scully goes up and finds the bleeding corpse of Jackson Van De Kamp. As they leave the room and the door clicks closed, the zipper opens slowly. Jackson sits up and escapes the room. Mulder meets with Skinner at the Chimera, telling him to drop the investigation. Mulder confirms that Jackson's DNA matches Scully's. At the hospital, Jackson explains to Brianna that he’s been hiding because there are people after him. He reveals that Ghouli doesn't exist and it's just something he "made up". Jackson escapes the hospital after the death of the DOD members. The next day, Scully spots a rural gas station that has a windmill just outside. Scully meets with Peter Wong with Wong mentioning that he wishes he could know her better. The agents ask to see the recording tapes. In the recording, Scully is having a conversation with William. She smiles as Mulder holds her while they see their son, alive. Over the course of the season, they search for William. In the third episode of the "Plus One", Scully and Mulder are intimate again. In the season 11 finale, "My Struggle IV", she reveals to Mulder that she is pregnant with his child. Also in the finale, the Smoking Man shoots William, who has made himself look like Mulder.


title: The X-Files (season 11)

text: In May 2015, in an interview with "Entertainment Weekly", co-star David Duchovny stated that if the 2016 revival were successful, he would be interested in another renewal, stating, "I would be open to doing another cycle. I don't know that I could do a 20-episode version of this show at this point in my life, and I don't know that Gillian could. But I think everybody is open ended on what happens after this. Certainly, we didn't bring it back with the idea of ending it." At the 2016 Television Critics Association panel for the series, creator Chris Carter stated, "If we do well in the ratings, I can't imagine we wouldn't be asked to do more." Fox Television Group chairman and CEO Gary Newman stated that he and fellow executive Dana Walden would be open to another renewal, stating, "We would love to do this again, so we'd be on board if schedules can be worked out." In an interview with "Variety" prior to the premiere, co-star Gillian Anderson, Duchovny, and Walden stated their willingness for another renewal. In an interview with "TV Guide", Carter reaffirmed plans for more episodes, but stressed that everyone involved is waiting on the success of the season. In May 2016, Walden confirmed that there had been conversations about an eleventh season possibly for the 2017–18 television season.


title: The X-Files (season 11)

text: On April 20, 2017, Fox officially announced that "The X-Files" would be returning for an eleventh season of ten episodes, which would air in the 2017–18 television season after filming in mid-2017.


title: The X-Files (season 11)

text: The writing staff for the eleventh season consists of Chris Carter, Glen Morgan, Darin Morgan, James Wong, and newcomers who were all previously part of "The X-Files" production staff, Gabe Rotter (writers assistant), Benjamin Van Allen (writers assistant) and Brad Follmer (Carter's personal assistant). In August 2017, it was announced that three female writers were added to the staff; Karen Nielsen (who worked as a script coordinator on season 10) wrote one episode, and Kristen Cloke and Shannon Hamblin wrote another episode based on a story by Glen Morgan. The season, consisting of 10 episodes, has two mythology episodes (the premiere and finale) and eight standalone episodes; however, several critics have considered episode five, "Ghouli", to also be a mythology episode.


title: The X-Files (season 11)

text: In addition to Duchovny and Anderson, Mitch Pileggi was confirmed to reprise his role, as Walter Skinner. Also returning are William B. Davis as Cigarette Smoking Man and Annabeth Gish as Monica Reyes. In August 2017, it was confirmed that Robbie Amell and Lauren Ambrose would reprise their roles Agents Miller and Einstein from season ten. In September 2017, it was announced that Karin Konoval–who played Mrs. Peacock in the fourth-season episode "Home"–would play new characters in the eleventh season, in what Carter described as a "tour-de-force performance". Anderson commented that this is her final season of "The X-Files", saying, "I've said from the beginning this is it for me." However, Chris Carter affirmed he would not do "The X-Files" without her character, saying, "For me, "The X-Files" is Mulder and Scully. I think if it were without Scully, I wouldn't do it. That's not my "X-Files"." The writers intended to bring back Robert Patrick as his character John Doggett, but he was unavailable due to scheduling issues as he was filming for his TV series "Scorpion". In February 2018, Carter stated in an interview that he could see the show continuing without Anderson.


title: The X-Files (season 11)

text: Filming began in August 2017 in Vancouver, British Columbia, where the previous season was filmed, along with the show's original five seasons. After controversy sparked regarding the lack of female writers or directors on the series, it was announced in August 2017 that Carol Banker, a script supervisor on the original series who also directed an episode of "The Lone Gunmen" and Holly Dale were added as directors.


title: The X-Files (season 11)

text: The eleventh season received generally positive reviews from critics and currently has a Metacritic score of 67 out of 100 based on 18 reviews. On Rotten Tomatoes, the season has an approval rating of 77% with an average rating of 6.65 out of 10 based on 170 reviews. The site's consensus reads, "Though it may not make many new believers, "The X-Files" return to business as usual is a refreshing upgrade from the show's underwhelming previous outing." Similar to season 10, the premiere and finale episodes of season 11 received poor reviews, while the stand-alone episodes occurring between them were much more favorably received.


title: The X-Files (season 11)

text: Based on the first five episodes available for review, Liz Shannon Miller of IndieWire gave the season a positive review with a "B+" grade. While Miller wrote that the season premiere "is not good", she was much more positive of the following four standalone episodes, writing that "there are some intriguing mysteries, some eerie moments, solid action" and praised Darin Morgan's comedy installment, calling it "fantastic". Overall, she concluded, "Season 11 so far isn't flawless, but it's a lively, character-focused affair that feels far more unified than we'd ever anticipated, a massive improvement over Season 10 that gives us genuine hope for the second half. For the first time in a while, we're truly excited to see more." Matt Zoller Seitz of "Vulture" stated that compared to the previous season, "This new batch of episodes is considerably stronger. Even the ones that don't really do much but spin their wheels do so with feeling, and when the show is great—as it is, yet again, in Darin Morgan's episode—it's downright sublime."


title: Jon Bass (actor)

text: Jon Bass (born September 22, 1989) is an American actor, known for his roles in "", "Super Pumped", "Baywatch", and the comedy series "Big Time in Hollywood, FL".


title: Jon Bass (actor)

text: Bass grew up in Bellaire, Texas, and attended Bellaire High School, graduating in 2005. He graduated from Boston University in 2011 with a Bachelor of Fine Arts degree in Theatre Arts. He is Jewish.


title: Jon Bass (actor)

text: Following college, he moved to New York City and began his professional acting career. Bass auditioned for the role of Elder Cunningham in the Broadway musical "The Book of Mormon", but was not cast. A year later, he was cast in the role in the Denver and Los Angeles productions and went on to replace Josh Gad in the role on Broadway.


title: Jon Bass (actor)

text: In 2014, he played a small role in the HBO comedy series "Girls", and then had minor guest roles in "The Newsroom" and "House of Lies". Later in 2015, he was cast in a lead role in the Comedy Central's series "Big Time in Hollywood, FL", portraying Del Plimpton.


title: Jon Bass (actor)

text: In 2016, he played real-life attorney Philip Hirschkop in the historical film "Loving". In 2017, he appeared in the film "All Nighter". He played the role of C.J. Parker's significant other, Ronnie Greenbaum in the action comedy film "Baywatch", along with Zac Efron and Dwayne Johnson, and appeared in "Molly's Game", directed by Aaron Sorkin.


title: Jon Bass (actor)

text: Bass portrays a fictionalized version of Uber cofounder Garrett Camp opposite Joseph Gordon-Levitt in the drama series "Super Pumped" which premiered in 2022. The book is based on Mike Isaac's 2019 book of the same name.


title: The Beauty Inside (2015 film)

text: The Beauty Inside (; lit. "Beauty Inside") is a 2015 South Korean romantic comedy film based on the 2012 American social film "The Beauty Inside", about a man who wakes up every day in a different body, starring Han Hyo Joo. It is Baik's feature film debut, after a career directing commercials.


title: The Beauty Inside (2015 film)

text: One fateful day, on his eighteenth birthday, Woo-jin wakes up to see a face and body that is not his own. He is very shocked and confused, he confronts his mother with his new appearance and she is also shocked but tearfully accepts him for who he is. With the help of his mother (Mun Suk) and his best friend (Song-beck), Woo-jin is able to cope with his strange condition. Ever since this day Woo-jin, now a furniture designer, wakes up in a different body every day, regardless of age, gender and nationality. Sometimes he's a man, a woman, old, young, or even a foreigner. He can even speak different languages, depending on who he is for the day. He's the same person on the inside, but on the outside he's always someone new. Looking at a different face in the mirror every morning is hard for him to get used to.


title: The Beauty Inside (2015 film)

text: Every morning Woo-jin records himself on his computer, letting himself know who he was that day. And every morning he has to accustom himself to the changes of being a different person. He has to adjust to his new body, eyesight, voice etc. After many years of changing into different people Woo-jin has devised a system where he has all sorts of clothes and shoes to fit any and every type of body type, and of course different types of toiletries depending on if he is male or female. He also has a phoropter in order to test his vision and a Brannock foot measuring device to measure his feet so that he can choose the right-sized shoes.


title: The Beauty Inside (2015 film)

text: As a furniture designer Woo-jin is able to work in the privacy of his own home and avoid others from finding out his secret. He owns a furniture company named ALX that specializes on handcrafted furniture designed for each individual client. His best friend Song-beck works with him, taking care of sales and going to meet Woo-jin's clients in person.


title: The Beauty Inside (2015 film)

text: One day, Woo-jin develops a crush on a woman named Yi-soo who works in a furniture store. He begins to visit her everyday to see her and occasionally talk to her but she doesn’t realize this because he comes in as someone else each day. He waits until the right day when he is someone handsome (Park Seo-Joon) to finally approach her and ask her out on a date. He succeeds in asking her out and wants to continue seeing her as the same person. As a result he goes for several days without sleep in order to stay as the same person that first went out with Yi-soo. He inevitably fails to keep the same body due to sleep deprivation and decides to stop contacting Yi-soo because he does not want to reveal his secret to her. Woo-Jin becomes a temp where Yi-soo works and asks her to dinner. She is hesitant but goes with the female Woo-Jin to his house where he tells her who she/he is. She is shocked and it takes her some time to comprehend and accept Woo-jin for who he is on the inside.


title: The Beauty Inside (2015 film)

text: They remain together and devise a plan to reunite with each other every time Woo-jin transforms. When ever Woo-jin grabs Yi-soo’s hand she’ll know that it’s him. Or at least that's the idea. Yi-soo, after some time starts having difficulty with their relationship. She never truly knows who Woo-jin is and has to fully trust that the stranger grabbing her hand is Woo-jin. People begin to gossip about Yi-soo, saying that she is always going out with different men. This pushes her to a breaking point where she relies on medication to be able to cope with her stress, anxiety, and insomnia. In order to help her, Woo-jin decides to disappear from her life. Time goes by but Yi-soo never stops loving Woo-jin and is determined to find him.


title: The Beauty Inside (2015 film)

text: Woo-Jin finds out from his mother that his father had the same condition and that is why his father left them.


title: The Beauty Inside (2015 film)

text: Yi-soo is able to find Woo-jin once again in a different country (the Czech Republic). She confesses to him that she still loves him and wants to spend her life with him. After this confession Woo-jin proposes to Yi-soo and she accepts.


title: The Beauty Inside (2015 film)

text: "The Beauty Inside" pre-sold its distribution rights at the Cannes Film Market to 11 Asian countries, including Japan, Hong Kong, Macau, Taiwan, Singapore, Malaysia, Indonesia, Brunei and the Philippines.


title: The Beauty Inside (2015 film)

text: Well Go USA released the film theatrically on September 11, 2015 with a DVD and Blu-ray release set for February 2, 2016.


title: The Beauty Inside (2015 film)

text: The Beauty Inside earned a total gross of $14,291,242 USD from 2,057,896 total admissions. There was a total of 646 screenings for the film.


title: The Beauty Inside (2015 film)

text: On the website Rotten Tomatoes, the film had an approval rating of 70% based on 10 reviews, with a weighted average of 5.7/10. Another media aggregator website, Metacritic, weighted the film with an average score of 48 out of 100, based on 5 critics. Katie Walsh from the Los Angeles Times writes, “It’s satisfying, charming and surprising - a film that keeps its supernatural elements grounded in reality, with the focus on the spirituality of true love.


title: The Beauty Inside (2015 film)

text: In January 2017, it was announced that Emilia Clarke had been cast as the female lead in an upcoming American remake of the film, with Scott Neustadter and Michael H. Weber writing the script.


title: The Beauty Inside (2015 film)

text: In July 2018, it was announced that Seo Hyun-jin has been cast as the female lead in a Korean drama remake of the film, alongside Lee Min-ki.


title: Retaining wall

text: Retaining walls are relatively rigid walls used for supporting soil laterally so that it can be retained at different levels on the two sides.


title: Retaining wall

text: Retaining walls are structures designed to restrain soil to a slope that it would not naturally keep to (typically a steep, near-vertical or vertical slope). They are used to bound soils between two different elevations often in areas of terrain possessing undesirable slopes or in areas where the landscape needs to be shaped severely and engineered for more specific purposes like hillside farming or roadway overpasses. A retaining wall that retains soil on the backside and water on the frontside is called a seawall or a bulkhead.


title: Retaining wall

text: A wall for holding in place a mass of earth or the like, as at the edge of a terrace or excavation. A retaining wall is a structure designed and constructed to resist the lateral pressure of soil, when there is a desired change in ground elevation that exceeds the angle of repose of the soil.


title: Retaining wall

text: A basement wall is thus one kind of retaining wall. But the term usually refers to a cantilever retaining wall, which is a freestanding structure without lateral support at its top. These are cantilevered from a footing and rise above the grade on one side to retain a higher level grade on the opposite side. The walls must resist the lateral pressures generated by loose soils or, in some cases, water pressures.


title: Retaining wall

text: Every retaining wall supports a "wedge" of soil. The wedge is defined as the soil which extends beyond the failure plane of the soil type present at the wall site, and can be calculated once the soil friction angle is known. As the setback of the wall increases, the size of the sliding wedge is reduced. This reduction lowers the pressure on the retaining wall.


title: Retaining wall

text: The most important consideration in proper design and installation of retaining walls is to recognize and counteract the tendency of the retained material to move downslope due to gravity. This creates lateral earth pressure behind the wall which depends on the angle of internal friction (phi) and the cohesive strength (c) of the retained material, as well as the direction and magnitude of movement the retaining structure undergoes.


title: Retaining wall

text: Lateral earth pressures are zero at the top of the wall and – in homogeneous ground – increase proportionally to a maximum value at the lowest depth. Earth pressures will push the wall forward or overturn it if not properly addressed. Also, any groundwater behind the wall that is not dissipated by a drainage system causes hydrostatic pressure on the wall. The total pressure or thrust may be assumed to act at one-third from the lowest depth for lengthwise stretches of uniform height.


title: Retaining wall

text: It is important to have proper drainage behind the wall in order to limit the pressure to the wall's design value. Drainage materials will reduce or eliminate the hydrostatic pressure and improve the stability of the material behind the wall. Drystone retaining walls are normally self-draining.


title: Retaining wall

text: As an example, the International Building Code requires retaining walls to be designed to ensure stability against overturning, sliding, excessive foundation pressure and water uplift; and that they be designed for a safety factor of 1.5 against lateral sliding and overturning.


title: Retaining wall

text: Gravity walls depend on their mass(stone, concrete or other heavy material) to resist pressure from behind and may have a 'batter' setback to improve stability by leaning back toward the retained soil. For short landscaping walls, they are often made from mortarless stone or segmental concrete units (masonry units). Dry-stacked gravity walls are somewhat flexible and do not require a rigid footing.


title: Retaining wall

text: Earlier in the 20th century, taller retaining walls were often gravity walls made from large masses of concrete or stone. Today, taller retaining walls are increasingly built as composite gravity walls such as: geosynthetics such as geocell cellular confinement earth retention or with precast facing; gabions (stacked steel wire baskets filled with rocks); crib walls (cells built up log cabin style from precast concrete or timber and filled with granular material).


title: Retaining wall

text: Cantilevered retaining walls are made from an internal stem of steel-reinforced, cast-in-place concrete or mortared masonry (often in the shape of an inverted T). These walls cantilever loads (like a beam) to a large, structural footing, converting horizontal pressures from behind the wall to vertical pressures on the ground below. Sometimes cantilevered walls are buttressed on the front, or include a counterfort on the back, to improve their strength resisting high loads. Buttresses are short wing walls at right angles to the main trend of the wall. These walls require rigid concrete footings below seasonal frost depth. This type of wall uses much less material than a traditional gravity wall.


title: Retaining wall

text: Diaphragm walls are a type of retaining walls that are very stiff and generally watertight. Diaphragm walls are expensive walls, but they save time and space, and hence are used in urban constructions.


title: Retaining wall

text: Sheet pile retaining walls are usually used in soft soil and tight spaces. Sheet pile walls are driven into the ground and are composed of a variety of material including steel, vinyl, aluminum, fiberglass or wood planks. For a quick estimate the material is usually driven 1/3 above ground, 2/3 below ground, but this may be altered depending on the environment. Taller sheet pile walls will need a tie-back anchor, or "dead-man" placed in the soil a distance behind the face of the wall, that is tied to the wall, usually by a cable or a rod. Anchors are then placed behind the potential failure plane in the soil.


title: Retaining wall

text: Bored pile retaining walls are built by assembling a sequence of bored piles, followed by excavating away the excess soil.


title: Retaining wall

text: Depending on the project, the bored pile retaining wall may include a series of earth anchors, reinforcing beams, soil improvement operations and shotcrete reinforcement layer.


title: Retaining wall

text: This construction technique tends to be employed in scenarios where sheet piling is a valid construction solution, but where the vibration or noise levels generated by a pile driver are not acceptable.


title: Retaining wall

text: An anchored retaining wall can be constructed in any of the aforementioned styles but also includes additional strength using cables or other stays anchored in the rock or soil behind it. Usually driven into the material with boring, anchors are then expanded at the end of the cable, either by mechanical means or often by injecting pressurized concrete, which expands to form a bulb in the soil. Technically complex, this method is very useful where high loads are expected, or where the wall itself has to be slender and would otherwise be too weak.


title: Retaining wall

text: Soil nailing is a technique in which soil slopes, excavations or retaining walls are reinforced by the insertion of relatively slender elements – normally steel reinforcing bars. The bars are usually installed into a pre-drilled hole and then grouted into place or drilled and grouted simultaneously. They are usually installed untensioned at a slight downward inclination. A rigid or flexible facing (often sprayed concrete) or isolated soil nail heads may be used at the surface.


title: Retaining wall

text: A number of systems exist that do not consist of just the wall, but reduce the earth pressure acting directly on the wall. These are usually used in combination with one of the other wall types, though some may only use it as facing, "i.e.", for visual purposes.


title: Retaining wall

text: This type of soil strengthening, often also used without an outside wall, consists of wire mesh "boxes", which are filled with roughly cut stone or other material. The mesh cages reduce some internal movement and forces, and also reduce erosive forces.


title: Retaining wall

text: Gabion walls are free-draining retaining structures and as such are often built in locations where ground water is present. However, management and control of the ground water in and around all retaining walls is important.


title: Retaining wall

text: Mechanically stabilized earth, also called MSE, is soil constructed with artificial reinforcing via layered horizontal mats (geosynthetics) fixed at their ends. These mats provide added internal shear resistance beyond that of simple gravity wall structures. Other options include steel straps, also layered. This type of soil strengthening usually needs outer facing walls (S.R.W.'s – Segmental Retaining Walls) to affix the layers to and vice versa.


title: Retaining wall

text: The wall face is often of precast concrete units that can tolerate some differential movement. The reinforced soil's mass, along with the facing, then acts as an improved gravity wall. The reinforced mass must be built large enough to retain the pressures from the soil behind it. Gravity walls usually must be a minimum of 50 to 60 percent as deep or thick as the height of the wall, and may have to be larger if there is a slope or surcharge on the wall.


title: Retaining wall

text: Cellular confinement systems (geocells) are also used for steep earth stabilization in gravity and reinforced retaining walls with geogrids. Geocell retaining walls are structurally stable under self- weight and externally imposed loads, while the flexibility of the structure offers very high seismic resistance. The outer fascia cells of the wall can be planted with vegetation to create a green wall.


title: Mario Cristobal

text: Mario Manuel Cristobal (born September 24, 1970) is head football coach of the Miami Hurricanes football team at the University of Miami.


title: Mario Cristobal

text: Cristobal previously was the head football coach at Florida International University (FIU) from 2007 to 2012 and the University of Oregon from 2017 to 2021. He was an all-conference offensive tackle on the Miami Hurricanes football team that won national championships in 1989 and 1991. Mario is the first Cuban-American Head Coach in NCAA Division I college football history.


title: Mario Cristobal

text: Cristobal played high school football at Christopher Columbus High School in Miami and then went to play for the University of Miami, where he was a four-year letterman between 1988 and 1992. Cristobal played under Hall of Fame coach Jimmy Johnson and Dennis Erickson during the rise of the University of Miami as one of the nation's elite collegiate football programs. During his four seasons at the University of Miami, he was a member of two national championship-winning teams (1989 and 1991). In 1992, Cristobal earned First-team All-Big East Conference as an offensive tackle.


title: Mario Cristobal

text: Cristobal graduated from the University of Miami in 1993 with a Bachelor of Business Administration degree from the University of Miami School of Business and later earned a master's degree there in 2001. Cristobal is one of several University of Miami players from the late 1980s who appears in the documentary "The U", which premiered December 12, 2009 on ESPN, and chronicles the program's rapid ascent and national championships and the era's associated scandals that proved costly to it. The documentary drew 2.3 million viewers, making it then the most watched documentary in ESPN history.


title: Mario Cristobal

text: Following his collegiate career at the University of Miami, Cristobal signed a free agent contract with the Denver Broncos in 1994. He played for the Amsterdam Admirals of NFL Europe for two seasons, in 1995 and 1996, and then launched his collegiate coaching career.


title: Mario Cristobal

text: Cristobal's coaching career began at the University of Miami where he served as a graduate assistant under head football coach Butch Davis from 1998 to 2000. From 2001 to 2003, Cristobal was the tight ends and offensive line coach at Rutgers University under Greg Schiano. He returned to Miami to serve as tight ends coach and offensive line coach under Larry Coker for three seasons from 2004 to 2006.


title: Mario Cristobal

text: On December 19, 2006, Cristobal was named the second head coach in FIU's history. He also was the first Cuban-American head coach in Division I-A. Cristobal inherited a team with a winless record the previous season. He implemented a spread offense, and stated that he expected FIU to achieve success "faster than what we did at Rutgers", a process which "took five years".


title: Mario Cristobal

text: FIU struggled for most of his first season as head coach, losing their first eleven games. However, on December 1, the Golden Panthers finally broke a Football Bowl Subdivision-leading 23-game losing skid with a 38–19 victory over North Texas.


title: Mario Cristobal

text: His second season showed considerable signs of improvement. After three straight nonconference losses to Kansas, Iowa, and USF, the Golden Panthers under Cristobal pulled together an upset win against MAC opponent Toledo. The team used this momentum to build a three-game winning streak, defeating Sun Belt Conference opponents North Texas and MTSU before it continued on to finish with a 5–7 record. The team was two wins away from a bowl game before falling out of contention in the 2008 Shula Bowl against in-state rivals FAU in a 57–50 overtime loss, before finishing its season with a home victory over Western Kentucky.


title: Mario Cristobal

text: The third season under Cristobal came with high expectations after winning five games the previous year. The team regressed under his leadership and took a step back going 3–9 overall, with wins coming against North Texas, Western Kentucky, and Louisiana-Lafayette. During the offseason recruiting period, Cristobal was able to secure FIU's first ESPN 150 player, Willis Wright, from nearby Miami Springs High, the same school that produced T. Y. Hilton.


title: Mario Cristobal

text: After being predicted to finish sixth in the conference in the preseason by the Sun Belt Writers Association, Cristobal led his young Panthers team to their first Sun Belt Conference championship after four years at the helm. FIU, who had never had a winning season prior to the 2010 campaign, saw themselves atop the conference tied with Troy University who shared a similar 6–2 conference record. FIU did win their head-to-head matchup with Troy, 52–35. At the conclusion of the season FIU was selected to participate in their first bowl game, the Little Caesars Pizza Bowl. They won with a field goal in the closing seconds against Toledo, 34–32, after Toledo went for a two-point conversion to take the lead, 32–31. That win gave them a 7–6 record, their first ever winning record.


title: Mario Cristobal

text: Cristobal carries a reputation of being an excellent recruiter, setting up for his third season at FIU by putting together an impressive recruiting class of 23 student athletes, at least 20 of them from Florida. He wears a customary shirt and tie along with dress pants for each and every game to honor his idol, Joe Paterno. He was also named the fittest coach currently in the FBS according to an ESPN blog to which he confirmed on "The Dan Le Batard Show" on May 29, 2009. As of the 2009 season Mario Cristobal has retired the "shirt-and-tie" look and has opted to wear traditional collared shirts during games.


title: Mario Cristobal

text: On December 5, 2012, Cristobal was relieved of his position as head coach of the FIU football program. FIU Athletic Director Pete Garcia explained his reasoning for firing Cristobal as "He's done a very good job for this program, but we’ve gone backwards over the last year and a half. Over the last 22 games, we've gone 8-14." The decision by Garcia was heavily criticized as rash.


title: Mario Cristobal

text: After his dismissal as head coach at FIU, Cristobal was hired by Miami to serve as associate head coach and tight ends coach on January 10, 2013. Six weeks later, he was hired by Nick Saban to become Alabama's assistant head coach, offensive line coach, and recruiting coordinator.


title: Mario Cristobal

text: Cristobal was an elite recruiter at Alabama, finishing No. 1 in the national 247Sports.com composite rankings in each of his four seasons. He was named the National Recruiter of the Year by 247Sports in the 2015 cycle and in 2016 he was ranked as the nation's No. 2 recruiter in the country by 247Sports.


title: Mario Cristobal

text: Cristobal's Alabama offensive line was awarded as the nation's best in 2015, winning the inaugural Joe Moore Award given to the toughest, most physical line in the nation. His offensive line ranked in the top 25 nationally in sacks allowed in each of his first two seasons. Alabama's offensive lines produced standout players and NFL draft picks under Cristobal, including first-team All-American and 2015 first-round draft pick Ryan Kelly and 2014 freshman All-American Cam Robinson, who went on to win the Outland Trophy in Cristobal's final year with Alabama.


title: Mario Cristobal

text: In January 2017, Mario Cristobal joined Willie Taggart's staff at Oregon as offensive line coach, with additional duties as co-offensive coordinator (shared with quarterbacks coach Marcus Arroyo) and run game coordinator (along with running backs coach Donte Pimpleton). On December 5, 2017, he was given the title of interim head coach upon Willie Taggart's departure to Florida State; then, three days later, on Friday, December 8, 2017, Cristobal was officially announced as permanent head coach of the Ducks.


title: Mario Cristobal

text: After Taggart's abrupt departure, Cristobal fielded a team in 2018 that improved to 9-4 and won the Redbox Bowl (formerly the San Francisco Bowl) against Michigan State.


title: Mario Cristobal

text: In 2019, Cristobal was voted Pac-12 Coach of the Year by the Associated Press after going 11-2 during the regular season, winning the North division, beating Utah in the Conference Championship, and earning a trip to the Rose Bowl. That year, Cristobal and offensive line coach Alex Mirabal coached All-American Penei Sewell, who went on to win the Outland Trophy for best interior linemen in the country. The Oregon offensive line unit was a finalist for the 2019 Joe Moore Award for best overall group in the country. Oregon finished the post season with a Rose Bowl victory over the Wisconsin Badgers.


title: Mario Cristobal

text: In 2020, Cristobal again led Oregon to a Pac-12 Championship, posting a 4–2 record against a conference-only schedule due to the COVID-19 pandemic. Oregon would finish the season with a loss in the Fiesta Bowl to Iowa State.


title: Mario Cristobal

text: On December 6, 2021, Cristobal was named head coach of the University of Miami Hurricanes football team, replacing Manny Diaz. Cristobal signed a 10-year, $80 million contract with the Hurricanes.


title: Mario Cristobal

text: Cristobal is known for his accomplishments and skills as recruiter of elite collegiate football prospects. During his four seasons at Alabama, the Crimson Tide finished with the top-ranked recruiting class in each year of Cristobal's involvement with the program. Cristobal was a key part of the Tide’s recruiting dominance as the primary recruiter for multiple 5-star recruits and future first round NFL draft picks. In 2015. Cristobal was named the top recruiter in the nation by 247Sports, ESPN, Rivals and Scout.


title: Mario Cristobal

text: In 2017, Cristobal joined Willie Taggart’s staff at Oregon, where he helped the Ducks sign the 13th ranked recruiting class. After Taggart left Oregon for a head coaching job at Florida State, Cristobal replaced him as head coach of Oregon. In his three years as head coach, Oregon signed the 8th, 12th and 6th ranked recruiting classes, which included #1 overall recruit and future #5 overall draft pick Kayvon Thibodeaux.


title: Mario Cristobal

text: On December 6, 2021, Cristobal was named head coach at the University of Miami, his alma mater. Prior to commencement of the 2022 season, he was credited with a successful recruiting season that ranked as high as 16th nationally in independent assessment of the year's recruitment of high school football prospects. Among his recruitment successes was securing four of the top-ranked recruitment prospects of the year.


title: Mario Cristobal

text: After his football playing career ended, Cristobal went through a two-year application process to become a U.S. Secret Service agent and was offered a job in 1998. Then a first-year graduate assistant at the University of Miami, Cristobal said his goodbyes to fellow Hurricanes players but then abruptly changed his mind the following morning and chose instead to remain with collegiate football coaching.


title: Fairy ring

text: A fairy ring, also known as fairy circle, elf circle, elf ring or pixie ring, is a naturally occurring ring or arc of mushrooms. They are found mainly in forested areas, but also appear in grasslands or rangelands. Fairy rings are detectable by sporocarps (fungal spore pods) in rings or arcs, as well as by a necrotic zone (dead grass), or a ring of dark green grass. Fungus mycelium is present in the ring or arc underneath. The rings may grow to over in diameter, and they become stable over time as the fungus grows and seeks food underground.


title: Fairy ring

text: Fairy rings are the subject of much folklore and myth worldwide—particularly in Western Europe. They are often seen as hazardous or dangerous places, and linked with witches or the Devil in folklore. Conversely, they can sometimes be linked with good fortune.


title: Fairy ring

text: The mycelium of a fungus growing in the ground absorbs nutrients by secretion of enzymes from the tips of the hyphae (threads making up the mycelium). This breaks down larger molecules in the soil into smaller molecules that are then absorbed through the walls of the hyphae near their growing tips. The mycelium moves outward from the center, and when the nutrients in the center are exhausted, the center dies, thereby forming a living ring, from which the fairy ring arises.


title: Fairy ring

text: There are two theories regarding the process involved in creating fairy rings. One states that the fairy ring is begun by a spore from the sporocarpus. The underground presence of the fungus can also cause withering or varying colour or growth of the grass above. The second theory, which is presented in the investigations of Japanese scientists on the "Tricholoma matsutake" species, shows that fairy rings could be established by connecting neighbouring oval genets of these mushrooms. If they make an arc or a ring, they continuously grow about the centre of this object.


title: Fairy ring

text: One of the manifestations of fairy ring growth is a necrotic zone—an area in which grass or other plant life has withered or died. These zones are caused by the mycelia which, during a dry year, coat the roots of grasses and other herbs in meadows. After some time they are removed by biotic factors from the ground, at which stage a zone on the surface soil becomes visible. Patterns other than the basic ring or arc are also possible: circles, doubled arcs, sickle-shaped arcs, and other complicated formations are also formed by this process. Fungi can deplete the soil of readily available nutrients such as nitrogen, causing plants growing within the circle to be stressed which leads to plant discoloration. Some fungi also produce chemicals which act like hormones called gibberellins, which affect plant growth, causing rapid luxuriant growth.


title: Fairy ring

text: Long-term observations of fairy rings on Shillingstone Hill in Dorset, England, further suggested that the cycle depended on the continuous presence of rabbits. Chalky soils on higher elevations in the counties of Wiltshire and Dorset in southern England used to support many meadow-type fairy rings. Rabbits crop grass short in open areas and produce nitrogen-rich droppings. Mushrooms need more soil nitrogen than grass does. A ring can start from only a few spores from which the mycelium develops; the fruiting bodies of the mushrooms appearing only later when sufficient mycelial mass has been generated to support them. Subsequent generations of fungi grow only outward, because the parent generations have depleted their local nitrogen levels. Meanwhile, rabbits keep cropping the grass, but do not eat the fungi, allowing them to grow through their competition to tower, relatively, above the grass. By the time a circle of mushrooms reaches about in diameter, rabbit droppings have replenished the nitrogen levels near the centre of the circle, and a secondary ring may start to grow inside the first.


title: Fairy ring

text: Soil analysis of soil containing mycelium from a wood blewit ("Clitocybe nuda") fairy ring under Norway spruce ("Picea abies") and Scots pine ("Pinus sylvestris") in southeast Sweden yielded fourteen halogenated low molecular weight organic compounds, three of which were brominated and the others chlorinated. It is unclear whether these were metabolites or pollutants. Brominated compounds are unknown as metabolites from terrestrial fungi.


title: Fairy ring

text: There are two generally recognised types of fairy ring fungus. Those found in the woods are called "tethered", because they are formed by mycorrhizal fungi living in symbiosis with trees. Meadow fairy rings are called "free", because they are not connected with other organisms. These mushrooms are saprotrophic. The effects on the grass depend on the type of fungus that is growing; when "Calvatia cyathiformis" is growing in the area, grass grows more abundantly; however, "Leucopaxillus giganteus" causes the grass to wither.


title: Fairy ring

text: There are about 60 mushroom species which can grow in the fairy ring pattern. The best known is the edible Scotch bonnet ("Marasmius oreades"), commonly known as the fairy ring champignon.


title: Fairy ring

text: One of the largest rings ever found is near Belfort in northeastern France. Formed by "Infundibulicybe geotropa", it is thought to be about in diameter and over 700 years old. On the South Downs in southern England, "Calocybe gambosa" has formed huge fairy rings that also appear to be several hundred years old.


title: Fairy ring

text: A great deal of folklore surrounds fairy rings. Their names in European languages often allude to supernatural origins; they are known as "ronds de sorcières" ("witches' circles") in French, and "Hexenringe" ("witches' rings") in German. In German tradition, fairy rings were thought to mark the site of witches' dancing on Walpurgis Night, and Dutch superstition claimed that the circles show where the Devil set his milk churn. In Tyrol, folklore attributed fairy rings to the fiery tails of flying dragons; once a dragon had created such a circle, nothing but toadstools could grow there for seven years. European superstitions routinely warned against entering a fairy ring. French tradition reported that fairy rings were guarded by giant bug-eyed toads that cursed those who violated the circles. In other parts of Europe, entering a fairy ring would result in the loss of an eye. Fairy rings are associated with diminutive spirits in the Philippines.


title: Fairy ring

text: Western European traditions, including English, Scandinavian and Celtic, claimed that fairy rings are the result of elves or fairies dancing. Such ideas dated to at least the mediæval period; The Middle English term "elferingewort" ("elf-ring"), meaning "a ring of daisies caused by elves' dancing" dates to the 12th century. In his "History of the Goths" (1628), Swedish writer Olaus Magnus makes this connection, saying that fairy rings are burned into the ground by the dancing of elves. British folklorist Thomas Keightley noted that in Scandinavia in the early 19th century, beliefs persisted that fairy rings ("elfdans") arose from the dancing of elves. Keightley warned that while entering an "elfdans" might allow the interloper to see the elves—although this was not guaranteed—it would also put the intruder in thrall to their illusions.


title: Fairy ring

text: The folklores of Britain and Ireland contain a wealth of fairy lore, including the idea from which fairy rings take their name: the phenomena result from the dancing of fairies. In 19th-century Wales, where the rings are known as "cylch y Tylwyth Teg", fairies were almost invariably described as dancing in a group when encountered, and in Scotland and Wales in the late 20th century, stories about fairy rings were still common; some Welshmen even claimed to have joined a fairy dance. Victorian folklorists regarded fairies and witches as related, based in part on the idea that both were believed to dance in circles. These revels are particularly associated with moonlit nights, the rings becoming visible to mortals only the following morning. Local variants add other details. An early 20th-century Irish tradition says that fairies enjoy dancing around the hawthorn tree so that fairy rings often centre on one. One resident of Balquhidder, Scotland, said that the fairies sit on the mushrooms and use them as dinnertables, and a Welsh woman claimed that fairies used the mushrooms as parasols and umbrellas. Olaus Magnus in "Historia de Gentibus Septentrionalibus" wrote that the brightness of the fairy ring comes not from the dancing of the fairies, who harm it with their feet, but from Puck, who refreshes the grass. A Devon legend says that a black hen and chickens sometimes appear at dusk in a large fairy ring on the edge of Dartmoor. A Welsh and Manx variant current in the 1960s removes dancing from the picture and claims that fairy rings spring up over an underground fairy village. These associations have become linked to specific sites. For example, "The Pixies' Church" was a rock formation in Dartmoor surrounded by a fairy ring, and a stone circle tops Cader Idris in northern Wales, believed to be a popular spot for fairy dances.


title: Fairy ring

text: Many folk beliefs generally paint fairy rings as dangerous places, best avoided. American writer Wirt Sikes traces these stories of people trespassing into forbidden territory and being punished for it to the tale of Psyche and Eros. In it, Psyche is forbidden to view her lover, and when she does so, her palace disappears and she is left alone. Superstition calls fairy circles sacred and warns against violating them lest the interloper (such as a farmer with a plough) anger the fairies and be cursed. In an Irish legend recorded by Wilde, a farmer builds a barn on a fairy ring despite the protests of his neighbours. He is struck senseless one night, and a local "fairy doctor" breaks the curse. The farmer says that he dreamed that he must destroy the barn. Even collecting dew from the grass or flowers of a fairy ring can bring bad luck. Destroying a fairy ring is unlucky and fruitless; superstition says it would simply grow back.


title: Fairy ring

text: Numerous legends focus on mortals entering a fairy ring—and the consequences. One superstition is that anyone who steps into an empty fairy ring will die at a young age. A 20th-century tradition from Somerset calls the fairy ring a "galley-trap" and says that a murderer or thief who walks in the ring will be hanged. Most often, someone who violates a fairy perimeter becomes invisible to mortals outside and may find it impossible to leave the circle. Often, the fairies force the mortal to dance to the point of exhaustion, death, or madness. In Welsh tales, fairies actively try to lure mortals into their circles to dance with them. A tale from the Cambrian Mountains of Wales, current in the 19th century, describes a mortal's encounter with a fairy ring:


title: Fairy ring

text: Entering the ring on May Eve or Halloween night was especially dangerous. One source near Afon fach Blaen y Cae, a tributary of the Dwyfach, tells of a shepherd accidentally disturbing a ring of rushes where fairies are preparing to dance; they capture him and hold him captive, and he even marries one of them. In variants from Scotland recorded by Edwin Sidney Hartland in 1891, the ring is replaced by a cavern or an old mill.