number game: 18th and 19th centuries: …four volumes in 1694, his Récréations mathématique et physiques went through many editions; based on the works of Bachet, Mydorge, Leurechon, and Schwenter, it was later revised and enlarged by Montucla, then translated into English by Charles Hutton (1803, 1814) and again revised by Edward Riddle (1840, 1844).

number game: Pioneers and imitators: …name of van Etten, published Récréations mathématiques. This volume struck the popular fancy, passing through at least 30 editions before 1700, despite the fact that it was based largely on the work of Bachet, from whom he took the simpler problems, disregarding the more significant portions. Yet it did contain…

Lorenzo Valla: Valla responded with his “Recriminations Against Facio,” written in dialogue form and recalling the debates among the court humanists, to which the king loved to listen. This work also contains Valla’s celebrated emendations to the text of the Roman historian Livy.

testis: Spermatogenesis: …this process is known as recrudescence.

typhus: Epidemic typhus: …complication of epidemic typhus is Brill-Zinsser disease, or recrudescent typhus, in which mild symptoms of epidemic louse-borne typhus reappear after a latent period, sometimes of many years, in persons who at one time had contracted epidemic typhus. The disease was first noted when cases of typhus occurred in communities that…

Takeshita Noboru: …stocks, donations, and loans from Recruit, a Japanese telecommunications firm that had made large financial contributions to many politicians in the hope of obtaining governmental favours. Deepening public dissatisfaction with Takeshita’s involvement in the scandal prompted him on April 25, 1989, to announce his intention to resign. He left office…

English literature: Drama by Dryden and others: …key text here being Farquhar’s The Recruiting Officer (1706), in which the worlds of soldier and civilian are placed in suggestive proximity.

human nervous system: Reflex actions: …and immediate, some reflexes, called recruiting reflexes, can hardly be evoked by a single stimulus. Instead, they require increasing stimulation to induce a response. The reflex contraction of the bladder, for example, requires an increasing amount of urine to stretch the muscle and to obtain muscular contraction.

guerrilla warfare: Leaders and recruits: Such are the vicissitudes of guerrilla warfare that outstanding leadership is necessary at all levels if a guerrilla force is to survive and prosper. A leader must not only be endowed with intelligence and courage but must be buttressed by an almost fanatical belief…

human ear: Audiometry: …the threshold level is called recruitment. When the opposite ear has normal hearing, recruitment can be measured by the alternate binaural loudness balance test. The subject is asked to set the controls so that the loudness of the tone heard in the defective ear matches that of the tone heard…

metamorphic rock: …have altered their form (recrystallized) as a result of changes in their physical environment. Metamorphism comprises changes both in mineralogy and in the fabric of the original rock. In general, these alterations are brought about either by the intrusion of hot magma into cooler surrounding rocks (contact metamorphism) or…

glacier: …originates on land by the recrystallization of snow or other forms of solid precipitation and that shows evidence of past or present flow.

human digestive system: Rectum and anus: …a dilated portion called the rectal ampulla, which in front is in contact with the rear surface of the prostate in the male and with the posterior vaginal wall in the female. Posteriorly, the rectal ampulla is in front of the tip of the coccyx (the small bone at the…

colorectal cancer, disease characterized by uncontrolled growth of cells within the large intestine (colon) or rectum (terminal portion of the large intestine). Colon cancer (or bowel cancer) and rectal cancer are sometimes referred to separately. Colorectal cancer develops slowly but can spread to

human digestive system: Rectum and anus: …large crescentlike folds known as rectal valves are located in the rectal ampulla. These valves are caused by an invagination, or infolding, of the circular muscle and submucosa. The columnar epithelium of the rectal mucosa, innervated by the autonomic nervous system, changes to the stratified squamous (scalelike) type, innervated by…

reference frame: …another on the plane (rectangular coordinates), or (2) the length of a line with one end fixed at the origin and the other end at the moving point and the angle that the line makes with a fixed axis (polar coordinates). Motion in three dimensions can be described by…

rectifier, device that converts alternating electric current into direct current. It may be an electron tube (either a vacuum or a gaseous type), vibrator, solid-state device, or mechanical device. Direct current is necessary for the operation of many devices such as laptop computers, televisions,

quadrature: A similar process called rectification is used in determining the length of a curve. The curve is divided into a sequence of straight line segments of known length. Because the definite integral of a function determines the area under its curve, integration is still sometimes referred to as quadrature.

Mao Zedong: The road to power of Mao Zedong: …the time of the so-called Rectification Campaign of 1942–43. That program aimed at giving a basic grounding in Marxist theory and Leninist principles of party organization to the many thousands of new members who had been drawn into the party in the course of the expansion since 1937. But a…

Confucianism: The Five Classics: The social vision, contained in the Liji, shows society not as an adversarial system based on contractual relationships but as a community of trust with emphasis on communication. Society organized by the four functional occupations—the scholar, the farmer, the artisan, and the merchant—is, in the true…

Xunzi: …the technical, linguistically oriented “Rectification of Names” is liberally sprinkled with comments about the adverse social consequences attending the abuse and misuse of language. Among his other famous essays, “A Discussion of Music” became the classic work on the subject in China. Here, too, social issues are under consideration…

distilled spirit: The rectification still: Rectification is the process of purifying alcohol by repeatedly or fractionally distilling it to remove water and undesirable compounds. As mentioned above, a fermentation mixture primarily contains water and ethyl alcohol and distillation involves increasing the percentage of ethyl alcohol in the mixture. Water…

rectifier, device that converts alternating electric current into direct current. It may be an electron tube (either a vacuum or a gaseous type), vibrator, solid-state device, or mechanical device. Direct current is necessary for the operation of many devices such as laptop computers, televisions,

mathematics: The Elements: …is inferred from that of rectilinear figures; for a particular curved figure, a sequence of rectilinear figures is considered in which succeeding figures in the sequence become continually closer to the curved figure; the particular method used by Euclid derives from Eudoxus. The solid constructions in Book XIII derive from…

locomotion: Rectilinear locomotion: Unlike the three preceding patterns of movement, in which the body is thrown into a series of curves, in rectilinear locomotion in snakes the body is held relatively straight and glides forward in a manner analogous to the pedal locomotion of snails. The…

linear motion, motion in one spatial dimension. According to Newton’s first law (also known as the principle of inertia), a body with no net force acting on it will either remain at rest or continue to move with uniform speed in a straight line, according to its initial condition of motion. In

Claro Mayo Recto was a statesman and leader of the “Filipino-first” movement that attacked U.S. “neo-colonialism” in the Philippines. Recto graduated with a law degree from the University of Santo Tomás in 1913. He was elected in 1919 to the Philippine House of Representatives and served for three

rectocele, disorder in which the rectum bulges into the back wall of the vagina. It is caused when the muscles and connective tissues supporting the rectum and back wall of the vagina are weakened, usually due to repeated childbirth or to aging, and the rectum sags until it abuts the vagina. A

Louis Auchincloss: Others, notably The Rector of Justin (1964) and Diary of a Yuppie (1987), are studies of a single character, often from many points of view. Auchincloss frequently linked the stories in his collections by theme or geography, as in, for example, Tales of Manhattan (1967) and Skinny…

Dubrovnik: The contemporary city: The Rector’s Palace, dating from the 15th century and built in the late Gothic style, was the seat of government of the Dubrovnik Republic and is a masterpiece of Dalmatian architecture. Other notable structures include numerous fortresses (such as Lovrijenac, which sits atop a cliff); a…

clay mineral: Interstratified clay minerals: , rectorite (dioctahedral mica/montmorillonite), tosudite (dioctahedral chlorite/smectite), corrensite (trioctahedral vermiculite/chlorite), hydrobiotite (trioctahedral mica/vermiculite), aliettite (talc/saponite), and kulkeite (talc/chlorite). Other than the ABAB

Lewis Carroll: Early life: 1850, mostly unpublished), The Rectory Umbrella (1850–53), and Mischmasch (1853–62; published with The Rectory Umbrella in 1932).

bird: Feathers: …wing (remiges) and tail (rectrices) and their coverts function in flight. Contour feathers grow in tracts (pterylae) separated by bare areas (apteria) and develop from follicles in the skin.

bird: Feathers: …wing (remiges) and tail (rectrices) and their coverts function in flight. Contour feathers grow in tracts (pterylae) separated by bare areas (apteria) and develop from follicles in the skin.

rectum, terminal segment of the digestive system in which feces accumulate just prior to discharge. The rectum is continuous with the sigmoid colon and extends 13 to 15 cm (5 to 6 inches) to the anus. A muscular sheet called the pelvic diaphragm runs perpendicular to the juncture of the rectum and

abdominal muscle: …midline, where they surround the rectus abdominis in a sheath before they meet the fibres from the opposite side at the linea alba. Strength is developed in these rather thin walls by the crisscrossing of fibres. Thus, the fibres of the external oblique are directed downward and forward, those of…

space perception: Cues from the eye muscles: …the ciliary muscles and the rectus muscles. The ciliary effect is called accommodation (focusing the lens for near or far vision), and the rectus effect is called convergence (moving the entire eyeball). Each of these muscle systems contracts as a perceived object approaches. The effect of accommodation in this case…

Recuay, pre-Columbian culture and site near present-day Recuay in the Callejón de Huaylas Valley of the northern highlands of Peru. Recuay culture dates to the Early Intermediate Period (c. 200 bc–ad 600) and was contemporaneous with the Moche culture of the neighbouring northern coast. Recuay is

furniture: 19th century: …were incorporated and propagated in Recueil de décorations intérieures (1801 and 1812; “Collection of Interior Decoration”).

Fyodor Fyodorovich Martens: …most ambitious work of editing, Recueil des traités et conventions conclus par la Russie . . . (15 vol., 1874–1909), contains not only the texts of treaties between Russia and other countries but also histories (based on unpublished Russian documents) of the diplomatic conditions necessitating the treaties. It was printed…

Spanish literature: Theatre: …exponents of social-protest theater include José Martín Recuerda, whose subject matter is hypocrisy, cruelty, and repression in Andalusian towns and villages, and José María Rodríguez Méndez, a novelist, story writer, essayist, and critic whose dramas expose the plight of common people, especially the youth, portrayed as victims (soldiers recruited to…

Jura Mountains: … (5,636 feet [1,718 metres]) and Le Reculet (5,633 feet [1,717 metres]), both in France, and Mount Tendre and La Dôle, both more than 5,500 feet (1,680 metres), in Switzerland. Toward the northeast and along the outer ridges of the arc, the elevations of the crests are lower.

bicycle: Basic types: Recumbents are often recommended for riders who are uncomfortable on traditional bicycles. There is no standard design, but the wheelbase is usually extended and the front wheel reduced in size. The design reduces wind resistance. Other variations include the tricycle, which has two rear wheels…

fold: A recumbent fold has an essentially horizontal axial plane. When the two limbs of a fold are essentially parallel to each other and thus approximately parallel to the axial plane, the fold is called isoclinal.

bicycle: Basic types: Recumbent frames allow the rider to sit low to the ground in a slightly reclined position, with the legs driving cranks attached to a horizontal tube. Recumbents are often recommended for riders who are uncomfortable on traditional bicycles. There is no standard design, but the…

industrial glass: The melting chamber: …type of furnace is the recuperative furnace, in which the flue gases continuously exchange heat with the incoming combustible mixture through metal or ceramic partitions. Yet another means of improving combustion efficiency is to use oxygen-rich air or even pure oxygen. The use of oxygen is a particularly important technology,…

hydrologic sciences: Precipitation: …of this frequency, or the recurrence interval of the rainfall from the sample of available data, is a statistical problem generally involving the assumption of a particular probability distribution to represent the characteristics of rainfalls. Such analyses must assume that this distribution is not changing over time, even though it…

combinatorics: Recurrence relations and generating functions: If fn is a function defined on the positive integers, then a relation that expresses fn + k as a linear combination of function values of integer index less than n + k, in which a fixed constant in the…

pregnancy: Abortion: …are said to suffer from recurrent abortion. An infected abortion is an abortion associated with infection of the genital organs.

coronal mass ejection: Properties: Recurrent storms are caused by features on the Sun called coronal holes that live for several months and generate corotating interaction regions (disturbances in the solar wind where the fast solar wind from the coronal holes catches up with the slow solar wind) that repeat…

number game: Number patterns and curiosities: On the other hand, a recurring digital invariant is illustrated by:

history of logic: Theory of recursive functions and computability: In addition to proof theory and model theory, a third main area of contemporary logic is the theory of recursive functions and computability. Much of the specialized work belongs as much to computer science as to logic. The origins…

recursive function, in logic and mathematics, a type of function or expression predicating some concept or property of one or more variables, which is specified by a procedure that yields values or instances of that function by repeatedly applying a given relation or routine operation to known

history of logic: Theory of recursive functions and computability: In addition to proof theory and model theory, a third main area of contemporary logic is the theory of recursive functions and computability. Much of the specialized work belongs as much to computer science as to logic. The origins…

Alejo Carpentier: …El recurso del método (1974; Reasons of State), and El arpa y la sombra (1979; The Harp and the Shadow). In the latter, the protagonist is Christopher Columbus, involved in a love affair with the Catholic Queen Isabella of Castile. Carpentier’s last novel, La consagración de la primavera (1979; “The…

avocet, any of several large shorebirds belonging to the genus Recurvirostra, family Recurvirostridae. Avocets have boldly contrasting plumage, long bluish legs, and a long black bill upturned at the tip. They inhabit fresh and salt marshes that have areas of open shallow water and mud flats, and

avocet: The slightly larger American avocet (R. americana), which is about 45 cm (18 inches) long (including the bill), differs chiefly in having the head and neck pinkish brown in breeding season, white in winter. It nests in western North America and winters from California and Texas to Guatemala.…

avocet: The Andean avocet (R. andina), with a primarily white body, black back and wings, is confined to alkali lakes of the high Andes. The red-necked, or Australian, avocet (R. novaehollandiae) is black and white with red-brown head and neck.

avocet: The Old World avocet (R. avosetta) has the crown and hindneck black, the wings black and white. It breeds in central Asia and in scattered localities in Europe. Many winter in Africa’s Rift Valley. The slightly larger American avocet (R. americana), which is about 45 cm…

Recurvirostridae, bird family (order Charadriiformes) composed of seven species of moderately large (29–48 cm [11–19 inches] ) wading birds characterized by extremely long legs, a relatively small head, and a long, slender bill. Better-known members of the family include the avocet, ibisbill, and

Gunpowder Plot: Aftermath and cultural legacy: …the rigorous enforcement of the recusancy law, which fined those who refused to attend Anglican services. In January 1606 Parliament established November 5 as a day of public thanksgiving. The day, known as Guy Fawkes Day, is still celebrated with bonfires, fireworks, and the carrying of “guys” through the streets.

recusant, English Roman Catholic from the period about 1570 to 1791 who refused to attend services of the Church of England and thereby committed a statutory

Troy: Medieval legends: …be printed in English as The Recuyell of the Histories of Troye (c. 1474).

Christian Marclay: …extremity of Marclay’s manipulations—for his Recycled Records (1980–86) series, he sliced apart vinyl and reassembled the shards to form new sequences of sound—was considered innovative. As an avant-garde deejay (or “turntablist”) in New York City in the 1980s, he collaborated with such musicians as John Zorn and the band Sonic…

ZZ Top: With Recycler (1990), ZZ Top scaled back the electronics. Though the massive following of the band’s 1980s commercial peak had dissipated, subsequent albums such as Antenna (1994) and La Futura (2012) still commanded a substantial audience, and XXX (1999), which commemorated 30 years of playing together,…

particle accelerator: Proton storage rings: …ring and then to the Recycler ring (see below), where they were stored until there were a sufficient number for injection into the Main Injector. This provided acceleration to 150 GeV before transfer to the Tevatron. Protons and antiprotons were accelerated simultaneously in the Tevatron to about 1 TeV, in…

recycling, recovery and reprocessing of waste materials for use in new products. The basic phases in recycling are the collection of waste materials, their processing or manufacture into new products, and the purchase of those products, which may then themselves be recycled. Typical materials that

King Crimson: Formation and early success: …and Bible Black (1974), and Red (1974).

Taylor Swift: Kanye West incident at the VMAs, Red, and 1989: …her next collection of songs, Red (2012). While she remained focused on the vagaries of young love, her songwriting reflected a deepened perspective on the subject, and much of the album embraced a bold pop-rock sound. In its first week on sale in the United States, Red sold 1.2 million…

quark: Quark colours: The colours red, green, and blue are ascribed to quarks, and their opposites, antired, antigreen, and antiblue, are ascribed to antiquarks. According to QCD, all combinations of quarks must contain mixtures of these imaginary colours that cancel out one another, with the resulting particle having no net…

Krzysztof Kieślowski: … (1994; White), and Rouge (1994; Red); respectively, they explored the themes of liberty, equality, and fraternity. The films were released several months apart and, although each can stand on its own, they were designed to be seen as a single entity. One theme, the frailty of human relations, emerged from…

Michael Grandage: He later directed Red, a drama that centres on painter Mark Rothko and his fictional assistant. It premiered at the Donmar in 2009 and made its Broadway debut the following year. Grandage won the Tony Award for best direction of a play for it in 2010. That same…

Richard Dreyfuss: …villain in the action comedy RED. Dreyfuss’s roles from 2018 included a man courting a successful judge (played by Candice Bergen) in the romantic comedy Book Club and a Russian gangster in Cuba Gooding, Jr.’s directorial debut, Bayou Caviar. The Last Laugh and Astronaut were among

red, in physics, the longest wavelength of light discernible to the human eye. It falls in the range of 620–750 nanometres in the visible spectrum. In art, red is a colour on the conventional colour wheel, located between violet and orange and opposite green, its complementary colour. Red was the

Poland: The January 1863 uprising and its aftermath: Subsequently called the Reds, these radicals acted as a pressure group on the Agricultural Society and staged demonstrations commemorating Polish patriots or historic events. In 1861, the year of the peasant emancipation decree in the Russian Empire, demonstrators in Warsaw clashed with Russian troops, and several were killed…

Taylor Swift: Reputation, Lover, Folklore, Evermore, and controversies: …2021 Fearless (Taylor’s Version) and Red (Taylor’s Version) appeared. They were remakes of earlier albums with several previously unreleased tracks. In July 2023 Swift released Speak Now (Taylor’s Version), followed by 1989 (Taylor’s Version) in October that same year.

Anthony Hopkins: Later movie and television roles: In the ensemble action comedy Red 2 (2013) Hopkins stole scenes as an eccentric nuclear scientist, and in the biblical drama Noah (2014) he dispensed wisdom to the title character as Methuselah. In 2015 he starred in the crime drama Solace, playing a doctor who is assisting in the hunt…

abalone: …largest abalone is the 30-cm red abalone (H. rufescens) of the western coast of the United States. H. rufescens and several other species are raised commercially in abalone farms, particularly in Australia, China, Japan, and along the western coast of the United States. Commercial fisheries for abalones exist in California,…

acouchy: The coarse fur of the red acouchy (Myoprocta acouchy) is dark chestnut red or orange on the sides of the body and legs and black or dark red on the rump; underparts range from dark red to orange. Upperparts of the green acouchy (M. pratti) are covered by grizzled fur,…

admiral: The migratory red admiral (Vanessa atalanta), placed in the subfamily Nymphalinae, is widespread in Europe, Scandinavia, North America, and North Africa and feeds on stinging nettles. The western, or Weidemeyer’s, admiral (Limenitis weidemeyerii) is found in the western United States. The

alder: Major species: …North American alders are the red alder (Alnus rubra), a tall tree whose leaves have rusty hairs on their lower surfaces; the white, or Sierra, alder (A. rhombifolia), an early-flowering tree with orange-red twigs and buds; the gray, or speckled, alder (A. incana), a small shrubby tree, often with conspicuous…

Stanley Kubrick: Breakthrough to success: …Peter George (on whose novel Red Alert it was based). In the planning stages, Kubrick sought to treat the material seriously, but he kept finding himself gravitating toward farce and eventually gave in to that impulse while still managing to powerfully convey the horrible prospect of nuclear annihilation. He made…

red algae, (division Rhodophyta), any of about 6,000 species of predominantly marine algae, often found attached to other shore plants. Their morphological range includes filamentous, branched, feathered, and sheetlike thalli. The taxonomy of the group is contentious, and organization of the

Amaranthaceae: Major genera and species: …wheat, or love-lies-bleeding (Amaranthus caudatus), red amaranth (A. cruentus), and quinoa (Chenopodium quinoa)—are high-protein pseudo-grain crops of interest to agricultural researchers. Quinoa in particular, touted as a health food, grew in popularity worldwide during the early 21st century.

Gerrit Thomas Rietveld: …time he created his famous red-and-blue armchair, which, in its emphasis on geometry and in its use of primary colours, was a realization of de Stijl principles (see photograph). In 1921 he designed a small Amsterdam jewelry shop, one of the first examples of the application of these principles to…

The Red and the Black, novel by Stendhal, published in French in 1830 as Le Rouge et le noir. The novel, set in France during the Second Restoration (1815–30), is a powerful character study of Julien Sorel, an ambitious young man who uses seduction as a tool for advancement. The Red and the Black

Iris Murdoch: …as A Severed Head (1961), The Red and the Green (1965), The Nice and the Good (1968), The Black Prince (1973), Henry and Cato (1976), The Sea, the Sea (1978, Booker Prize), The Philosopher’s Pupil (1983), The Good Apprentice (1985), The

Ogata Kōrin: …this period is the screen Red and White Plum Blossoms (c. 18th century). In this work, Kōrin’s sense of flat decorative design and his feeling for nature, combined with an emphasis on an abstract colour pattern, are seen at their very best. Although he died at the age of 59,…

angel’s trumpet: Species: insignis, red angel’s trumpet (B. sanguinea), B. versicolor, and B. vulcanicola were variously distributed in the Andes region of South America, ranging from Colombia to northern Chile. Angel’s tears (B. suaveolens) was native to the Atlantic coast of southeastern

Angus: …breed, a strain known as Red Angus has gained in popularity since the mid-20th century, particularly for purposes of outcrossing and crossbreeding. The Brangus, developed from Brahman and Angus stocks, is notable for its resistance to heat.

Red Army, Soviet army created by the Communist government after the Bolshevik Revolution of 1917. The name Red Army was abandoned in 1946. The Russian imperial army and navy, together with other imperial institutions of tsarist Russia, disintegrated after the outbreak of the Russian Revolution of

People’s Liberation Army, Unified organization of China’s land, sea, and air forces. It is one of the largest military forces in the world. The People’s Liberation Army traces its roots to the 1927 Nanchang Uprising of the communists against the Nationalists. Initially called the Red Army, it grew

Red Army Faction (RAF), West German radical leftist group formed in 1968 and popularly named after two of its early leaders, Andreas Baader (1943–77) and Ulrike Meinhof (1934–76). The group had its origins among the radical elements of the German university protest movement of the 1960s, which

Red Army Faction (RAF), West German radical leftist group formed in 1968 and popularly named after two of its early leaders, Andreas Baader (1943–77) and Ulrike Meinhof (1934–76). The group had its origins among the radical elements of the German university protest movement of the 1960s, which

Jacqueline Woodson: Writing career: …including Another Brooklyn (2016) and Red at the Bone (2019). Another Brooklyn follows the main character as she reminisces about growing up in New York. Red at the Bone examines the decisions and experiences of two families from different social classes. Woodson’s books for young children, for which she worked…

avadavat, (species Amandava, or Estrilda, amandava), plump, 8-centimetre- (3-inch-) long bird of the waxbill (q.v.) group (order Passeriformes), a popular cage bird. The avadavat is abundant in marshes and meadows of southern Asia (introduced in Hawaii). The male, in breeding plumage, is bright red

John Huston: Films of the 1950s of John Huston: Crane’s literary classic The Red Badge of Courage. Real-life World War II hero Audie Murphy starred in this story of a young Union soldier who deserts his company during the American Civil War. With the Korean War raging, MGM executives felt that the film’s antiwar message was too…

The Red Badge of Courage, novel of the American Civil War by Stephen Crane, published in 1895 and considered to be his masterwork because of its perceptive depiction of warfare and of a soldier’s psychological turmoil. Crane was 25 years old and had no personal experience of war when he wrote the

Rainforest Regeneration in Panama: …are tree species such as Manilkara, almendro, and the suicide tree, characterized by slower growth and lower light requirements, with the capacity for extended persistence under low light conditions. Such trees tend toward high wood densities, relatively delayed attainment of reproductive status, and larger, often animal-dispersed seeds. They also have…

baneberry: The red baneberry, or red cohosh (A. rubra), native to North America, closely resembles A. spicata. Its fruits are red or ivory. The roots and berries of baneberry plants contain irritant resins that have a cathartic action and produce vomiting. The plants are useful subjects for…