knee-jerk reflex, sudden kicking movement of the lower leg in response to a sharp tap on the patellar tendon, which lies just below the kneecap. One of the several positions that a subject may take for the test is to sit with knees bent and with one leg crossed over the other so that the upper foot

fungus: Annotated classification: Order Patellariales (incertae sedis; not placed in any subclass) Parasitic and saprotrophic; flask-shaped (perithecium-like) fruiting bodies; example genus is Patellaria. Order Trypetheliales (incertae sedis; not placed in any subclass) Forms lichen; most have hyaline ascospores. Class

gastropod: Classification: …rocky shallow waters (Acmaeidae and Patellidae). Superfamily Trochacea Small to large spiral shells in shallow to deep ocean waters, often brightly coloured, with or without heavy shell ornamentation; Trochidae (top shells), Turbinidae (turban shells), and Phasianellidae (pheasant shells).

gastropod: Classification: ) Superfamily Patelliformia Brackish water or marine limpets with (Siphonariidae) gill-like structures or with a lung (Gadinidae). Superfamily Amphibolacea Operculum present; shell conical; with pulmonary cavity; brackish water; burrow in sand; 1 family. Superfamily

Carole Pateman is a British political scientist and educator known for her contribution to democratic theory and feminist political theory. After leaving school at 16 years of age and working in lesser clerical positions, Pateman decided to complete her education and entered Ruskin College in

Joachim Patinir was a Flemish painter, the first Western artist known to have specialized in landscape painting. Little is known of his early life, but his work reflects an early knowledge of the painting of Gerard David, the last of the Early Netherlandish painters. He may have studied under

patent, a government grant to an inventor of the right to exclude others from making, using, or selling an invention, usually for a limited period. Patents are granted for new and useful machines, manufactured products, and industrial processes and for significant improvements of existing ones.

anchor: The stockless anchor (Figure 2), which was patented in England in 1821, came into wide use principally because of its ease of handling and stowing. The crown, arms, and flukes of a stockless anchor are cast in one piece and can pivot slightly from side to…

patent: The 1970 Patent Cooperation Treaty simplified the filing of patent applications on the same invention in different countries by providing centralized filing procedures and a standardized application format. The European Patent Convention, which was implemented in 1977, created a European Patent Office that can issue a European…

patent ductus arteriosus, congenital heart defect characterized by the persistence of the ductus arteriosus, a channel that shunts blood between the pulmonary artery and the aorta. Normally, after birth the pulmonary artery carries blood depleted of oxygen and laden with carbon dioxide from the

cereal processing: Milling: …the mill, is often called patent flour. It has very low mineral (or ash) content and is remarkably free from traces of branny specks and other impurities. The bulk of the approximately 72 percent released is suited to most bread-making purposes, but special varieties are needed for some confectionery purposes.…

patent, a government grant to an inventor of the right to exclude others from making, using, or selling an invention, usually for a limited period. Patents are granted for new and useful machines, manufactured products, and industrial processes and for significant improvements of existing ones.

shoe: Materials: Patent leather, usually made from cattle hide, is given a hard, glossy surface finish. Suede is made from any of several leathers (calf, kid, or cattle hide) by buffing the inner surface to produce a napped finish.

navigation: Distance and speed measurements: …Humphry Cole, invented the so-called patent log, in which a vaned rotor was towed from the stern, and its revolutions were counted on a register. Logs of this kind did not become common until the mid-19th century, when the register was mounted on the aft rail, where it could be…

Bertha Benz: Invention of the Patent-Motorwagen: Benz struggled to market his Patent-Motorwagen, but his wife knew the value of the invention. During the application process, she could not legally apply for the patent alongside her husband despite her financial and practical engineering contributions.

National Portrait Gallery: …building, now known as the Donald W. Reynolds Center for American Art and Portraiture, reopened in 2006 after undergoing renovations to emphasize its strongest architectural features, including porticos, vaulted ceilings, and a curving double staircase.

energy conversion: Windmills: These so-called patent sails, however, found acceptance only in England and northern Europe.

patent theatre, any of several London theatres that, through government licensing, held a monopoly on legitimate dramatic production there between 1660 and 1843. In reopening the theatres that had been closed by the Puritans, Charles II issued Letters Patent to Thomas Killigrew and William Davenant

patent troll, pejorative term for a company, found most often in the American information technology industry, that uses a portfolio of patents not to produce products but solely to collect licensing fees or settlements on patent infringement from other companies. The term patent troll arose in the

shape-note hymnal, American hymnal incorporating many folk hymns and utilizing a special musical notation. The seven-note scale was sung not to the syllables do–re–mi–fa–sol–la–ti but to a four-syllable system carried with them by early English colonists: fa–sol–la–fa–sol–la–mi. Differently shaped

David Lloyd George: Early life: …on newly constructed ships; the Patents and Designs Act (1907), preventing foreign exploitation of British inventions; and the Port of London Act (1908), setting up the Port of London Authority. He also earned a high reputation by his patient work in settling strikes. He suffered a cruel bereavement in November…

Mithraism: Worship, practices, and institutions: …of (and to) the Sun; pater, Father. To each rank belonged a particular mask (Raven, Persian, Lion) or dress (Bridegroom). The rising of the Mithraist in grade prefigured the ascent of the soul after death. The series of the seven initiations seems to have been enacted by passing through seven…

parent: …a biological father, and a “pater” is a social one.

Lord’s Prayer, Christian prayer that, according to tradition, was taught by Jesus to his disciples. It appears in two forms in the New Testament: the shorter version in the Gospel According to Luke (11:2–4) and the longer version, part of the Sermon on the Mount, in the Gospel According to Matthew

fetial: Another member, called the pater patratus, served as the group’s representative. Upon reaching the border of the offending state, the pater patratus first announced his mission and addressed a prayer to Jupiter in which he affirmed the justness of his errand. Crossing the border, he repeated the same form…

pater patriae, in ancient Rome, a title originally accorded (in the form parens urbis Romanae, or “parent of the Roman city”) to Romulus, Rome’s legendary founder. It was next accorded to Marcus Furius Camillus, who led the city’s recovery after its capture by the Gauls (c. 390 bc). The title was

Walter Pater was an English critic, essayist, and humanist whose advocacy of “art for art’s sake” became a cardinal doctrine of the movement known as Aestheticism. Pater was educated at King’s School, Canterbury, and at Queen’s College, Oxford, where he studied Greek philosophy under Benjamin

Walter Pater was an English critic, essayist, and humanist whose advocacy of “art for art’s sake” became a cardinal doctrine of the movement known as Aestheticism. Pater was educated at King’s School, Canterbury, and at Queen’s College, Oxford, where he studied Greek philosophy under Benjamin

Seattle Seahawks: …in 1978, earning head coach Jack Patera NFL Coach of the Year honors. The early Seahawks teams were led by quarterback Jim Zorn, running back Curt Warner, and wide receiver Steve Largent, who retired as the NFL’s all-time leading receiver and in 1995 was the first Seahawk inducted into the…

Velleius Paterculus was a Roman soldier, political figure, and historian whose work on Rome is a valuable if amateurish source for the reigns of Augustus and Tiberius. Velleius’s father was of equestrian status, and his mother belonged to a distinguished Campanian family. He served as military

inheritance: Roman law: … ruled by its head, the paterfamilias, to whom his wife, his slaves, and possibly several generations of his descendants were subject and in whom title to all property was vested, so that a son or any other member of the house, even as an adult, did not own anything until…

Russian literature: The Kievan period: The Kievo-Pechersky paterik (The Paterik of the Kievan Caves Monastery), closely related to hagiography, collects stories from the lives of monks, along with other religious writings. A saint’s life of quite a different sort, Zhitiye Aleksandra Nevskogo (“Life of Alexandr Nevsky”) (d. 1263), celebrates a pious warrior prince.…

lamp shells: Annotated classification: Order Paterinida Shell with phosphate, rounded or elliptical; pedicle opening partly closed by cover called homeodeltidium; dorsal valve similar to the ventral but with a convex homeochilidium; 7 genera; Early Cambrian to mid-Ordovician. Class Articulata Shells articulate by means of teeth and sockets; shells always calcareous;…

Paterna ware, tin-glazed earthenware produced in the 14th and 15th centuries at Paterna, near Valencia, in eastern Spain. Although pottery was produced in Paterna as early as the 12th century under the Almohads, it was not famous until the reign of the Naṣrids (1230–1492), the last Islāmic dynasty

paternalism, attitude and practice that are commonly, though not exclusively, understood as an infringement on the personal freedom and autonomy of a person (or class of persons) with a beneficent or protective intent. Paternalism generally involves competing claims between individual liberty and

human genetic disease: Imprinted gene mutations: …from the father, and so-called paternally imprinted genes are generally expressed only when inherited from the mother. The disease gene associated with Prader-Willi syndrome is maternally imprinted, so that although every child inherits two copies of the gene (one maternal, one paternal), only the paternal copy is expressed. If the…

blood group: Paternity testing: …a male is not the father of a particular child. Since the red cell antigens are inherited as dominant traits, a child cannot have a blood group antigen that is not present in one or both parents. For example, if the child in question belongs to group A and both…

Sweden: Labour and taxation: …known for its maternity and parental leave schemes that allow up to 13 months’ leave at about four-fifths of their pay. Employers pay additional fees of more than two-fifths of gross wages for statutory social benefits, including pensions. As of 1999, a new general pension system was introduced, which allowed…

fingerprint: …test has been used in paternity testing as well as in forensics.

Barry Levinson: …Ponzi scheme in history; and Paterno (2018), about Penn State football coach Joe Paterno, whose legacy was tarnished by a sex-abuse scandal that occurred during his tenure. In 2021 Levinson directed several episodes of the miniseries Dopesick, about the opioid crisis in the United States. He

Paternò, town, eastern Sicily, Italy, situated at the southwestern foot of Mount Etna, overlooking the Simeto River, just northwest of Catania. Paternò is believed to occupy the site of the ancient Siculian town of Hybla Major or Hybla Geleatis. Paternò suffered heavily from Allied bombing in World

Joe Paterno was an American collegiate gridiron football coach, who, as head coach at Pennsylvania State University (1966–2011), was the winningest major-college coach in the history of the sport, with 409 career victories, but whose accomplishments were in many ways overshadowed by a sex-abuse

Joe Paterno was an American collegiate gridiron football coach, who, as head coach at Pennsylvania State University (1966–2011), was the winningest major-college coach in the history of the sport, with 409 career victories, but whose accomplishments were in many ways overshadowed by a sex-abuse

glacial landform: Paternoster lakes: Some glacial valleys have an irregular, longitudinal bedrock profile, with alternating short, steep steps and longer, relatively flat portions. Even though attempts have been made to explain this feature in terms of some inherent characteristic of glacial flow, it seems more likely that…

Jim Jarmusch: …he also wrote and directed Paterson, which presents a week in the life of a bus driver. The contemplative dramedy received widespread acclaim. Jarmusch then offered his wry take on the zombie movie genre with The Dead Don’t Die (2019).

Paterson, city, seat (1837) of Passaic county, northeastern New Jersey, U.S., situated on the Passaic River, 11 miles (18 km) northwest of New York City. It was founded after the American Revolution by advocates of American industrial independence from Europe (including the statesman Alexander

Paterson, long poem by William Carlos Williams, published in five consecutive parts, each a separate book, between 1946 and 1958. Fragments of a sixth volume were published posthumously in 1963. According to Williams, “a man in himself is a city,” and Paterson is both an industrial city in New

Stewart Island/Rakiura: …coastline is deeply creased by Paterson Inlet (east), Port Pegasus (south), and Doughboy and Mason bays (west). The numerous small Mutton Bird Islands lie close offshore. Stewart Island/Rakiura was seen (1770) by Capt. James Cook, who thought it was a peninsula of South Island. This initial description was disproved in…

New Jersey Plan, one of two major competing proposals for the structure and functioning of the United States government that were introduced at the Constitutional Convention in 1787 in Philadelphia. Put forth in June by William Paterson, the head of the New Jersey delegation, the New Jersey Plan

Banjo Paterson was an Australian poet and journalist noted for his composition of the internationally famous song “Waltzing Matilda.” He achieved great popular success in Australia with The Man from Snowy River and Other Verses (1895), which sold more than 100,000 copies before his death, and Rio

Banjo Paterson was an Australian poet and journalist noted for his composition of the internationally famous song “Waltzing Matilda.” He achieved great popular success in Australia with The Man from Snowy River and Other Verses (1895), which sold more than 100,000 copies before his death, and Rio

Banjo Paterson was an Australian poet and journalist noted for his composition of the internationally famous song “Waltzing Matilda.” He achieved great popular success in Australia with The Man from Snowy River and Other Verses (1895), which sold more than 100,000 copies before his death, and Rio

Sir Alexander Paterson was a penologist who modified the progressive Borstal system of English reformatories for juvenile offenders to emphasize its rehabilitative aspects. Before serving as a prison commissioner (1922–47), Paterson had worked with discharged Borstal boys. He was therefore well

MS-DOS: American computer programmer Timothy Paterson, a developer for Seattle Computer Products, wrote the original operating system for the Intel Corporation’s 8086 microprocessor in 1980, initially calling it QDOS (Quick and Dirty Operating System), which was soon renamed 86-DOS. A year later, fledgling company Microsoft purchased exclusive rights to…

William Paterson was a Scottish founder of the Bank of England, writer on economic issues, and the prime mover behind an unsuccessful Scottish settlement at Darién on the Isthmus of Panama. By 1686 Paterson was a London merchant and a member of the Merchant Taylors’ Company. Prior to this time, he

Orange River: Study and exploration: …Jacob Gordon, a Dutch officer; William Paterson, an English traveler; and the French explorer François Le Vaillant. They explored the river from its middle course to its mouth, and Gordon named it in honour of the Dutch house of Orange. Mission stations were established north of the Orange from the…

William Paterson was an Irish-born American jurist, one of the framers of the U.S. Constitution, U.S. senator (1789–90), and governor of New Jersey (1790–93). He also served as an associate justice of the U.S. Supreme Court from 1793 to 1806. Paterson immigrated to America with his family in 1747.

digestive system disease: Cancer: …by long-standing iron deficiency, or Plummer-Vinson (Paterson-Kelly) syndrome. Dysphagia is the first and most prominent symptom. Later swallowing becomes painful as surrounding structures are involved. Hoarseness indicates that the nerve to the larynx is affected. The diagnosis is suggested by X ray and proved by endoscopy with multiple biopsies from…

pathet, in the gamelan (Southeast Asian orchestra consisting mostly of gongs and other metal percussion instruments) music of Java, Indonesia, the concept of mode, which serves as a framework for melodies. Three pathet may be generated by each of the music’s scale systems: slendro, which has five

Ukraine: Theatre and motion pictures: …playwrights was Mykola Kulish, whose Patetychna Sonata (“Sonata Pathétique”) combined Expressionist techniques with the forms of the Ukrainian vertep. From the mid-1930s, however, the theatre in Ukraine was dominated by Socialist Realism, the style enforced by the Communist Party. Oleksander Korniychuk was the most favoured of the playwrights writing in…

Johanne Luise Heiberg was a Danish actress and manager, lionized by the intelligentsia of her day. Heiberg began performing at an early age, singing for the patrons of her father’s tavern and billiard parlour. She made her initial appearance as a singer-dancer at the Royal Theatre at age 14. In

ballistics: A trajectory is the path of a shot, subject to the forces of gravity, drag, and lift. Under the sole influence of gravity, a trajectory is parabolic. Drag retards motion along the trajectory. Below the speed of sound, the drag is roughly proportional to the square…

graph theory: …in graph theory is the path, which is any route along the edges of a graph. A path may follow a single edge directly between two vertices, or it may follow multiple edges through multiple vertices. If there is a path linking any two vertices in a graph, that graph…

path dependence, the tendency of institutions or technologies to become committed to develop in certain ways as a result of their structural properties or their beliefs and values. As a theory, path dependence is based on the straightforward assumption that “history matters.” It attempts to explain

Peter Abrahams: The Path of Thunder (1948) depicts a young mixed-race couple under the menacing shadow of enforced segregation. Wild Conquest (1950) follows the great northern trek of the Boers, and A Night of Their Own (1965) sets forth the plight of Indians in South Africa. The…

Obafemi Awolowo: …Awolowo also wrote the influential Path to Nigerian Freedom (1947), in which he made his case for the need of a federal form of government in an independent Nigeria to safeguard the interests of each ethnic nationality and region and to create a sustainable basis for Nigerian unity. He also…

Paul Ryan: …that year he unveiled “Path to Prosperity: Restoring America’s Promises,” a revised budget plan that called for individual and corporate tax cuts, trillions of dollars in spending cuts, and an overhaul of Medicaid; privatization of Social Security was not mentioned. The plan also included the repeal of Pres. Barack…

Hilaire Belloc: In The Path to Rome (1902) he interspersed his account of a pilgrimage on foot from Toul to Rome with comments on the nature and history of Europe. Born and brought up a Roman Catholic, he showed in almost everything he wrote an ardent profession of…

Italo Calvino: …dei nidi di ragno (1947; The Path to the Nest of Spiders), which views the Resistance through the experiences of an adolescent as helpless in the midst of events as the adults around him; and the collection of stories entitled Ultimo viene il corvo (1949; Adam, One Afternoon, and Other…

John Frankenheimer: Later work: …note with the HBO production Path to War (2002). The drama featured Michael Gambon as the headstrong Pres. Lyndon B. Johnson during the early years of the Vietnam conflict. Frankenheimer died of a stroke following back surgery shortly after his last film aired.

Deepika Padukone: Actress and producer: Padukone appeared in Bollywood blockbusters Pathaan and Jawan in 2023, starring with superstar Shah Rukh Khan, and acted in Fighter, a movie about aviators, and Kalki 2898 AD, a science fiction, in 2024.

Pashtun, ethnolinguistic group residing primarily in the region that lies between the Hindu Kush in northeastern Afghanistan and the northern stretch of the Indus River in Pakistan. The Pashtun constitute the largest ethnic group of the population of Afghanistan and bore the exclusive name of

South Asian arts: Modern theatre: …lead, the most successful was Pathan (1946), which ran for 558 nights. It deals with the friendship between a tribal Muslim leader and a Hindu administrator and is set in the rugged frontier from which Prithvi came. This tragedy of two archetypes in which the tribal leader sacrifices his son…

ṭol, informal Bengali school of instruction, usually in grammar, law, logic, and philosophy. Ṭols were usually found at places of holiness and learning, such as Vārānasi (Benares), Nadia, and Nāsik. The teacher was a Brahman who taught orally and boarded a circle of pupils living in the simplest

Hui, an official nationality of China, composed of nearly 10 million people. The Hui are Chinese Muslims (i.e., neither Turkic nor Mongolian) who have intermingled with the Han Chinese throughout China but are relatively concentrated in western China—in the provinces or autonomous regions of

apathy: …being totally free from the pathē, which roughly are the emotions and passions, notably pain, fear, desire, and pleasure. Although remote origins of the doctrine can probably be found in the Cynics (second half of the 4th century bc), it was Zeno of Citium (4th–3rd century bc) who explicitly taught…

History of film: Early growth of the film industry: …entire European cinema by the Pathé Frères company, founded in 1896 by the former phonograph importer Charles Pathé. Financed by some of France’s largest corporations, Pathé acquired the Lumière patents in 1902 and commissioned the design of an improved studio camera that soon dominated the market on both sides of…

newsreel: …England and France, and the Pathé Weekly (1912), produced for American audiences. The March of Time (1935), produced in the United States by Time, Inc., illustrated the influence of the documentary film by combining filmed news with interpretive interviews and dramatizations. With the rising popularity of television news reports, documentaries,…

Charles Pathé was a French pioneer motion-picture executive who controlled a vast network of production and distribution facilities that dominated the world film market during the first years of the 20th century. With his brother Émile, he founded Pathé Frères (Pathé Brothers, 1896) in Paris, a

Charles Pathé: …his brother Émile, he founded Pathé Frères (Pathé Brothers, 1896) in Paris, a company that manufactured and sold phonographs and phonograph cylinders. The company placed the Kinetoscope, Thomas A. Edison’s newly invented viewing device, in theatres throughout France. Using the camera developed by Louis and Auguste Lumière, Pathé Frères filmed…

newsreel: …early newsreel series were the Pathé-Journal (1908), shown first in England and France, and the Pathé Weekly (1912), produced for American audiences. The March of Time (1935), produced in the United States by Time, Inc., illustrated the influence of the documentary film by combining filmed news with interpretive interviews and…

History of film: Introduction of color: In Pathé’s Pathécolor system, for example, a stencil was cut for each color desired (up to six) and aligned with the print; color was then applied through the stencil frame by frame at high speeds. With the advent of the feature and the conversion of the industry…

Pathein, city, southern Myanmar (Burma). It lies on the Bassein River, which is the westernmost distributary of the Irrawaddy River and is navigable by ships up to 10,000 tons. The city is a deepwater port and has several rice mills; rice is exported from there. It also has sawmills and machine

Irrawaddy River: Physiography: …of the delta is the Bassein (Pathein) River, while the easternmost stream is the Yangon River, on the left bank of which stands Myanmar’s largest city, Yangon (Rangoon). Because the Yangon River is only a minor channel, the flow of water is insufficient to prevent Yangon Harbour from silting up,…

Satyajit Ray: Early life: …illustrated (1944) was the novel Pather Panchali by Bibhuti Bhushan Banarjee, the cinematic possibilities of which began to intrigue him. Ray had long been an avid filmgoer, and his deepening interest in the medium inspired his first attempts to write screenplays and his cofounding (1947) of the Calcutta Film Society.…

Satyajit Ray: Early life: …he should attempt to film Pather Panchali.

pathet, in the gamelan (Southeast Asian orchestra consisting mostly of gongs and other metal percussion instruments) music of Java, Indonesia, the concept of mode, which serves as a framework for melodies. Three pathet may be generated by each of the music’s scale systems: slendro, which has five

Pathet Lao, left-oriented nationalist group in Laos that took control of the country in 1975. Founded in 1950, the Pathet Lao (Lao Country) movement joined with the Viet Minh, the Communist-oriented Vietnamese nationalist organization, in armed resistance to French rule in Indochina. In 1956 a

pathetic fallacy, poetic practice of attributing human emotion or responses to nature, inanimate objects, or animals. The practice is a form of personification that is as old as poetry, in which it has always been common to find smiling or dancing flowers, angry or cruel winds, brooding mountains,

Pathétique Sonata, sonata for piano and orchestra by Ludwig van Beethoven, published in 1799. Unlike most of the nicknames given to Beethoven’s works, Pathétique is believed to have been picked by the composer himself to convey the romantic and even sorrowful mood of the sonata. The first movement

Pathétique Symphony, final composition by Peter Tchaikovsky. Called the “Passionate Symphony” by the composer, from the Russian patetitcheskaja, meaning “passionate” or “emotional,” it was mistranslated into French after his death, earning the title by which it became henceforth known, Pathétique

Natty Bumppo, fictional character, a mythic frontiersman and guide who is the protagonist of James Fenimore Cooper’s five novels of frontier life that are known collectively as The Leatherstocking Tales. The character is known by various names throughout the series, including Leather-Stocking,

Mars Pathfinder, robotic U.S. spacecraft launched to Mars to demonstrate a new way to land a spacecraft on the planet’s surface and the operation of an independent robotic rover. Developed by NASA as part of a low-cost approach to planetary exploration, Pathfinder successfully completed both

history of publishing: Time magazine: … magazine’s immediate forerunner was the Pathfinder (1894–1954), a weekly rewriting of the news for rural readers. There had also been attempts at compression of the digest type (see below Digests and pocket magazines). But Time was the first to aim at a brief and systematic presentation of the whole of…

The Pathfinder, novel by James Fenimore Cooper, published in two volumes in 1840, the fourth of five novels published as The Leatherstocking Tales. In terms of the chronological narrative, The Pathfinder is third in the series. Natty Bumppo is a 40-year-old wilderness scout living near Lake Ontario

The Pathfinder, novel by James Fenimore Cooper, published in two volumes in 1840, the fourth of five novels published as The Leatherstocking Tales. In terms of the chronological narrative, The Pathfinder is third in the series. Natty Bumppo is a 40-year-old wilderness scout living near Lake Ontario

poultry processing: Air chilling: …contains a high number of pathogens, this pathogen count will remain on the bird. Thus, water chilling may actually result in a lower overall bacterial load, because many of the pathogens are discarded in the water.

bacteria: Bacteria in medicine: …continue to evolve, creating increasingly virulent strains and acquiring resistance to many antibiotics.

Sir Benjamin Collins Brodie, 1st Baronet: …his most important work was Pathological and Surgical Observations on the Diseases of the Joints (1818), in which he attempted to trace the beginnings of disease in the different tissues that form a joint and to give an exact value to the symptom of pain as evidence of organic disease.…

number game: Pathological curves: A mathematical curve is said to be pathological if it lacks certain properties of continuous curves. For example, its tangent may be undefined at some—or indeed any—point; the curve may enclose a finite area but be infinite in length; or its curvature may…