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#1 Re: This is Cool » Miscellany » Today 01:00:50

510) Halley's Comet

Halley’s Comet, also called Comet Halley, the first comet whose return was predicted and, almost three centuries later, the first to be imaged up close by interplanetary spacecraft.

In 1705 English astronomer Edmond Halley published the first catalog of the orbits of 24 comets. His calculations showed that comets observed in 1531, 1607, and 1682 had very similar orbits. Halley suggested that they were really one comet that returned approximately every 76 years, and he predicted that comet’s return in 1758. Halley did not live to see his prediction come true (he died in 1742), but the comet was sighted late in 1758, passed perihelion (closest distance to the Sun) in March 1759, and was named in Halley’s honour. Its periodic returns demonstrated that it was in orbit around the Sun and, thus, that at least some comets were members of the solar system.

Earlier passages of Halley’s Comet were later calculated and checked against historical records of comet sightings. Some have speculated that a comet observed in Greece between 467 and 466 BCE may have been Halley. However, the generally accepted date for its earliest recorded appearance, which was witnessed by Chinese astronomers, was in 240 BCE. Halley’s closest approach to Earth took place on April 10, 837, at a distance of only 0.04 astronomical units (AU; 6 million km [3.7 million miles]). It was the large bright comet seen six months before the Norman Conquest of England in 1066 and depicted in the Bayeux Tapestry from that time. Its passage in 1301 may have inspired the form of the Star of Bethlehem that the Italian painter Giotto used in his ‘The Adoration of the Magi’, painted around 1305. Its passages have taken place every 76 years on average, but the gravitational influence of the planets on the comet’s orbit has caused the orbital period to vary from 74.5 to slightly more than 79 years over time. During the comet’s return in 1910, Earth passed through Halley’s dust tail, which was millions of kilometres in length, with no apparent effect.

The most-recent appearance of Halley’s Comet in 1986 was greatly anticipated. Astronomers first imaged the comet with the 200-inch Hale Telescope at Palomar Observatory in California on October 16, 1982, when it was still beyond the orbit of Saturn at 11.0 AU (1.65 billion km [1 billion miles]) from the Sun. It reached perihelion at 0.587 AU (88 million km [55 million miles]) from the Sun on February 9, 1986, and came closest to Earth on April 10 at a distance of 0.417 AU (62 million km [39 million miles]).

Five interplanetary spacecraft flew past the comet in March 1986: two Japanese spacecraft (Sakigake and Suisei), two Soviet spacecraft (Vega 1 and Vega 2), and a European Space Agency spacecraft (Giotto) that passed only 596 km [370 miles] from the comet’s nucleus. Close-up images of the nucleus obtained by Giotto showed a dark potato-shaped object with dimensions of about 15 × 8 km (9 × 5 miles). As expected, the nucleus proved to be a mixture of water and other volatile ices and rocky (silicate) and carbon-rich (organic) dust. About 70 percent of the nucleus surface was covered by a dark insulating “crust” that prevented water ice below it from sublimating, but the other 30 percent was active and produced huge bright jets of gas and dust. The crust turned out to be very black (blacker than coal), reflecting only about 4 percent of the sunlight it received back into space, and it was apparently a surface coating of less-volatile organic compounds and silicates. The dark surface helped explain the high temperature of about 360 kelvins (87 °C [188 °F]) as measured by Vega 1 when the comet was 0.79 AU (118 million km [73 million miles]) from the Sun. As the comet rotated on its axis, the rate of dust and gas emission varied as different active areas on the surface came into sunlight.

The spacecraft encounters proved that the comet nucleus was a solid body, in effect a “dirty snowball,” as proposed by American astronomer Fred Whipple in 1950. This discovery put to rest an alternate explanation known as the sandbank model, promoted by English astronomer R.A. Lyttleton from the 1930s to the 1980s, that the nucleus was not a solid body but rather a cloud of dust with adsorbed gases.

Dust particles shed during the comet’s slow disintegration over the millennia are distributed along its orbit. The passage of Earth through this debris stream every year is responsible for the Orionid and Eta Aquarid meteor showers in October and May, respectively.

Halley’s Comet is next expected to return to the inner solar system in 2061.

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#2 Re: Ganesh's Puzzles » 10 second questions » Today 00:33:12

Hi,

#7737. Hubert is 40 years old and Robert is 60 years old. How many years ago was the ratio of their ages 3:5?

#3 Re: Ganesh's Puzzles » General Quiz » Today 00:15:26

Hi,

#7493. Name the primary international airport in United Arab Emirates, and the world's busiest airport by international passenger traffic.

#7494. Name the  International Airport and one of the major airports in Southeast Asia and worldwide. It is located in Sepang District of Selangor, approximately 45 kilometres (28 mi) south of the city centre and serves the Greater Klang Valley conurbation.

#4 Re: Dark Discussions at Cafe Infinity » crème de la crème » Yesterday 00:50:22

670) Lord Rayleigh

Lord Rayleigh, in full John William Strutt, 3rd Baron Rayleigh of Terling Place, (born November 12, 1842, Langford Grove, Maldon, Essex, England—died June 30, 1919, Terling Place, Witham, Essex), English physical scientist who made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He received the Nobel Prize for Physics in 1904 for his successful isolation of argon, an inert atmospheric gas.

Strutt suffered from poor health throughout his childhood and youth, and it was necessary for him to be withdrawn from both Eton and Harrow. In 1857 he began four years of private study under a tutor. In 1861 Strutt entered Trinity College, Cambridge, from which he was graduated with a B.A. in 1865. He early developed an absorbing interest in both the experimental and mathematical sides of physical science, and in 1868 he purchased an outfit of scientific apparatus for independent research. In his first paper, published in 1869, he gave a lucid exposition of some aspects of the electromagnetic theory of James Clerk Maxwell, the Scottish physicist, in terms of analogies that the average man would understand.

An attack of rheumatic fever shortly after his marriage in 1871 threatened his life for a time. A recuperative trip to Egypt was suggested, and Strutt took his bride, Evelyn Balfour, the sister of Arthur James Balfour, on a houseboat journey up the Nile for an extended winter holiday. On this excursion he began work on his great book, The Theory of Sound, in which he examined questions of vibrations and the resonance of elastic solids and gases. The first volume appeared in 1877, followed by a second in 1878, concentrating on acoustical propagation in material media. After some revision during his lifetime and successive reprintings after his death, the work has remained the foremost monument of acoustical literature.

Shortly after returning to England he succeeded to the title of Baron Rayleigh in 1873, on the death of his father. Rayleigh then took up residence at Terling Place, where he built a laboratory adjacent to the manor house. His early papers deal with such subjects as electromagnetism, colour, acoustics, and diffraction gratings. Perhaps his most significant early work was his theory explaining the blue colour of the sky as the result of scattering of sunlight by small particles in the atmosphere. The Rayleigh scattering law, which evolved from this theory, has since become classic in the study of all kinds of wave propagation.

Rayleigh’s one excursion into academic life came in the period 1879–84, when he agreed to serve as the second Cavendish Professor of Experimental Physics at Cambridge, in succession to James Clerk Maxwell. There Rayleigh carried out a vigorous research program on the precision determination of electrical standards. A classical series of papers, published by the Royal Society, resulted from this ambitious work. After a tenure of five years he returned to his laboratory at Terling Place, where he carried out practically all his scientific investigations.

A few months after resigning from Cambridge, Rayleigh became secretary of the Royal Society, an administrative post that, during the next 11 years, allowed considerable freedom for research.

Rayleigh’s greatest single contribution to science is generally considered to have been his discovery and isolation of argon, one of the rare gases of the atmosphere. Precision measurements of the density of gases conducted by him in the 1880s led to the interesting discovery that the density of nitrogen obtained from the atmosphere is greater by a small though definite amount than is the density of nitrogen obtained from one of its chemical compounds, such as ammonia. Excited by this anomaly and stimulated by some earlier observations of the ingenious but eccentric 18th-century scientist Henry Cavendish on the oxidation of atmospheric nitrogen, Rayleigh decided to explore the possibility that the discrepancy he had discovered resulted from the presence in the atmosphere of a hitherto undetected constituent. After a long and arduous experimental program, he finally succeeded in 1895 in isolating the gas, which was appropriately named argon, from the Greek word meaning “inactive.” Rayleigh shared the priority of the discovery with the chemist William Ramsay, who also isolated the new gas, though he began his work after Rayleigh’s publication of the original density discrepancy. Shortly before winning the Nobel Prize, Rayleigh wrote the entry on argon for the 10th edition (1902) of the Encyclopædia Britannica. In 1904 Rayleigh was awarded the Nobel Prize for Physics; Ramsay received the award in chemistry for his work on argon and other inert elements. The next year Rayleigh was elected president of the Royal Society.

In his later years, when he was the foremost leader in British physics, Rayleigh served in influential advisory capacities in education and government. In 1908 he accepted the post of chancellor of the University of Cambridge, retaining this position until his death. He was also associated with the National Physical Laboratory and government committees on aviation and the treasury. Retaining his mental powers until the end, he worked on scientific papers until five days before his death, on June 30, 1919.

Rayleigh.jpeg

#5 Jokes » Worm Jokes - 3 » Yesterday 00:33:02

ganesh
Replies: 0

Q: Why do worms have trouble getting up in the morning?
A: Because the early bird catches the worm.
* * *
Q: What eats laptops?
A: Computer worms.
* * *
Q: How can you tell if you are looking at a police glow worm?
A: It has a blue light!
* * *
Q: How can you tell which end of a worm is which?
A: Tickle it in the middle and see which end laughs!
* * *
Q: How do you make a glow worm happy?
A: Cut off his tail, he'll be de-lighted!
* * *
Q: What does a bookworm do during a baseball game?
A: Worm the bench.
* * *
Q: What did the worm say to the other when he was late home?
A: Where in earth have you been!
* * *
Q: When should you stop for a glow worm?
A: When he has a red light!
* * *

#6 Re: Ganesh's Puzzles » Oral puzzles » Yesterday 00:23:53

Hi,

#4747. In a box, there are 8 red, 7 blue, and 6 green balls. One balls is picked up randomly. What is the probability of it being neither blue nor green?

#7 Re: Ganesh's Puzzles » Doc, Doc! » Yesterday 00:12:53

Hi,

#1440. Plastic surgery is a surgical specialty involving the restoration, reconstruction, or alteration of the human body. What are the two main categories?

#8 Re: Ganesh's Puzzles » English language puzzles » Yesterday 00:04:23

Hi,

#3493. What does the verb (used with object) emanate mean?

#3494. What does the verb (used with object) emancipate mean?

#9 Re: This is Cool » Miscellany » 2020-04-02 22:10:23

509) Some breeds of dogs

(1)    German shepherd

German shepherd (Alternative Title: Alsatian), breed of working dog developed in Germany from traditional herding and farm dogs. Until the 1970s the breed was known as the Alsatian in the United Kingdom. A strongly built, relatively long-bodied dog, the German shepherd stands 22 to 26 inches (56 to 66 cm) and weighs 75 to 95 pounds (34 to 43 kg). Its coat is of coarse, medium-long outer hair and shorter, dense inner hair and ranges from white or pale gray to black and is often gray and black or black and tan. Noted for intelligence, alertness, and loyalty, the German shepherd is used as a guide for the blind and as a watchdog and also serves in police and military work.

file_23188_german-shepherd-dog-460x290.jpg

(2)    Dalmatian

Dalmatian, dog breed named after the Adriatic coastal region of Dalmatia, Croatia, its first definite home. The origins of the breed are unknown. The Dalmatian has served as a sentinel, war dog, fire department mascot, hunter, shepherd, and performer. It is best known, however, as a coach or carriage dog, functioning as an escort and guard for horse-drawn vehicles. A sleek, symmetrically built, short-haired dog, the Dalmatian is characterized by its dark-spotted white coat. The pups are born white, and the spots develop a few weeks after birth. The Dalmatian stands 19 to 23 inches (48 to 58 cm) and weighs 50 to 55 pounds (23 to 25 kg). In general, it is even-tempered and friendly. Among its nicknames are English coach dog, firehouse dog, and plum-pudding dog.

file_23146_dalmatian-460x290.jpg

(3)    Dachshund

Dachshund, (German: “badger dog”) dog breed of hound and terrier ancestry developed in Germany to pursue badgers into their burrows. The dachshund is a long-bodied, characteristically lively dog with a deep chest, short legs, tapering muzzle, and long ears. Usually reddish brown or black-and-tan, it is bred in two sizes—standard and miniature—and in three coat types—smooth, longhaired, and wirehaired. The standard dachshund stands about 7 to 10 inches (18 to 25 cm) and weighs 16 to 32 pounds (7 to 14.5 kg); the miniature is shorter and weighs no more than 11 pounds (5 kg).

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(4)    Labrador retriever

Labrador retriever, breed of sporting dog that originated in Newfoundland and was brought to England by fishermen about 1800. It is an outstanding gun dog, consistently dominating field trials. Standing 21.5 to 24.5 inches (55 to 62 cm) and weighing 55 to 80 pounds (25 to 36 kg), it is more solidly built than other retrievers and has shorter legs. Distinctive features include its otterlike tail, thick at the base and tapered toward the end, and its short, dense coat of black, brown (“chocolate”), or yellow. The Labrador retriever is characteristically rugged, even-tempered, and gentle. In England it has been used in military and police work, as a rescue dog, and as a guide dog for the blind. An ideal family pet, the Labrador retriever became in the 1990s the most popular dog breed in the United States.

file_22988_labrador-retriever-460x290.jpg

(5)    Poodle

Poodle, breed of dog thought to have originated in Germany but widely associated with France, where it is hugely popular. The poodle was developed as a water retriever, and the distinctive clipping of its heavy coat was initiated to increase the animal’s efficiency in the water. The breed has been used for such diverse undertakings as performing in circuses and hunting for truffles (scenting and digging up the edible fungus).

An elegant-looking dog, often ranked as one of the most intelligent of all breeds, the poodle has been bred in three size varieties—standard, miniature, and toy. All three are judged by the same standard of appearance, which calls for a well-proportioned dog with a long, straight muzzle, heavily haired, hanging ears, a docked pompom tail, and a characteristic springy gait and proud manner of carrying itself. The coat consists of a woolly undercoat and a dense wiry topcoat; if allowed to grow, the hair forms ropelike cords, and the dog is called a corded poodle. The coat should be solid, not variegated, and may be any of a number of colours, among them gray, white, black, brown, apricot, and cream. The standard poodle stands more than 15 inches (38 cm); the miniature is in excess of 10 inches (25 cm) and no more than 15 inches (38 cm); the toy is 10 inches (25 cm) or under. Weight variations range from as much as 70 pounds (32 kg) to as little as 7 pounds (3 kg). The standard and miniature poodles are classed by the American Kennel Club as Non-Sporting dogs, the toy as a Toy dog.

In the late 20th century, breeders began to cross poodles with other purebred dogs in what was called the “designer dog” fad; the goal was the incorporation into the offspring of the poodle’s intelligence and non-shedding coat. All sizes of poodles were crossed with other breeds, resulting in such mixed breeds as the Labradoodle (Labrador retriever + poodle), schnoodle (schnauzer + poodle), and Pekepoo (Pekingese + poodle). However, many poodle breeders deplored the trend and regretted the dilution of carefully managed bloodlines.

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(6)    Pomeranian

Pomeranian, breed of toy dog that can be traced back, like the related Keeshond, Samoyed, and Norwegian elkhound, to early sled-dog ancestors. The breed is named for the duchy of Pomerania, where, in the early 19th century, it is said to have been bred down in size from a 30-pound (13.5-kg) sheepdog. Characteristically spirited but docile, the Pomeranian is a compactly built dog with a foxlike head and small, erect ears. Its long coat, especially full on the neck and chest, may be any of a variety of colours, including white, black, brown, and reddish brown. The Pomeranian stands about 6 to 7 inches (15 to 18 cm) high and weighs about 3 to 7 pounds (1.5 to 3 kg).

file_23122_pomeranian-460x290.jpg

(7)    Golden retriever

Golden retriever, breed of sporting dog developed in Scotland in the 19th century as a water retriever. Typically a strong and hardy all-around dog and an excellent swimmer, it stands 21.5 to 24 inches (55 to 61 cm) and weighs 55 to 75 pounds (25 to 34 kg). Its thick coat is long on the neck, thighs, tail, and back of the legs and may be any shade of golden brown. The golden retriever was first shown in England in 1908 and was registered with the American Kennel Club in 1925. In 2002 it was the second most-popular dog breed in the United States, after the Labrador retriever. The golden retriever is noted for its friendly, gentle temperament and willingness to work. It has been trained as a guide dog for the blind and makes an excellent family pet.

file_22980_golden-retriever-460x290.jpg

(8)    Rottweiler

Rottweiler, a breed of working dog which is thought to be descended from drover dogs (cattle-driving dogs) left by the Roman legions in Rottweil, Germany, after the Romans abandoned the region during the 2nd century CE. The Rottweiler accompanied local butchers on buying expeditions from the Middle Ages to about 1900, carrying money in a neck pouch to market. It has also served as a guard dog, a drover’s dog, a draft dog, a rescue dog, and a police dog.

Characteristically stocky and strongly built, the Rottweiler stands approximately 22 to 27 inches (56 to 68.5 cm) tall and weighs between 90 and 110 pounds (41 and 50 kg). It has a short, coarse, black coat with tan markings on its head, chest, and legs. The Rottweiler’s historic role as a guardian and herder has honed the breed’s instinct for wariness and protectiveness when encountering strangers. Rottweilers are known for their confidence and intelligence; however, they also require a steady training regimen to learn social skills.

The formal history of the breed dates back to 1901, with the production of the first standard Rottweiler by the International Club for Leonbergers and Rottweiler Dogs in Germany. The breed was officially recognized by the American Kennel Club in 1931.

file_22942_rottweiler-460x290.jpg

(9)    Bulldog

Bulldog, also called English bulldog, breed of dog developed centuries ago in Great Britain for use in fighting bulls (bullbaiting). Characteristically powerful and courageous, often vicious, and to a great extent unaware of pain, the bulldog nearly disappeared when dogfighting was outlawed in 1835. Fanciers of the breed, however, saved it and bred out its ferocity. Nicknamed the “sourmug,” the bulldog is a stocky dog that moves with a rolling gait. It has a large head, folded ears, a short muzzle, a protruding lower jaw, and loose skin that forms wrinkles on the head and face. Its short, fine coat is tan, white, reddish brown, brindle, or piebald. The bulldog stands 13 to 15 inches (33 to 38 cm) and weighs 40 to 50 pounds (18 to 23 kg). Typically gentle and reliable, it is placed in the Non-Sporting Dog group of the American Kennel Club.

file_23140_bulldog-460x290.jpg

(10)    Pug

Pug, breed of toy dog that probably originated in China and was introduced to England near the end of the 17th century by Dutch traders. The pug has a short muzzle and a tightly curled tail. It is a squarely built, muscular dog, with a large head, prominent, dark eyes, and small, drooping ears. At maturity it stands 10 to 11 inches (25.5 to 28 cm) and weighs about 14 to 18 pounds (6 to 8 kg). Its coat is short and glossy; colour is given in the breed standard as black or as silver or apricot fawn with a black line on the back and a black mask on the face. Typically loyal and alert, the pug is a valued companion dog.

file_23124_pug-460x290.jpg

(11)    Doberman Pinscher

Doberman Pinscher, also called Doberman or Dobe, breed of working dog developed in Apolda, Germany, by Karl Friedrich Louis Dobermann, a tax collector, night watchman, dogcatcher, and keeper of a dog pound, about 1890. The Doberman Pinscher is a sleek, agile, and powerful dog standing 24 to 28 inches (61 to 71 cm) and weighing 60 to 88 pounds (27 to 40 kg). It has a short smooth coat, black, blue, fawn, or red in colour, with rust markings on the head, throat, chest, base of the tail, and feet. The breed has a reputation for fearlessness, alertness, loyalty, and intelligence.

During his time as a dogcatcher and pound keeper, Dobermann was thought to have crossed several breeds—including the Rottweiler, German Pinscher, Black and Tan Terriers, Weimaraner, and short-haired shepherds—to develop the breed, which was first registered with the American Kennel Club (AKC) in 1908. The Doberman Pinscher Club of America, an organization devoted to promoting the purity of the breed, was founded in Michigan in 1921, by George Earle III, an American diplomat who also served as governor of Pennsylvania from 1935 to 1939. Doberman Pinschers have been used in police and military work (such as in message delivery, scouting, and guarding) and as a watchdog and as a guide dog for the blind.

file_22920_doberman-pinscher-460x290.jpg

(12)    Boxer

Boxer, smooth-haired working dog breed named for its manner of “boxing” with its sturdy front paws when fighting. The boxer, developed in Germany, includes strains of bulldog and Great Dane in its heritage. Because of its reputation for courage, aggressiveness, and intelligence, it has been used in police work but is also valued as a watchdog and companion. It is a trim, squarely built dog with a short, square-shaped muzzle, a black mask on its face, and a shiny shorthaired coat of fawn (reddish brown) or brindle. It stands 21 to 25 inches (53 to 63.5 cm) and weighs 60 to 70 pounds (27 to 32 kg).

file_22916_boxer-460x290.jpg

(13)    Chihuahua

Chihuahua, smallest recognized dog breed, named for the Mexican state of Chihuahua, where it was first noted in the mid-19th century. The Chihuahua is thought to have been derived from the Techichi, a small, mute dog kept by the Toltec people of Mexico as long ago as the 9th century AD. Typically a saucy-looking, alert dog that is sturdier than its small build would suggest, the Chihuahua stands about 5 inches (13 cm) and weighs 1 to 6 pounds (0.5 to 3 kg). It has a rounded head, large, erect ears, prominent eyes, and a compact body. The coat is variable in colour and may be either smooth and glossy or long and soft. It is valued as a spirited companion especially suited to apartment living.

file_23102_chihuahua-460x290.jpg

(14)    Mastiff

Mastiff, breed of large working dog used as a guard and fighting dog in England for more than 2,000 years. Dogs of this type are found in European and Asian records dating back to 3000 BC. Sometimes called the Molossian breeds for a common ancestor, numerous large, heavily built dog breeds incorporate the name mastiff. They often function as war dogs or guardians. The Roman invaders of England sent the English mastiff to compete in the arenas of ancient Rome, where the dog was pitted against bears, lions, tigers, bulls, other dogs, and human gladiators. The breed also fought in the later bullbaiting and bearbaiting rings of England.

A powerful but characteristically gentle dog, the mastiff has a broad head, drooping ears, a broad, short muzzle, and a short, coarse coat. Colour, as specified by the breed standard, is apricot, silver fawn, or brindled fawn and black. Ears and muzzle are dark. According to the American Kennel Club, male mastiffs must stand at least 30 inches (76 cm) and females at least 27.5 inches (70 cm). The breed weighs 165 to 185 pounds (75 to 84 kg).

The bullmastiff, a cross between the mastiff and the bulldog, was developed in 19th-century England; it was used chiefly to discourage poaching on estates and game preserves and was known as the “gamekeeper’s night-dog.” The bullmastiff is a tan, reddish brown, or brindled dog, with black on the face and ears. It stands 24 to 27 inches (61 to 69 cm) and weighs 100 to 130 pounds (45 to 59 kg). It is frequently used as a police and guard dog.

file_22934_mastiff-460x290.jpg

#11 Re: Dark Discussions at Cafe Infinity » crème de la crème » 2020-04-02 01:02:59

669) Diophantus

Diophantus, byname Diophantus of Alexandria, (flourished c. CE 250), Greek mathematician, famous for his work in algebra.

What little is known of Diophantus’s life is circumstantial. From the appellation “of Alexandria” it seems that he worked in the main scientific centre of the ancient Greek world; and because he is not mentioned before the 4th century, it seems likely that he flourished during the 3rd century. An arithmetic epigram from the ‘Anthologia Graeca’ of late antiquity, purported to retrace some landmarks of his life (marriage at 33, birth of his son at 38, death of his son four years before his own at 84), may well be contrived. Two works have come down to us under his name, both incomplete. The first is a small fragment on polygonal numbers (a number is polygonal if that same number of dots can be arranged in the form of a regular polygon). The second, a large and extremely influential treatise upon which all the ancient and modern fame of Diophantus reposes, is his ‘Arithmetica’. Its historical importance is twofold: it is the first known work to employ algebra in a modern style, and it inspired the rebirth of number theory.

The ‘Arithmetica’ begins with an introduction addressed to Dionysius—arguably St. Dionysius of Alexandria. After some generalities about numbers, Diophantus explains his symbolism—he uses symbols for the unknown (corresponding to our x) and its powers, positive or negative, as well as for some arithmetic operations—most of these symbols are clearly scribal abbreviations. This is the first and only occurrence of algebraic symbolism before the 15th century. After teaching multiplication of the powers of the unknown, Diophantus explains the multiplication of positive and negative terms and then how to reduce an equation to one with only positive terms (the standard form preferred in antiquity). With these preliminaries out of the way, Diophantus proceeds to the problems. Indeed, the ‘Arithmetica’ is essentially a collection of problems with solutions, about 260 in the part still extant.

The introduction also states that the work is divided into 13 books. Six of these books were known in Europe in the late 15th century, transmitted in Greek by Byzantine scholars and numbered from I to VI; four other books were discovered in 1968 in a 9th-century Arabic translation by Qusṭā ibn Lūqā. However, the Arabic text lacks mathematical symbolism, and it appears to be based on a later Greek commentary—perhaps that of Hypatia (c. 370–415)—that diluted Diophantus’s exposition. We now know that the numbering of the Greek books must be modified: Arithmetica thus consists of Books I to III in Greek, Books IV to VII in Arabic, and, presumably, Books VIII to X in Greek (the former Greek Books IV to VI). Further renumbering is unlikely; it is fairly certain that the Byzantines only knew the six books they transmitted and the Arabs no more than Books I to VII in the commented version.

The problems of Book I are not characteristic, being mostly simple problems used to illustrate algebraic reckoning. The distinctive features of Diophantus’s problems appear in the later books: they are indeterminate (having more than one solution), are of the second degree or are reducible to the second degree (the highest power on variable terms is 2, i.e., x^2), and end with the determination of a positive rational value for the unknown that will make a given algebraic expression a numerical square or sometimes a cube. (Throughout his book Diophantus uses “number” to refer to what are now called positive, rational numbers; thus, a square number is the square of some positive, rational number.) Books II and III also teach general methods. In three problems of Book II it is explained how to represent: (1) any given square number as a sum of the squares of two rational numbers; (2) any given non-square number, which is the sum of two known squares, as a sum of two other squares; and (3) any given rational number as the difference of two squares. While the first and third problems are stated generally, the assumed knowledge of one solution in the second problem suggests that not every rational number is the sum of two squares. Diophantus later gives the condition for an integer: the given number must not contain any prime factor of the form 4n + 3 raised to an odd power, where n is a non-negative integer. Such examples motivated the rebirth of number theory. Although Diophantus is typically satisfied to obtain one solution to a problem, he occasionally mentions in problems that an infinite number of solutions exists.

In Books IV to VII Diophantus extends basic methods such as those outlined above to problems of higher degrees that can be reduced to a binomial equation of the first- or second-degree. The prefaces to these books state that their purpose is to provide the reader with “experience and skill.” While this recent discovery does not increase knowledge of Diophantus’s mathematics, it does alter the appraisal of his pedagogical ability. Books VIII and IX (presumably Greek Books IV and V) solve more difficult problems, even if the basic methods remain the same. For instance, one problem involves decomposing a given integer into the sum of two squares that are arbitrarily close to one another. A similar problem involves decomposing a given integer into the sum of three squares; in it, Diophantus excludes the impossible case of integers of the form 8n + 7 (again, n is a non-negative integer). Book X (presumably Greek Book VI) deals with right-angled triangles with rational sides and subject to various further conditions.

The contents of the three missing books of the ‘Arithmetica’ can be surmised from the introduction, where, after saying that the reduction of a problem should “if possible” conclude with a binomial equation, Diophantus adds that he will “later on” treat the case of a trinomial equation—a promise not fulfilled in the extant part.

Although he had limited algebraic tools at his disposal, Diophantus managed to solve a great variety of problems, and the ‘Arithmetica’ inspired Arabic mathematicians such as al-Karajī (c. 980–1030) to apply his methods. The most famous extension of Diophantus’s work was by Pierre de Fermat (1601–65), the founder of modern number theory. In the margins of his copy of ‘Arithmetica’, Fermat wrote various remarks, proposing new solutions, corrections, and generalizations of Diophantus’s methods as well as some conjectures such as Fermat’s last theorem, which occupied mathematicians for generations to come. Indeterminate equations restricted to integral solutions have come to be known, though inappropriately, as Diophantine equations.

diofant.jpg?w=256&h=300

#12 Re: Ganesh's Puzzles » 10 second questions » 2020-04-02 00:51:19

Hi,

#7736. Martin and Stanley are 35 years old and 40 years old respectively. After how many years would the ratio of their ages become 9:10?

#13 Re: Ganesh's Puzzles » Mensuration » 2020-04-02 00:26:40

Hi,

The solution M # 589 is correct. Good work!

M # 590. A tent constructed in the form of a square pyramid of base perimeter 80 meters and lateral edge 26 meters.
(a) Calculate the slant height of the tent.
(b) Calculate the area of tarpaulin sheet required to cover the lateral faces of the tent.

#14 Re: Ganesh's Puzzles » General Quiz » 2020-04-02 00:09:53

Hi,

#7491. Name the main international airport of the Netherlands. It is located 9 kilometres (5.6 miles) southwest of Amsterdam, in the municipality of Haarlemmermeer in North Holland. It is the third-busiest airport in Europe in terms of passenger volume and the busiest in Europe in terms of aircraft movement. The airport is built as a single-terminal concept: one large terminal split into three large departure halls.

#7492. Name the major international airport situated in Kempton Park, Gauteng, South Africa. It serves as the primary airport for domestic and international travel to/from South Africa and is Africa's busiest airport, with a capacity to handle up to 28 million passengers annually. The airport serves as the hub for South African Airways. The airport handled over 21 million passengers in 2017.

#15 Re: Introductions » Hello! » 2020-04-01 12:23:10

Hi keiraec,

There were only 3 people. Grandfather, father and son.

Welcome to the forum!

#16 Re: Ganesh's Puzzles » Algebra » 2020-04-01 01:58:52

Hi,

A # 73. Which number added to the polynomial

gives polynomial with (x - 1) as a factor.

#17 Re: Ganesh's Puzzles » Series and Progressions » 2020-04-01 01:29:08

Hi,

SP#606. Show that

form an Arithmetic Progression where
is defined as
. Also, find the sum of the first 15 terms.

#18 Re: Ganesh's Puzzles » Mensuration » 2020-04-01 01:06:35

Hi,

M # 589. If the number of square centimeters in the surface area of a sphere is equal to the number of cubic centimeters in its volume, find the diameter of the sphere.

#19 Re: This is Cool » Miscellany » 2020-04-01 00:47:45

508) Cow

Cow, in common parlance, a domestic bovine, regardless of gender and age, usually of the species ‘Bos taurus’. In precise usage, the name is given to mature females of several large mammals, including cattle (bovines), moose, elephants, sea lions, and whales.

Domestic cows are one of the most common farm animals around the world, and the English language has several words to describe these animals at various ages. A baby cow is called a calf. A female calf is sometimes called a heifer calf and a male a bull calf. A heifer is a female that has not had any offspring. The term usually refers to immature females; after giving birth to her first calf, however, a heifer becomes a cow. An adult male is known as a bull. Many male cattle are castrated to reduce their aggressive tendencies and make them more tractable. Young neutered males, which are primarily raised for beef, are called steers or bullocks, whereas adult neutered males, which are usually used for draft purposes, are known as oxen. A group of cows, cattle, or kine (an archaic term for more than one cow) constitutes a herd. English lacks a gender-neutral singular form, and so “cow” is used for both female individuals and all domestic bovines.

Domestic Cattle

Cows are members of the order Artiodactyla. The order contains even-toed hoofed mammals, and cows have distinctive cloven hooves (derived from the toenails from the middle two digits of each foot). Cows belong to the family Bovidae (hollow-horned ruminants, which also includes antelope, sheep, and goats), subfamily Bovinae (which includes buffaloes and spiral-horned antelope), tribe Bovini (which includes cattle, bison, and yak), and genus Bos—the names of which are all derived from bos, the Latin word for cow.

Natural history

The size and weight of a cow is highly dependent on the breed. Mature males weigh 450–1,800 kg (1,000–4,000 pounds) and females weigh 360–1,100 kg (800–2,400 pounds). Both males and females have horns, and although these may be short in many breeds, they can grow to be spectacularly large, such as in Texas longhorns and African Ankole-Watusi cows. Some breeds are genetically polled (hornless), and many other cows may be dehorned (that is, have their horn buds destroyed) at young age to make them easier to transport and safer to work around. Cows are renowned for their large milk-producing (mammary) glands known as udders.

Cows are well adapted for grazing (feeding on grass), with a wide mouth and specialized teeth for eating tough vegetation. Adults have 32 teeth but lack upper incisors and canines—they have a gummy pad instead that is used to help rip up grass. The molars have moon-shaped ridges that run parallel to the tongue, and thus chewing must be done with a circular motion to be effective.

The most specialized adaptation that cows (and other ruminants) have is their massive four-chambered stomach, which acts as a fermentation vat. Inside the rumen, the largest chamber of the stomach, bacteria and other microorganisms digest tough plant fibres (cellulose). To aid in this process, cows regurgitate and re-chew food multiple times before it passes on to the rest of the digestive system via the other stomach chambers. This process, called “chewing the cud,” helps sort the digesta (the material being digested) and absorb nutrients. By taking time to re-chew their food later, cows avoid the need to chew well when they eat. This enables them to quickly ingest large quantities of grass while in the vulnerable head-down position required for grazing.

Domestication and economic production

Cows are currently the most common domesticated ungulate (hoofed mammal), and they are found wherever humans live. Global stocks of cows were estimated at nearly one billion animals in 2016, with India, Brazil, and China having the largest populations (together maintaining approximately one-third of all cows).

Cows were first domesticated between 8,000 and 10,000 years ago from the aurochs (B. taurus primigenius), a wild species of cattle that once ranged across Eurasia. The wild aurochs became extinct in the early 1600s, the result of overhunting and loss of habitat due to the spread of agriculture (and domestic herds). Today, there are two broadly recognized forms of cow: the zebu or humped cattle from eastern Asia (B. taurus indicus) and cattle without humps (B. taurus taurus) from western Eurasia, although the two forms readily interbreed. Genetic studies suggest that both forms descend from the aurochs, but they are the products of independent domestication events.

Cows were first domesticated as “all-purpose” animals, used as draft animals and also for their milk and meat products. Regional specializations led to the formation of a range of varieties, or breeds, that were adapted to different climates or that were selectively bred to emphasize valuable characteristics, such as milk or meat production. Cows are used by humans in many other ways, such as a source of leather for clothing and other products and, albeit controversially, as participants in sporting events (e.g., bullfighting, bull riding, and rodeo events). Cows may also serve as a measure of wealth, and they are even worshipped as sacred animals in some religions. Historically, northern Europeans constructed their dwellings alongside or on top of cow stables, creating “housebarns” warmed by the body heat of cows.

All mammals produce milk to feed their young, but dairy cattle, such as the well-known Holstein-Friesian cow, have been specially bred to produce very large quantities of milk. Since only females produce milk, they are far more common in the dairy industry. Dairy bulls are often large, powerful, and aggressive and are more challenging to keep. As a result, most breeding in modern dairy operations occurs through artificial insemination, with bulls living at just a few specialized facilities. Different breeds of dairy cows have been bred for specific milk characteristics, such as to maximize yield or to produce a desired level of fat in the milk. Milk from cows is a significant part of many food items; in addition to its direct consumption as a beverage, it is used to make a wide range of products including butter, yogurt, cheese, and ice cream.

Dairy cows produce milk for around 10 months following the birth of the calf. A typical western dairy cow is usually milked twice per day and produces on average 30 litres (8 gallons) of milk daily; however, the actual amount produced depends upon the age and breed of the cow. Most modern milking is not done by hand but by machines.

Cows usually have their first calf when they are just under two years old—with single calves being typical, although twins sometimes occur—and each cow may have ten or more calves over the course of her life. Even though cows can live for 20 years or more, older dairy cows are often culled from commercial herds and used for meat when their milk yield begins to decline.

Sanctity of the cow

Sanctity of the cow, in Hinduism, the belief that the cow is representative of divine and natural beneficence and should therefore be protected and venerated. The cow has also been associated with various deities, notably Shiva (whose steed is Nandi, a bull), Indra (closely associated with Kamadhenu, the wish-granting cow), Krishna (a cowherd in his youth), and goddesses in general (because of the maternal attributes of many of them).

luxury-1.jpg

#20 Jokes » Worm Jokes - 2 » 2020-04-01 00:34:57

ganesh
Replies: 0

Q: Why are glow worms good to carry in your bag?
A: They can lighten your load!
* * *
Q: What do you get if you cross a glow worm with a python?
A: A 15 foot strip light that can strangle you to death!
* * *
Q: What is a worm's favorite band?
A: Mud!
* * *
Q: How do you make a glow worm happy?
A: Cut off its tail and it will be de-lighted.
* * *
Q: What is the maggot army called?
A: The Apple Corps!
* * *
Q: Why didn't the two worms get on Noah's Ark in an apple?
A: Because everyone had to go on in pairs!
* * *
Q: What does a turtle do during winter?
A: Sit by the fire and worm himself up.
* * *
Q: What kind of computer does a worm have?
A: A Macintosh.
* * *

#21 Re: Ganesh's Puzzles » Oral puzzles » 2020-04-01 00:29:11

Hi,

#4746. A die is thrown twice. What is the probability of getting a sum of 7 from both the throws?

#22 Re: Ganesh's Puzzles » Doc, Doc! » 2020-04-01 00:17:46

Hi,

#1439. What does the medical term 'Medical ultrasound' mean?

#23 Re: Ganesh's Puzzles » English language puzzles » 2020-04-01 00:07:52

Hi,

#3491. What does the verb (used with object) elude mean?

#3492. What does the verb (used with object) emaciate mean?

#24 Re: Dark Discussions at Cafe Infinity » crème de la crème » 2020-03-31 01:03:40

668) Pieter Zeeman

Pieter Zeeman was born on May 25, 1865, at Zonnemaire, a small village in the isle of Schouwen, Zeeland, The Netherlands, as the son of the local clergyman Catharinus Forandinus Zeeman and his wife, née Wilhelmina Worst. After having finished his secondary school education at Zierikzee, the main town of the island, he went to Delft for two years to receive tuition in the classical languages, an adequate knowledge of which was required at that time for entrance to the university. Taking up his abode at the house of Dr. J.W. Lely, conrector of the Gymnasium and brother of Dr. C. Lely (Minister of Public Works and known for initiating and developing the work for reclamation of the Zuyderzee), Zeeman came into an environment which was beneficial for the development of his scientific talents. It was here also that he came into contact with Kamerlingh Onnes (Nobel Prize in Physics for 1913), who was twelve years his senior. Zeeman’s wide reading, which included a proper mastery of works such as Maxwell’s Heat, and his passion for performing experiments amazed Kamerlingh Onnes in no small degree, and formed the basis for a fruitful friendship between the two scientists.

Zeeman entered Leyden University in 1885 and became mainly a pupil of Kamerlingh Onnes (mechanics) and Lorentz (experimental physics): the latter was later to share the Nobel Prize with him. An early reward came in 1890 when he was appointed assistant to Lorentz, enabling him to participate in an extensive research programme which included the study of the Kerr effect – an important foundation for his future great work. He obtained his doctor’s degree in 1893, after which he left for F. Kohlrausch’s institute at Strasbourg, where for one semester he carried out work under E. Cohn. He returned to Leyden in 1894 and became “privaat-docent” (extra-mural lecturer) from 1895 to 1897.

In 1897, the year following his great discovery of the magnetic splitting of spectral lines, he was called to a lectureship at the University of Amsterdam; in 1900 came his appointment as Extraordinary Professor. In 1908 Van der Waals (Nobel Prize in Physics for 1910) reached the retiring age of 70 and Zeeman was chosen as his successor, at the same time functioning as Director of the Physics Laboratory. In 1923 a new laboratory, specially erected for him, was put at his disposal, a prominent feature being a concrete block weighing a quarter of a million kilograms, erected free from the floor, as a suitable platform for vibration-free experiments. The institute is now known as the Zeeman Laboratory of Amsterdam University. Many world-famous scientists have visited Zeeman there or worked with him for some time. He remained in this dual function for 35 years – on numerous occasions refusing an invitation to occupy a Chair abroad – until in 1935 he had to resign on account of his pensionable age. An accomplished teacher and of kind disposition he was much loved by his pupils. One of these was C.J. Bakker, who was from 1955 until his untimely death in an aircraft accident in 1960 the General Director of the Organisation Européenne pour la Recherche Nucléaire (CERN) at Geneva. Another worker in his laboratory was S. Goudsmit, who in 1925 with G.E. Uhlenbeck originated the concept of electron spin.

Zeeman’s talent for natural science first became apparent in 1883, when, while still attending the secondary school, he gave an apt description and drawing of an aurora borealis – then clearly to be observed in his country – which was published in ‘Nature’.

Zeeman’s main theme of investigation has always concerned optical phenomena. His first treatise ‘Mesures relatives du phénomène de Kerr’, written in 1892, was rewarded with a Gold Medal from the Dutch Society of Sciences at Haarlem; his doctor’s thesis dealt with the same subject. In Strasbourg he studied the propagation and absorption of electrical waves in fluids. His principal work, however, was the study of the influence of magnetism on the nature of light radiation, started by him in the summer of 1896, which formed a logical continuation of his investigation into the Kerr effect. The discovery of the so-called Zeeman effect, for which he has been awarded the Nobel Prize, was communicated to the Royal Academy of Sciences in Amsterdam – through H. Kamerlingh Onnes (1896) and J.D. van der Waals (1897) – in the form of papers entitled ‘Over den Invloed eener Magnetisatie op den Aard van het door een Stof uitgezonden Licht’ (On the influence of a magnetization on the nature of light emitted by a substance) and ‘Over Doubletten en Tripletten in het Spectrum teweeggebracht door Uitwendige Magnetische Krachten’ (On doublets and triplets in the spectrum caused by external magnetic forces) I, II and III. (The English translations of these papers appeared in ‘The Philosophical Magazine’; of the first paper a French version appeared in ‘Archives Néerlandaises des Sciences Exactes et Naturelles’, and in a short form in German in ‘Verhandlungen der Physikalischen Gesellschaft zu Berlin’.)

The importance of the discovery can at once be judged by the fact that at one stroke the phenomenon not only confirmed Lorentz’ theoretical conclusions with regard to the state of polarization of the light emitted by flames, but also demonstrated the negative nature of the oscillating particles, as well as the unexpectedly high ratio of their charge and mass (e/m). Thus, when in the following year the discovery of the existence of free electrons in the form of cathode rays was established by J.J. Thomson, the identity of electrons and the oscillating light particles could be established from the negative nature and the e/m ratio of the particles. The growing number of observations made by other investigators on studying the effects of using various substances as light emitters – not all of them explicable by Lorentz’ original theory (the so-called ‘anomalous Zeeman effect’ could only adequately be explained at a later date, with the advent of Bohr’s atomic theory, quantum wave mechanics, and the concept of the electron spin) – was assembled by him in his book ‘Researches in Magneto-Optics’ (London 1913, German translation in 1914). Not only has the Zeeman effect thrown much light on the mechanism of light radiation and on the nature of matter and electricity, but its immense importance lies in the fact that even to this day it offers the ultimate means for revealing the intimate structure of the atom and the nature and behaviour of its components. It still serves as the final test in any new theory of the atom.

Already in his second communication Zeeman expressed the opinion that the accepted existence of strong magnetic fields on the surface of the sun could be verified, since these should alter spectral lines derived from the celestial body. (It is typical of Zeeman to extend physical concepts into the realm of celestial phenomena.) In a letter to him (1908) the astronomer G.E. Hale, Director of Mount Wilson Observatory, corroborated this opinion by means of photographs which indicated that in solar vortices the spectral lines indeed appeared to be affected by magnetic fields. Even the theoretical prediction concerning the probable interrelationship between the directions of polarization and those of the magnetic fields was subsequently confirmed by Hale.

With regard to Zeeman’s activities outside the field of the magnetic splitting of spectral lines, mention should first be made of his work on the Doppler effect in optics and in canal rays (laboratory tests). A second field of study was that on the propagation of light in moving media (justification of the existence of the Lorentz-term in the Fresnel drag coefficient). Other investigations were those into the influence of the magnetic moment of the nucleus on the hyperfine structure of spectral lines. He also succeeded, with J. de Gier, in discovering a number of new isotopes (38Ar, 64Ni, amongst others) by means of Thomson’s parabola mass spectrograph. Zeeman’s predilection for testing fundamental laws also found expression in his verification – carried out with an accuracy of 7 – of the equality of heavy and inert masses.

Zeeman was Honorary Doctor of the Universities of Göttingen, Oxford, Philadelphia, Strasbourg, Liège, Ghent, Glasgow, Brussels and Paris. He was also a member or honorary member of numerous learned academies, including the very rare distinction of Associé Etranger of the Académie des Sciences of Paris. He was also member and Chairman of the Commission ‘Internationale des Poids et Mesures’, Paris. Appointed member of the Royal Academy of Sciences of Amsterdam in 1898, he served as the Secretary of the Mathematical-Physical Section from 1912 to 1920. Among the other distinctions may be mentioned the Rumford Medal of the Royal Society of London, the Prix Wilde of the Academie des Sciences of Paris, the Baumgartner-Preis of the Akademie der Wissenschaften of Vienna, the Matteucci Medal of the Italian Society of Sciences, the Franklin Medal of the Franklin Institute of Philadelphia, the Henry Draper Medal of the National Academy of Sciences of Washington. He was also made a Knight of the Order of Orange-Nassau and Commander of the Order of the Netherlands Lion.

Outside his field of study Zeeman showed much interest in literature and the stage. An entertaining host, he loved to invite his collaborators and pupils to dine with him at his home, an event preceded by a learned talk in his study and followed by a gathering in the family circle.

Zeeman married Johanna Elisabeth Lebret in 1895; they had one son and three daughters. During the last year of his professorship he suffered from ill-health. He died after a short illness on October 9, 1943.

zeeman_pieter_a1.jpg

#25 Re: Ganesh's Puzzles » Coordinate Geometry » 2020-03-31 00:57:31

Hi,

The solution CG#93 is correct. Neat work!

CG#94. Find a relation between x and y if the points (x,y), (1,2), and (7,0) are collinear.

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