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Artiodactyl

Artiodactyls are placental mammals belonging to the order Artiodactyla. Typically, they are ungulates which bear weight equally on two (an even number) of their five toes: the third and fourth, often in the form of a hoof. The other three toes are either present, absent, vestigial, or pointing posteriorly. By contrast, most perissodactyls bear weight on an odd number of the five toes. Another difference between the two is that many artiodactyls (except for Suina) digest plant cellulose in one or more stomach chambers rather than in their intestine as perissodactyls do. The advent of molecular biology, along with new fossil discoveries, found that cetaceans (whales, dolphins, and porpoises) fall within this taxonomic branch, being most closely related to hippopotamuses. Some modern taxonomists thus apply the name Cetartiodactyla to this group, while others opt to include cetaceans within the existing name of Artiodactyla. Some researchers use "even-toed ungulates" to exclude cetaceans and only include terrestrial artiodactyls, making the term paraphyletic in nature.

The roughly 270 land-based even-toed ungulate species include pigs, peccaries, hippopotamuses, antelopes, deer, giraffes, camels, llamas, alpacas, sheep, goats and cattle. Many are herbivores, but suids are omnivorous, whereas cetaceans are entirely carnivorous. Many of these are of great dietary, economic, and cultural importance to humans.

Evolutionary history
The oldest fossils of even-toed ungulates date back to the early Eocene (about 53 million years ago). Since these findings almost simultaneously appeared in Europe, Asia, and North America, it is very difficult to accurately determine the origin of artiodactyls. The fossils are classified as belonging to the family Diacodexeidae; their best-known and best-preserved member is Diacodexis. These were small animals, some as small as a hare, with a slim build, lanky legs, and a long tail. Their hind legs were much longer than their front legs. The early to middle Eocene saw the emergence of the ancestors of most of today's mammals. Two formerly widespread, but now extinct, families of even-toed ungulates were Entelodontidae and Anthracotheriidae. Entelodonts existed from the middle Eocene to the early Miocene in Eurasia and North America. They had a stocky body with short legs and a massive head, which was characterized by two humps on the lower jaw bone. Anthracotheres had a large, porcine (pig-like) build, with short legs and an elongated muzzle. This group appeared in the middle Eocene up until the Pliocene, and spread throughout Eurasia, Africa, and North America. Anthracotheres are thought to be the ancestors of hippos, and, likewise, probably led a similar aquatic lifestyle. Hippopotamuses appeared in the late Miocene and occupied Africa and Asia—they never got to the Americas.

The camels (Tylopoda) were, during large parts of the Cenozoic, limited to North America; early forms like Cainotheriidae occupied Europe. Among the North American camels were groups like the stocky, short-legged Merycoidodontidae. They first appeared in the late Eocene and developed a great diversity of species in North America. Only in the late Miocene or early Pliocene did they migrate from North America into Eurasia. The North American varieties became extinct around 10,000 years ago.

Suina (including pigs) have been around since the Eocene. In the late Eocene or the Oligocene, two families stayed in Eurasia and Africa; the peccaries, which became extinct in the Old World, exist today only in the Americas. South America was settled by even-toed ungulates only in the Pliocene, after the land bridge at the Isthmus of Panama formed some three million years ago. With only the peccaries, lamoids (or llamas), and various species of capreoline deer, South America has comparatively fewer artiodactyl families than other continents, except Australia, which has no native species.

Taxonomy and phylogeny
The classification of artiodactyls was hotly debated because ocean-dwelling cetaceans evolved from land-dwelling even-toed ungulates. Some semiaquatic even-toed ungulates (hippopotamuses) are more closely related to ocean-dwelling cetaceans than to other even-toed ungulates.

Phylogenetic classification only recognizes monophyletic taxa; that is, groups that descend from a common ancestor and include all of its descendants. To address this problem, the traditional order Artiodactyla and infraorder Cetacea are sometimes subsumed into the more inclusive Cetartiodactyla taxon. An alternative approach is to include both land-dwelling even-toed ungulates and ocean-dwelling cetaceans in a revised Artiodactyla taxon.

Classification

 * Order Artiodactyla/Clade Cetartiodactyla
 * Family †Diacodexeidae
 * Family †Amphimerycidae
 * Family †Robiacinidae
 * Family †Cainotheriidae
 * Suborder Tylopoda
 * Family †Anoplotheriidae?
 * Family †Merycoidodontidae
 * Family †Agriochoeridae
 * Family Camelidae: camels and lamoids or llamas (7 extant and 13 extinct species)
 * Family †Oromerycidae
 * Family †Xiphodontidae?
 * Family †Protoceratidae?
 * Clade Artiofabula
 * Suborder Suina
 * Family Suidae: pigs (19 species)
 * Family Tayassuidae: peccaries (4 species)
 * Family †Sanitheriidae
 * Family †Doliochoeridae
 * Clade Cetruminantia
 * Clade Cetancodontamorpha
 * Genus †Andrewsarchus?
 * Family †Entelodontidae
 * Suborder Whippomorpha
 * Family †Raoellidae
 * Superfamily Dichobunoidea – paraphyletic to Cetacea and Raoellidae
 * Family †Dichobunidae
 * Family †Helohyidae
 * Family †Choeropotamidae
 * Family †Cebochoeridae (Family contains Cebochoerus)
 * Family †Mixtotheriidae
 * Infraorder Ancodonta
 * Family †Anthracotheriidae – paraphyletic to Hippopotamidae
 * Family Hippopotamidae: hippos (two species)
 * Infraorder Cetacea: whales (about 90 species)
 * Parvorder †Archaeoceti
 * Family †Pakicetidae
 * Family †Ambulocetidae
 * Family †Remingtonocetidae
 * Family †Basilosauridae
 * Clade Neoceti
 * Parvorder Mysticeti: baleen whales
 * Superfamily Balaenoidea: right whales
 * Family Balaenidae: greater right whales (four species)
 * Family Cetotheriidae: pygmy right whale (one species)
 * Superfamily Balaenopteroidea: large baleen whales
 * Family Balaenopteridae: slender-back rorquals and humpback whale (eight species)
 * Family Eschrichtiidae: gray whale (one species)
 * Parvorder Odontoceti: toothed whales
 * Superfamily Delphinoidea: oceanic dolphins, porpoises, and others
 * Family Delphinidae: oceanic true dolphins (38 species)
 * Family Monodontidae: Arctic whales; narwhal and beluga (two species)
 * Family Phocoenidae: porpoises (six species)
 * Superfamily Physeteroidea: sperm whales
 * Family Kogiidae: lesser sperm whales (two species)
 * Family Physeteridae: sperm whale (one species)
 * Superfamily Platanistoidea: river dolphins
 * Family Iniidae: South American river dolphins (two species)
 * Family Lipotidae: Chinese river dolphin (one species, possibly extinct)
 * Family Platanistidae: South Asian river dolphin (one species)
 * Family Pontoporiidae: La Plata dolphin (one species)
 * Superfamily Ziphioidea
 * Family Ziphiidae: beaked whales (22 species)
 * Total-group Ruminantia
 * Family †Anoplotheriidae?
 * Family †Xiphodontidae?
 * Family †Cainotheriidae?
 * Family †Protoceratidae?
 * Suborder Ruminantia
 * Infraorder Tragulina
 * Family †Leptomerycidae
 * Family †Hypertragulidae
 * Family †Praetragulidae
 * Family †Gelocidae
 * Family †Bachitheriidae
 * Family Tragulidae: chevrotains (ten species)
 * Family †Archaeomerycidae
 * Family †Lophiomerycidae
 * Infraorder Pecora
 * Family †Palaeomerycidae
 * Family †Dromomerycidae
 * Family Antilocapridae: pronghorn (one species)
 * Family †Climacoceratidae
 * Family Giraffidae: okapi and four species of giraffe (five species total)
 * Family †Hoplitomerycidae
 * Family Cervidae: deer (49 species)
 * Family Moschidae: musk deer (seven species)
 * Family Bovidae: cattle, buffalo, goat-antelope, antelope, and others (135 species)

Research history
In the 1990s, biological systematics used not only morphology and fossils to classify organisms, but also molecular biology. Molecular biology involves sequencing an organism's DNA and RNA and comparing the sequence with that of other living beings—the more similar they are, the more closely they are related. Comparison of even-toed ungulate and cetaceans genetic material has shown that the closest living relatives of whales and hippopotamuses is the paraphyletic group Artiodactyla.

Dan Graur and Desmond Higgins were among the first to come to this conclusion, and included a paper published in 1994. However, they did not recognize hippopotamuses and classified the ruminants as the sister group of cetaceans. Subsequent studies established the close relationship between hippopotamuses and cetaceans; these studies were based on casein genes, SINEs, fibrinogen sequences, cytochrome and rRNA sequences, IRBP (and vWF) gene sequences, adrenergic receptors, and apolipoproteins.

In 2001, the fossil limbs of a Pakicetus (amphibioid cetacean the size of a wolf) and Ichthyolestes (an early whale the size of a fox) were found in Pakistan. They were both archaeocetes ("ancient whales") from about 48 million years ago (in the Eocene). These findings showed that archaeocetes were more terrestrial than previously thought, and that the special construction of the talus (ankle bone) with a double-rolled joint surface, previously thought to be unique to even-toed ungulates, were also in early cetaceans. The mesonychians, another type of ungulate, did not show this special construction of the talus, and thus was concluded to not have the same ancestors as cetaceans.

The oldest cetaceans date back to the early Eocene (53 million years ago), whereas the oldest known hippopotamus dates back only to the Miocene (15 million years ago). The hippopotamids are descended from the anthracotheres, a family of semiaquatic and terrestrial artiodactyls that appeared in the late Eocene, and are thought to have resembled small- or narrow-headed hippos. Research is therefore focused on anthracotheres (family Anthracotheriidae); one dating from the Eocene to Miocene was declared to be "hippo-like" upon discovery in the 19th century. A study from 2005 showed that the anthracotheres and hippopotamuses had very similar skulls, but differed in the adaptations of their teeth. It was nevertheless believed that cetaceans and anthracothereres descended from a common ancestor, and that hippopotamuses developed from anthracotheres. A study published in 2015 confirmed this, but also revealed that hippopotamuses were derived from older anthracotherians. The newly introduced genus Epirigenys from Eastern Africa is thus the sister group of hippos.

Historical classification of Artiodactyla
Linnaeus postulated a close relationship between camels and ruminants as early as the mid-1700s. Henri de Blainville recognized the similar anatomy of the limbs of pigs and hippos, and British zoologist Richard Owen coined the term "even-toed ungulates" and the scientific name "Artiodactyla" in 1848.

Internal morphology (mainly the stomach and the molars) were used for classification. Suines (including pigs) and hippopotamuses have molars with well-developed roots and a simple stomach that digests food. Thus, they were grouped together as non-ruminants (Porcine). All other even-toed ungulates have molars with a selenodont construction (crescent-shaped cusps) and have the ability to ruminate, which requires regurgitating food and re-chewing it. Differences in stomach construction indicated that rumination evolved independently between tylopods and ruminants; therefore, tylopods were excluded from Ruminantia.

The taxonomy that was widely accepted by the end of the 20th century was:

Historical classification of Cetacea
Modern cetaceans are highly adapted sea creatures which, morphologically, have little in common with land mammals; they are similar to other marine mammals, such as seals and sea cows, due to convergent evolution. However, they evolved from originally terrestrial mammals. The most likely ancestors were long thought to be mesonychians—large, carnivorous animals from the early Cenozoic (Paleocene and Eocene), which had hooves instead of claws on their feet. Their molars were adapted to a carnivorous diet, resembling the teeth in modern toothed whales, and, unlike other mammals, had a uniform construction.

The suspected relations can be shown as follows:

Inner systematics
Molecular findings and morphological indications suggest that artiodactyls, as traditionally defined, are paraphyletic with respect to cetaceans. Cetaceans are deeply nested within the former; the two groups together form a monophyletic taxon, for which the name Cetartiodactyla is sometimes used. Modern nomenclature divides Artiodactyla (or Cetartiodactyla) in four subordinate taxa: camelids (Tylopoda), pigs and peccaries (Suina), ruminants (Ruminantia), and hippos plus whales (Whippomorpha).

The presumed lineages within Artiodactyla can be represented in the following cladogram:

The four summarized Artiodactyla taxa are divided into ten extant families:
 * The camelids (Tylopoda) comprise only one family, Camelidae. It is a species-poor artiodactyl suborder of North American origin that is well adapted to extreme habitats—the dromedary and Bactrian camels in the Old World deserts and the guanacos, llamas, vicuñas, and alpacas in South American high mountain regions.
 * The pig-like creatures (Suina) are made up of two families:
 * The pigs (Suidae) are limited to the Old World. These include the wild boar and the domesticated form, the domestic pig.
 * The peccaries (Tayassuidae) are named after glands on their belly and are indigenous to Central and South America.
 * The ruminants (Ruminantia) consist of six families:
 * The mouse deer (Tragulidae) are the smallest and most primitive even-toed-ruminants; they inhabit forests of Africa and Asia.
 * The giraffe-like creatures (Giraffidae) are composed of two species: the giraffe and the okapi.
 * The musk deer (Moschidae) is indigenous to East Asia.
 * The antilocaprids (Antilocapridae) of North America comprise only one extant species: the pronghorn.
 * The deer (Cervidae) are made up of about 45 species, which are characterized by a pair of antlers (generally only in males). They are spread across Europe, Asia, and the Americas. This group includes, among other species, the red deer, moose, elk (wapiti), and reindeer (caribou).
 * The bovids (Bovidae) are the most species-rich. Among them are cattle, sheep, caprines, and antelopes.
 * The whippomorphans include hippos and cetaceans:
 * The hippos (Hippopotamidae) comprise two groups, the hippo and the pygmy hippo.
 * The whales (Cetacea) comprise 72 species and two parvorders: toothed whales (Odontoceti) and baleen whales (Mysticeti)

Although deer, musk deer, and pronghorns have traditionally been summarized as cervids (Cervioidea), molecular studies provide different—and inconsistent—results, so the question of phylogenetic systematics of infraorder Pecora (the horned ruminants) for the time being, cannot be answered.

Anatomy
Artiodactyls are generally quadrupeds. Two major body types are known: Suinids and hippopotamuses are characterized by a stocky body, short legs, and a large head; camels and ruminants, though, have a more slender build and lanky legs. Size varies considerably; the smallest member, the mouse deer, often reaches a body length of only 45 cm and a weight of 1.5 kg. The largest member, the hippopotamus, can grow up to 5 m in length and weigh 4.5 MT, and the giraffe can grow to be 5.5 m tall and 4.7 m in body length. All even-toed ungulates display some form of sexual dimorphism: the males are consistently larger and heavier than the females. In deer, only the males boast antlers, and the horns of bovines are usually small or not present in females. Male Indian antelopes have a much darker coat than females.

Almost all even-toed ungulates have fur, with the exception being the nearly hairless hippopotamus. Fur varies in length and coloration depending on the habitat. Species in cooler regions can shed their coat. Camouflaged coats come in colors of yellow, gray, brown, or black tones.

Limbs
Even-toed ungulates bear their name because they have an even number of toes (two or four)—in some peccaries, the hind legs have a reduction in the number of toes to three. The central axis of the leg is between the third and fourth toe. The first toe is missing in modern artiodactyls, and can only be found in now-extinct genera. The second and fifth toes are adapted differently between species:

When camels have only two toes present, the claws are transformed into nails (while both are made of keratin, claws are curved and pointed while nails are flat and dull). These claws consist of three parts: the plate (top and sides), the sole (bottom), and the bale (rear). In general, the claws of the forelegs are wider and blunter than those of the hind legs, and they are farther apart. Aside from camels, all even-toed ungulates put just the tip of the foremost phalanx on the ground.

In even-toed ungulates, the bones of the stylopodium (upper arm or thigh bone) and zygopodiums (tibia and fibula) are usually elongated. The muscles of the limbs are predominantly localized, which ensures that artiodactyls often have very slender legs. A clavicle is never present, and the scapula is very agile and swings back and forth for added mobility when running. The special construction of the legs causes the legs to be unable to rotate, which allows for greater stability when running at high speeds. In addition, many smaller artiodactyls have a very flexible body, contributing to their speed by increasing their stride length.

Head
Many even-toed ungulates have a relatively large head. The skull is elongated and rather narrow; the frontal bone is enlarged near the back and displaces the parietal bone, which forms only part of the side of the cranium (especially in ruminants).

Horns and antlers
Four families of even-toed ungulates have cranial appendages. These Pecora (with the exception of the musk deer), have one of four types of cranial appendages: true horns, antlers, ossicones, or pronghorns.

True horns have a bone core that is covered in a permanent sheath of keratin, and are found only in the bovids. Antlers are bony structures that are shed and replaced each year; they are found in deer (members of the family Cervidae). They grow from a permanent outgrowth of the frontal bone called the pedicle and can be branched, as in the white-tailed deer (Odocoileus virginianus), or palmate, as in the moose (Alces alces). Ossicones are permanent bone structures that fuse to the frontal or parietal bones during an animal's life and are found only in the Giraffidae. Pronghorns, while similar to horns in that they have keratinous sheaths covering permanent bone cores, are deciduous.

All these cranial appendages can serve for posturing, battling for mating privilege, and for defense. In almost all cases, they are sexually dimorphic, and are often found only on the males. One exception is the species Rangifer tarandus, known as reindeer in Europe or caribou in North America, where both sexes can grow antlers yearly, though the females' antlers are typically smaller and not always present.

Teeth

There are two trends in terms of teeth within Artiodactyla. The Suina and hippopotamuses have a relatively large number of teeth (with some pigs having 44); their dentition is more adapted to a squeezing mastication, which is characteristic of omnivores. Camels and ruminants have fewer teeth; there is often a yawning diastema, a designated gap in the teeth where the molars are aligned for crushing plant matter.

The incisors are often reduced in ruminants, and are completely absent in the upper jaw. The canines are enlarged and tusk-like in the Suina, and are used for digging in the ground and for defense. In ruminants, the males' upper canines are enlarged and used as a weapon in certain species (mouse deer, musk deer, water deer); species with frontal weapons are usually missing the upper canines. The lower canines of ruminants resemble the incisors, so that these animals have eight uniform teeth in the frontal part of the lower jaw.

The molars of porcine have only a few bumps. In contrast, camels and ruminants have bumps that are crescent-shaped cusps (selenodont).

Senses
Artiodactyls have a well-developed sense of smell and sense of hearing. Unlike many other mammals, they have a poor sense of sight—moving objects are much easier to see than stationary ones. Similar to many other prey animals, their eyes are on the sides of the head, giving them an almost panoramic view.

Digestive system

The ruminants (Ruminantia) ruminate their food—they regurgitate and re-chew it. Ruminants' mouths often have additional salivary glands, and the oral mucosa is often heavily calloused to avoid injury from hard plant parts and to allow easier transport of roughly chewed food. Their stomachs are divided into three to four sections: the rumen, the reticulum, the omasum, and the abomasum. After the food is ingested, it is mixed with saliva in the rumen and reticulum and separates into layers of solid versus liquid material. The solids lump together to form a bolus (also known as the cud); this is regurgitated by reticular contractions while the glottis is closed. When the bolus enters the mouth, the fluid is squeezed out with the tongue and re-swallowed. The bolus is chewed slowly to completely mix it with saliva and to break it down. Ingested food passes to the "fermentation chamber" (rumen and reticulum), where it is kept in continual motion by rhythmic contractions. Cellulytic microbes (bacteria, protozoa, and fungi) produce cellulase, which is needed to break down the cellulose found in plant material. This form of digestion has two advantages: plants that are indigestible to other species can be digested and used, and the duration of the actual food consumption shortened; the animal spends only a short time out in the open with its head to the ground—rumination can take place later, in a sheltered area.

Tylopoda (camels, llamas, and alpacas) and chevrotains have three-chambered stomachs, while the rest of Ruminantia have four-chambered stomachs. The handicap of a heavy digestive system has increased selective pressure towards limbs that allow the animal to quickly escape predators. Most species within Suina have a simple two-chambered stomach that allows for an omnivorous diet. The babirusa, however, is a herbivore, and has extra maxillary teeth to allow for proper mastication of plant material. Most of the fermentation occurs with the help of cellulolytic microorganisms within the caecum of the large intestine. Peccaries have a complex stomach that contains four compartments. Their fore stomach has fermentation carried out by microbes and has high levels of volatile fatty acid; it has been proposed that their complex fore-stomach is a means to slow digestive passage and increase digestive efficiency. Hippopotamuses have three-chambered stomachs and do not ruminate. They consume around 68 kg of grass and other plant matter each night. They may cover distances up to 20 mi to obtain food, which they digest with the help of microbes that produce cellulase. Their closest living relatives, the whales, are obligate carnivores.

Unlike other even-toed ungulates, pigs have a simple sack-shaped stomach. Some artiodactyla, such as white-tailed deer, lack a gall bladder.

Genitourinary system
The penises of even-toed ungulates have an S-shape at rest and lie in a pocket under the skin on the belly. The corpora cavernosa are only slightly developed; and an erection mainly causes this curvature to extend, which leads to an extension, but not a thickening, of the penis. Cetaceans have similar penises. In some even-toed ungulates, the penis contains a structure called the urethral process.

The testicles are located in the scrotum and thus outside the abdominal cavity. The ovaries of many females descend—as the testicles descend of many male mammals—and are close to the pelvic inlet at the level of the fourth lumbar vertebra. The uterus has two horns (uterus bicornis).

Other
The number of mammary glands is variable and correlates, as in all mammals, with litter size. Pigs, which have the largest litter size of all even-toed ungulates, have two rows of teats lined from the armpit to the groin area. In most cases, however, even-toed ungulates have only one or two pairs of teats. In some species these form an udder in the groin region.

Secretory glands in the skin are present in virtually all species and can be located in different places, such as in the eyes, behind the horns, the neck, or back, on the feet, or in the anal region.

Artiodactyls have a carotid rete heat exchange that enables them, unlike perissodactyls which lack one, to regulate their brain temperature independently of their bodies. It has been argued that its presence explains the greater success of artiodactyls compared to perissodactyls in being able to adapt to diverse environments from the Arctic Circle to deserts and tropical savannahs.

Distribution and habitat
Artiodactyls are native to almost all parts of the world, with the exception of Oceania and Antarctica. Humans have introduced different artiodactyls worldwide as hunting animals. Artiodactyls inhabit almost every habitat, from tropical rainforests and steppes to deserts and high mountain regions. The greatest biodiversity prevails in open habitats such as grasslands and open forests.

Social behavior

The social behavior of even-toed ungulates varies from species to species. Generally, there is a tendency to merge into larger groups, but some live alone or in pairs. Species living in groups often have a hierarchy, both among males and females. Some species also live in harem groups, with one male, several females, and their common offspring. In other species, the females and juveniles stay together, while males are solitary or live in bachelor groups and seek out females only during mating season.

Many artiodactyls are territorial and mark their territory, for example, with glandular secretions or urine. In addition to year-round sedentary species, there are animals that migrate seasonally.

There are diurnal, crepuscular, and nocturnal artiodactyls. Some species' pattern of wakefulness varies with season or habitat.

Reproduction and life expectancy
Generally, even-toed ungulates tend to have long gestation periods, smaller litter sizes, and more highly developed newborns. As with many other mammals, species in temperate or polar regions have a fixed mating season, while those in tropical areas breed year-round. They carry out polygynous mating behavior, meaning a male mates with several females and suppresses all competition.

The length of the gestation period varies from four to five months for porcine, deer, and musk deer; six to ten months for hippos, deer, and bovines; ten to thirteen months with camels; and fourteen to fifteen months with giraffes. Most deliver one or two babies, but some pigs can deliver up to ten.

The newborns are precocial (born relatively mature) and come with open eyes and are hairy (with the exception of the hairless hippos). Juvenile deer and pigs have striped or spotted coats; the pattern disappears as they grow older. The juveniles of some species spend their first weeks with their mother in a safe location, where others may be running and following the herd within a few hours or days.

Life expectancy is typically twenty to thirty years; as in many mammals, smaller species often have a shorter lifespan than larger species. The artiodactyls with the longest lifespans are the hippos, cows, and camels, which can live 40 to 50 years.

Predators and parasites
Artiodactyls have different natural predators depending on their size and habitat. There are several carnivores that prey on them, including large cats (e.g., lions) and bears. Other predators are crocodiles, wolves and dogs, large raptors, and for small species and young animals, large snakes. For cetaceans, possible predators include sharks, polar bears, and other cetaceans; in the latter is the orca, the top predator of the oceans.

Parasites include nematodes, botflies, fleas, lice, or flukes, but they have debilitating effects only when the infestation is severe.

Domestication

Artiodactyls have been hunted by primitive humans for various reasons: for meat or fur, as well as to use their bones and teeth as weapons or tools. Their domestication began around 8000 BCE. To date, humans have domesticated goats, sheep, cattle, camels, llamas, alpacas, and pigs. Initially, livestock was used primarily for food, but they began being used for work activities around 3000 BCE. Clear evidence exists of antelope being used for food 2 million years ago in the Olduvai Gorge, part of the Great Rift Valley. Cro-Magnons relied heavily on reindeer for food, skins, tools, and weapons; with dropping temperatures and increased reindeer numbers at the end of the Pleistocene, they became the prey of choice. Reindeer remains accounted for 94% of bones and teeth found in a cave above the river Céou that was inhabited around 12,500 years ago. In general, most even-toed ungulates can be consumed as a Kosher meat, with the principal exception of Suina (pigs etc.) and hippopotamids, which are even-toed animals but do not chew the cud, and of Cetacea, which, for the purpose of Rabbinical Law, are considered to be scaleless fish, and thus not Kosher.

Today, artiodactyls are kept primarily for their meat, milk, and wool, fur, or hide for clothing. Domestic cattle, the water buffalo, the yak, and camels are used for work, as rides, or as pack animals.

Threats

The endangerment level of each even-toed ungulate is different. Some species are synanthropic (such as the wild boar) and have spread into areas that they are not indigenous to, either having been brought in as farm animals or having run away as people's pets. Some artiodactyls also benefit from the fact that their predators (e.g. the Tasmanian tiger) were severely decimated by ranchers, who saw them as competition.

Conversely, many artiodactyls have declined significantly in numbers, and some have even gone extinct, largely due to over-hunting, and, more recently, habitat destruction. Extinct species include several gazelles, the aurochs, the Malagasy hippopotamus, the bluebuck, and Schomburgk's deer. Two species, the Scimitar-horned oryx and Père David's deer, are extinct in the wild. Fourteen species are considered critically endangered, including the addax, the kouprey, the wild Bactrian camel, Przewalski's gazelle, the saiga, and the pygmy hog. Twenty-four species are considered endangered.

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title: Artiodactyl


text:
François Quesnay

 François Quesnay (4 June 1694 – 16 December 1774) was a French economist and physician of the Physiocratic school. He is known for publishing the "Tableau économique" (Economic Table) in 1758, which provided the foundations of the ideas of the Physiocrats. This was perhaps the first work attempting to describe the workings of the economy in an analytical way, and as such can be viewed as one of the first important contributions to economic thought. His Le Despotisme de la Chine, written in 1767, describes Chinese politics and society, and his own political support for enlightened despotism.

Life
Quesnay was born at Méré near Versailles, the son of an advocate and small landed proprietor. Apprenticed at the age of sixteen to a surgeon, he soon went to Paris, studied medicine and surgery there, and, having qualified as a master-surgeon, settled down to practice at Mantes. In 1737 he was appointed perpetual secretary of the academy of surgery founded by François Gigot de la Peyronie, and became surgeon in ordinary to King Louis XV. In 1744 he graduated as a doctor of medicine; he became the physician in ordinary to the king, and afterwards his first consulting physician, and was installed in the Palace of Versailles. His apartments were on the entresol, whence the Réunions de l'entresol received their name. Louis XV esteemed Quesnay highly, and used to call him his thinker. When he ennobled him he gave him for arms three flowers of the pansy (derived from pensée, in French meaning thought), with the Latin motto Propter cogitationem mentis.

He now devoted himself principally to economic studies, taking no part in the court intrigues which were perpetually going on around him. Around 1750 he became acquainted with Jacques C. M. V. de Gournay (1712–1759), who was also an earnest inquirer in the economic field; and round these two distinguished men was gradually formed the philosophic sect of the Économistes, or, as for distinction's sake they were afterwards called, the Physiocrates. The most remarkable men in this group of disciples were the elder Mirabeau (author of L'Ami des hommes, 1756–60, and Philosophie rurale, 1763), Nicolas Baudeau (Introduction a la philosophie économique, 1771), Guillaume-François Le Trosne (De l'ordre social, 1777), André Morellet (best known by his controversy with Galiani on the freedom of the grain trade during the Flour War), Lemercier de La Rivière, and du Pont de Nemours. Adam Smith, during his stay on the continent with the young Duke of Buccleuch in 1764–1766, spent some time in Paris, where he made the acquaintance of Quesnay and some of his followers; he paid a high tribute to their scientific services in his Wealth of Nations.

In 1717, Quesnay married Jeanne-Cathérine Dauphin, and had a son and a daughter; his grandson by the former was a member of the first Legislative Assembly. He died on 16 December 1774, having lived long enough to see his great pupil, Anne Robert Jacques Turgot, Baron de Laune, in office as minister of finance.

Works
His economic writings are collected in the 2nd vol. of the Principaux économistes, published by Guillaumin, Paris, with preface and notes by Eugène Daire; also his Oeuvres économiques et philosophiques were collected with an introduction and note by August Oncken (Frankfort, 1888); a facsimile reprint of the Tableau économique, from the original MS., was published by the British Economic Association (London, 1895). His other writings were the article "Évidence" in the Encyclopédie, and Recherches sur l'évidence des vérites geometriques, with a Projet de nouveaux éléments de géometrie, 1773. Quesnay's Eloge was pronounced in the Academy of Sciences by Grandjean de Fouchy (see the Recueil of that Academy, 1774, p. 134). See also F.J. Marmontel, Mémoires; Mémoires de Mme. du Hausset; H. Higgs, The Physiocrats (London, 1897).

Economics
In 1758 he published the Tableau économique (Economic Table), which provided the foundations of the ideas of the Physiocrats. This was perhaps the first work to attempt to describe the workings of the economy in an analytical way, and as such can be viewed as one of the first important contributions to economic thought.

The publications in which Quesnay expounded his system were the following: two articles, on "Fermiers" (Farmers) and on "Grains", in the Encyclopédie of Diderot and Jean le Rond d'Alembert (1756, 1757); a discourse on the law of nature in the Physiocratie of Dupont de Nemours (1768); Maximes générales de gouvernement economique d'un royaume agricole (1758), and the simultaneously published Tableau économique avec son explication, ou extrait des économies royales de Sully (with the celebrated motto, Pauvres paysans, pauvre royaume; pauvre royaume, pauvre roi); Dialogue sur le commerce et les travaux des artisans; and other minor pieces.

The Tableau économique, though on account of its dryness and abstract form it met with little general favor, may be considered the principal manifesto of the school. It was regarded by the followers of Quesnay as entitled to a place amongst the foremost products of human wisdom, and is named by the elder Mirabeau, in a passage quoted by Adam Smith, as one of the three great inventions which have contributed most to the stability of political societies, the other two being those of writing and of money. Its object was to exhibit by means of certain formulas the way in which the products of agriculture, which is the only source of wealth, would in a state of perfect liberty be distributed among the several classes of the community (namely, the productive classes of the proprietors and cultivators of land, and the unproductive class composed of manufacturers and merchants), and to represent by other formulas the modes of distribution which take place under systems of Governmental restraint and regulation, with the evil results arising to the whole society from different degrees of such violations of the natural order. It follows from Quesnay's theoretic views that the one thing deserving the solicitude of the practical economist and the statesman is the increase of the net product; and he infers also what Smith afterwards affirmed, on not quite the same ground, that the interest of the landowner is strictly and indissolubly connected with the general interest of the society. A small edition de luxe of this work, with other pieces, was printed in 1758 in the Palace of Versailles under the king's immediate supervision, some of the sheets, it is said, having been pulled by the royal hand. Already in 1767 the book had disappeared from circulation, and no copy of it is now procurable; but, the substance of it has been preserved in the Ami des hommes of Mirabeau, and the Physiocratie of Dupont de Nemours.

Orientalism and China
Quesnay is known for his writings on Chinese politics and society. His book Le Despotisme de la Chine, written in 1767, describes his views of the Chinese imperial system. He was supportive of the meritocratic concept of giving scholars political power, without the cumbersome aristocracy that characterized French politics, and the importance of agriculture to the welfare of a nation. Gregory Blue writes that Quesnay "praised China as a constitutional despotism and openly advocated the adoption of Chinese institutions, including a standardized system of taxation and universal education." Blue speculates that this may have influenced the 1793 establishment of the Permanent Settlement in Bengal by the British Empire. Quesnay's interests in Orientalism has also been a source of criticism. Carol Blum, in her book Strength in Numbers on 18th century France, labels Quesnay an "apologist for Oriental despotism."

Because of his admiration of Confucianism, Quesnay's followers bestowed him with the title "Confucius of Europe." Quesnay's infatuation for Chinese culture, as described by Jesuits, led him to persuade the son of Louis XV to mirror the "plowing of sacred land" by the Chinese emperor to symbolize the link between government and agriculture.

 On Taxation

Quesnay acknowledged three economic classes in France: the "proprietary" class consisting of only landowners, the "productive" class of agricultural workers, and the "sterile" class of merchants. Quesnay saw no benefit to the sterile class and believed the productive to be all important. Quesnay viewed France's agriculture as backward and unproductive compared to Britain during the time he was residing in the Palace of Versailles [13]. Despite residing in the Palace, Quesnay believed agriculture was the heart of the economy and of special importance to him. Quesnay argued that taxes placed on cultivators are only harmful to society as these taxes will reduce the incentive for agricultural production. Taxing proprietors (property holders) does not destroy the means of production meaning there is no decline in output. Quesnay wanted proprietors to bear the full burden of the tax in the country as taxing cultivators is a negative consequence for everyone. Removing incentive from cultivators reduces agricultural production and the agricultural surplus Quesnay believed to be the heart of the economy [14]. Quesnay also opposed indirect taxes in contrast to direct taxes. These "indirect taxes" are placed on the French public by proprietors whose greed demands immunity from taxation. Direct taxes on proprietors has no impact on reproduction and economic decline [14]. Reducing indirect taxes and increasing direct taxes gives the French a surplus of agriculture and the funding the country needs. However, this opinion was not very popular among the wealthy of which Quesnay spent time regularly with. He spent some of his time fearing for his life in the Palace.

title: François Quesnay


text:
Talk:Sacred geometry

'7 Classical Planets' and 4 don't cast shadows on Earth, 4 lunar phases of 7 days each: GOD=7_4 Code
I just wrote this on the 'talk page' of http://en.wikipedia.org/wiki/Classical_planet ...

'Seven Classical Planets' is the proper name and the title of this article should be corrected. These were/are the 7 moving objects seen in the heavens with the naked eye and 4 of them don't cast shadows on Earth (Venus does). They are the simple explanation for why the ancients considered the #7 sacred: "As above, so below" was/is the precept of sacred geometry. Also, the 29.5 day lunar months were/are divided into 4 phases of 7 days (~7.4 days) each. The lunar year + 7 day week + 4 days = solar year. The ancient Egyptians observed this sacred combination of 7 & 4 in the heavens and using "On Earth as it is in the heavens", took the standard cubit of 6 palms x 4 fingers and added a palm creating the Royal cubits of 7 palms x 4 fingers. All ancient Egyptian architects used royal cubits in their designs of sacred buildings going back to at least the first Step Pyramid of Djoser at Saqqara. The Jewish menorah mystically reflects this GOD=7_4 Code with its 7 lamps and 4 arms representing the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn. Having the Sun in the middle of the 7 - 4th from the right or left - was also used later by Ptolemy (see planets). This was a BIG aspect of the Ancient Mysteries! Note how the 7 days of the week in Latin were directly named after the 7 Classical Planets, but in English, 4 have been changed and named after Germanic and Norse gods. - Ben Franklin 71.196.95.141 (talk) 16:38, 13 December 2013 (UTC)
 * Interesting opinion, but please provide sources for all of the above. --Salimfadhley (talk) 17:47, 13 December 2013 (UTC)

It's well-known information that can be found on all the referenced Wikipedia articles. 73.57.35.183 (talk) 21:17, 30 June 2017 (UTC)
 * Wikipedia is a user-generated site and hence is never considered to be a reliable source itself. If there are reliable sources in those other article then those sources may be reused in this article. See WP:RS. Meters (talk) 23:12, 30 June 2017 (UTC)
 * These are socks of User:Brad Watson, Miami, striking his edits.  Doug Weller  talk 13:50, 1 July 2017 (UTC)

External links modified
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Sacred and geometric
I just reverted an addition that does not seem to belong here. Maybe there are other sources that do not actually talk about the subject; I had a quick look and could not find any. --Hob Gadling (talk) 07:06, 4 September 2022 (UTC)

This is woeful
To begin with, this article doesn't really define "sacred geometry". It suggests it's some ancient tradition using a scattered handful of mathematicians with spiritual views about the subject, or in the case of the Gauss and Yau quotes, even less. I can find no evidence of this term being so used, it seems to be a term and that has cropped up recently to refer to a decidedly modern cultural phenomenon. To quote some guy who was mean to Hilbert, "das ist nicht mathematik". This is hippie mysticism, with no ties to the serious discipline, which this article makes little attempt to elucidate. A guy who writes about "magic, feng shui, sacred geometry and alchemy" is quoted, without pointing out said. There are no sources linking Islamic and Hindu design principles to beliefs that God or gods want things designed that way. The Indic Today source is clearly unreliable as to the presence of fractal patterns in Hindu design, and conflates self-similarity with being a fractal. A line is self-similar but is not a fractal. Most fractals are not self-similar. Certainly, I don't think ancient Hindus had knowledge of Hausdorff dimension. The Christian section is better-sourced, but still doesn't clearly suggest that designs are divinely ordained and holding spiritual powers, so much as representative of religious themes. Overall, this article is rambling, misleading, vague and poorly sourced. BayesRawlsBoole (talk) 02:39, 1 October 2022 (UTC)
 * Yes, taking some trash out would do good. --Hob Gadling (talk) 03:19, 1 October 2022 (UTC)

There is no sacred geometry in Islam
Give me one authentic Islamic source that says Islam identifies any geometric shape or pattern as sacred. The fact that some artistic patterns are used to decorate certain Qur'an editions does not make that art in itself sacred. If you can't substantiate this claim, then remove the entire Islam section. 105.71.132.2 (talk) 11:06, 12 October 2023 (UTC)

 * "To express the sacred, one can also make use of abstract forms of sacred geometry, which symbolize the intelligible world, as in Islamic art and in certain other forms of art" (251)
 * Nasr, Seyyed Hossein, and Ramin Jahanbegloo. In Search of the Sacred: A Conversation with Seyyed Hossein Nasr on His Life and Thought. Praeger, 2010. https://ia801203.us.archive.org/34/items/HosseinNasr/Nasr%2C%20Seyyed%20Hossein%20-%20In%20Search%20of%20the%20Sacred%2C%20A%20Conversation%20with%20Seyyed%20Hossein%20Nasr%20on%20His%20Life%20and%20Thought%20%282010%29.pdf Permareperterra (talk) 08:01, 22 February 2024 (UTC)

title: Talk:Sacred geometry


text:
Léon Walras

Marie-Esprit-Léon Walras (16 December 1834 – 5 January 1910) was a French mathematical economist and Georgist. He formulated the marginal theory of value (independently of William Stanley Jevons and Carl Menger) and pioneered the development of general equilibrium theory. Walras is best known for his book Éléments d'économie politique pure, a work that has contributed greatly to the mathematization of economics through the concept of general equilibrium. The definition of the role of the entrepreneur found in it was also taken up and amplified by Joseph Schumpeter. For Walras, exchanges only take place after a Walrasian tâtonnement (French for "trial and error"), guided by the auctioneer, has made it possible to reach market equilibrium. It was the general equilibrium obtained from a single hypothesis, rarity, that led Joseph Schumpeter to consider him "the greatest of all economists". The notion of general equilibrium was very quickly adopted by major economists such as Vilfredo Pareto, Knut Wicksell and Gustav Cassel. John Hicks and Paul Samuelson used the Walrasian contribution in the elaboration of the neoclassical synthesis. For their part, Kenneth Arrow and Gérard Debreu, from the perspective of a logician and a mathematician, determined the conditions necessary for equilibrium.

Biography
Walras was the son of a French school administrator Auguste Walras. His father was not a professional economist, yet his economic thinking had a profound effect on his son. He found the value of goods by setting their scarcity relative to human wants.

Walras enrolled in the École des Mines de Paris, but grew tired of engineering. He worked as a bank manager, journalist, romantic novelist and railway clerk before turning to economics. Walras received an appointment as the professor of political economy at the University of Lausanne.

Walras also inherited his father's interest in social reform. Much like the Fabians, Walras called for the nationalization of land, believing that land's productivity would always increase and that rents from that land would be sufficient to support the nation without taxes. He also asserts that all other taxes (i.e. on goods, labor, capital) eventually realize effects exactly identical to a consumption tax, so they can hurt the economy (unlike a land tax).

Another of Walras's influences was Augustin Cournot, a former schoolmate of his father. Through Cournot, Walras came under the influence of rationalism and was introduced to the use of mathematics in economics.

As Professor of Political Economy at the University of Lausanne, Walras is credited with founding the Lausanne school of economics, along with his successor Vilfredo Pareto.

Because most of Walras's publications were only available in French, many economists were unfamiliar with his work. This changed in 1954 with the publication of William Jaffé's English translation of Walras's Éléments d'économie politique pure. Walras's work was also too mathematically complex for many contemporary readers of his time. On the other hand, it has a great insight into the market process under idealized conditions so it has been far more read in the modern era.

Although Walras came to be regarded as one of the three leaders of the marginalist revolution, he was not familiar with the two other leading figures of marginalism, William Stanley Jevons and Carl Menger, and developed his theories independently. Elements has Walras disagreeing with Jevons on the applicability, while the findings adopted by Carl Menger, he says, are completely in alignment with the ideas present in the book (even though expressed non-mathematically).

Walras's law
Walras's law implies that the sum of the values of excess demands across all markets must equal zero, whether or not the economy is in a general equilibrium. This implies that if positive excess demand exists in one market, negative excess demand must exist in some other market. Thus, if all markets but one are in equilibrium, then that last market must also be in equilibrium.

General equilibrium theory
In 1874 and 1877 Walras published the work that led him to be considered the father of the general equilibrium theory, Éléments d'économie politique pure [see next section for bibliographical details].

His main goal was to solve a problem presented by A. A. Cournot: Does a general equilibrium exist? Though it had been demonstrated that prices would equate supply and demand to clear individual markets ("partial equilibrium"), it was unclear that an equilibrium existed for all markets simultaneously ("general equilibrium").

While teaching at the Lausanne Academy, Walras began constructing a mathematical model that assumes a "regime of perfectly free competition", in which productive factors, products, and prices automatically adjust in equilibrium. Walras began with the theory of exchange in 1873 and proceeded to map out his theories of production, capitalization and money in his first edition.

His theory of exchange began with an expansion of Cournot's demand curve to include more than two commodities, also realizing the value of the quantity sold must equal the quantity purchased thus the ratio of prices must be equal to the inverse ratio of quantities. Walras then drew a supply curve from the demand curve and set equilibrium prices at the intersection. His model could now determine prices of commodities but only the relative price. In order to deduce the absolute price, Walras could choose one price to serve as the numeraire, such that all other prices are measured in units of this commodity. Using the numeraire, he determined that marginal utility [rareté] divided by the price must be equal for all commodities.

Then he argued that, because each individual consumer consumes as much value as the value of that individual's stock of goods, the value of total sales equals the value of total purchase. That is, Walras's law holds.

Walras then expanded the theory to include production with the assumption of an existence of fixed coefficients in said production making possible a generalization that the marginal productivity of the factors of production varied with the amount of input, making factor substitution possible.

Walras constructed his basic theory of general equilibrium by beginning with simple equations and then increasing the complexity in the next equations. He began with a two-person bartering system, then moved on to the derivation of downward-sloping consumer demands. Next he moved on to exchanges involving multiple parties, and finally ended with credit and money.

Walras wrote down four sets of equations:

 * the quantity of goods demanded;
 * relating the prices of goods to their costs of production;
 * the quantities of inputs supplied;
 * the quantities of inputs demanded.

There are four sets of variables to solve for:

 * the price of each good;
 * the quantity of each good sold;
 * the price of each factor of production;
 * the quantity of each of those factor bought by businesses.

To simplify matters, Walras added one further equation (the Walras's law equation), requiring that all the money received must be spent, one way or the other.

By Walras's law, any particular market must be in equilibrium if all other markets in an economy are also in equilibrium, because the excess market demands sum to zero. Thus, in an economy with n markets, it is sufficient to solve n-1 simultaneous equations for market clearing. Taking one good as the numéraire in terms of which prices are specified, the economy has n-1 unknown prices that can be determined by the n-1 simultaneous equations, he thus concluded that the general equilibrium exists.

Though this argument works when all equations are linear, it does not hold when the equations are nonlinear. It is easy to construct a pairs of equations in two variables with no solutions. A more rigorous version of the argument was developed independently by Lionel McKenzie and the pair Kenneth Arrow and Gérard Debreu in the 1950s.

Walrasian auction
The Walrasian auction is a type of simultaneous auction where each agent calculates its demand for the good at every possible price and submits this to an auctioneer. The price is then set so that the total demand across all agents equals the total amount of the good. Thus, a Walrasian auction perfectly matches the supply and the demand. Walras suggests that equilibrium will be achieved through a process of tâtonnement (French for "trial and error"), a form of incremental hill climbing.

Economic value definition of utility
Léon Walras provides a definition of economic utility based on economic value as opposed to an ethical theory of value:

"I state that things are useful as soon as they may serve whatever usage, as soon as they match whatever need and allow its fulfillment. Thus, there is here no point to deal with 'nuances' by way of which one classes, in the language of everyday conversation, utility beside what is pleasant and between the necessary and the superfluous. Necessary, useful, pleasant and superfluous, all of this is, for us, more or less useful. There is here as well no need to take into account the morality or immorality of the need that the useful things matches and permits to fulfill. Whether a substance is searched for by a doctor to heal an ill person, or by an assassin to poison his family, this is an important question from other points of view, albeit totally indifferent from ours. The substance is useful, for us, in both cases, and may well be more useful in the second case than in the first one."

In economic theories of value, the term "value" is unrelated to any notions of value used in ethics, they are homonyms.

Legacy

In 1941 George Stigler wrote about Walras: "There is no general history of economic thought in English which devotes more than passing reference to his work. ... This sort of empty fame in English-speaking countries is of course attributable in large part to Walras's use of his mother tongue, French, and his depressing array of mathematical formulas." What caused the re-appraisal of Walras's consideration in the US, was the influx of German-speaking scientists – the German version of his Théorie Mathématique de la Richesse Sociale was published in 1881.

According to Schumpeter: "Walras is ... greatest of all economists. His system of economic equilibrium, uniting, as it does, the quality of 'revolutionary' creativeness with the quality of classic synthesis, is the only work by an economist that will stand comparison with the achievements of theoretical physics."

Éléments d'Économie Politique Pure
The Éléments of 1874/1877 are the work by which Léon Walras is best known. The full title is The half title page uses only the title ('Éléments d'Économie Politique Pure') whereas inside the body (e.g. p. 1 and the contents page) the subtitle ('Théorie de la richesse sociale') is used as if it were the title.
 * Éléments d'Économie Politique Pure, ou Théorie de la richesse sociale.

Plan of work
The work was issued in two instalments (fascicules) in separate years. It was intended as the first of three parts of a systematic treatise as follows: Works with titles echoing those proposed for Parts II and III were published in 1898 and 1896. They are included in the list of other works below.
 * 1re partie:– Éléments d'Économie Politique Pure, ou Théorie de la richesse sociale.
 * Section I. Objet et divisions de l'économie politique et sociale.
 * Section II. Théorie mathématique de l'échange.
 * Section III. Du numéraire et de la monnaie.
 * Section IV. Théorie naturelle de la production et de la conommation de la richesse.
 * Section V. Conditions et conséquences du progrès économique.
 * Section VI. Effets naturels et nécessaires des divers modes d'organisation économique de la société.
 * 2e partie:– Éléments d'Économie Politique Appliquée, ou Théorie de la production agricole, industrielle et commerciale de la richesse.
 * 3e partie:– Éléments d'Économie Sociale, ou Théorie de la répartition de la richesse par la propriété et l'impôt.

Editions

 * First (1874/1877). Most readily available. Described by Walker and van Daal as a 'brilliant expression of pure originality, containing many theoretical innovations' which 'needed alteration and development in a variety of important respects'.
 * Second (1889). Revised, corrected and enlarged.
 * Third (1896). A minor revision with new appendices. This is considered the best edition by Walker and van Daal.
 * Fourth (1900). Revised and extended. According to Walker and van Daal, 'these changes resulted in an incomplete, internally contradictory, and occasionally incoherent text'.
 * Fifth (1926). Posthumous; published by his daughter Aline. 'Édition définitive, revue et augmentée'. Follows the fourth.

Derived work
The 'Théorie Mathématique de la Richesse Sociale' included in the list of other works (below) is described by the National Library of Australia as 'a series of lectures and articles that together summarize the mathematical elements of the author's Élements '.

English Translations
Walker and van Daal describe Jaffé's translation of the word crieur as 'a momentous error that has misled generations of readers'.
 * William Jaffé (1954) of the fifth edition as Elements of Pure Economics.
 * Donald A. Walker and Jan van Daal (2014) of the third edition as Elements of Theoretical Economics.

Online and facsimile editions
Both of these are made from the first edition and are defective in respect of illustrations. The original figures were included as folding plates (presumably at the end of each fascicule). The online edition contains only Figs. 3, 4, 10, and 12 whereas the facsimile contains only Figs. 5 and 6.
 * Online:
 * Facsimile: cheap photographic reprints are produced by facsimilepublisher.com.

Other works

 * Francis Saveur, 1858.
 * "De la propriété intellectuelle", 1859, Journal des économistes.
 * "Paradoxes économiques I", 1860, Journal des économistes.
 * "Théorie critique de l'impôt", 1861.
 * De l'impôt dans le Canton de Vaud, 1861.
 * "La bourse et le crédit", 1867, Paris Guide.
 * "Correspondance entre M. Jevons, professeur a Manchester, et M. Walras, professeur a Lausanne", 1874, Journal des économistes.
 * "Un nuovo ramo della matematica. Dell' applicazione delle matematiche all' economia politica", 1876, Giornale degli economisti.
 * Théorie mathématique de la richesse sociale, 1883.
 * "Notice autobiographique de Léon Walras", 1893.
 * Études d'économie sociale; Théorie de la répartition de la richesse sociale, 1896.
 * Études d'économie politique appliquée; Théorie de la production de la richesse sociale, 1898.
 * "Théorie du crédit", 1898, Revue d'économie politique.
 * "Sur les équations de la circulation", 1899, Giornale degli economisti
 * "Cournot et l'Économique Mathématique", 1905, Gazette de Lausanne.
 * "La Paix par la Justice Sociale et le Libre Échange", 1907, Questions Pratiques de Legislation Ouvrière.
 * L'état et le chemin de fer (1875).
 * "Leone Walras, Autobiografia", 1908, Giornale degli Economisti.
 * "Un initiateur en économie politique, A.A. Walras", 1908, La Revue du Mois.
 * "Économique et méchanique", 1909, Bulletin de la Société Vaudoise de Sciences Naturelles
 * Correspondence of Léon Walras and related papers (ed. by William Jaffé, 3 vols.), 1965.
 * "Leone Walras, Autobiografia", 1908, Giornale degli Economisti.
 * "Un initiateur en économie politique, A.A. Walras", 1908, La Revue du Mois.
 * "Économique et méchanique", 1909, Bulletin de la Société Vaudoise de Sciences Naturelles
 * Correspondence of Léon Walras and related papers (ed. by William Jaffé, 3 vols.), 1965.

title: Léon Walras


text:
Fixed-wing aircraft

A fixed-wing aircraft is a heavier-than-air flying machine, such as an airplane, which is capable of flight using aerodynamic lift. Fixed-wing aircraft are distinct from rotary-wing aircraft (in which a rotor mounted on a spinning shaft generates lift), and ornithopters (in which the wings oscillate to generate lift). The wings of a fixed-wing aircraft are not necessarily rigid; kites, hang gliders, variable-sweep wing aircraft, and airplanes that use wing morphing are all classified as fixed wing.

Gliding fixed-wing aircraft, including free-flying gliders and tethered kites, can use moving air to gain altitude. Powered fixed-wing aircraft (airplanes) that gain forward thrust from an engine include powered paragliders, powered hang gliders and ground effect vehicles. Most fixed-wing aircraft are operated by a pilot, but some are unmanned and controlled either remotely or autonomously.

Kites
Kites were used approximately 2,800 years ago in China, where kite building materials were available. Leaf kites may have been flown earlier in what is now Sulawesi, based on their interpretation of cave paintings on nearby Muna Island. By at least 549 AD paper kites were flying, as recorded that year, a paper kite was used as a message for a rescue mission. Ancient and medieval Chinese sources report kites used for measuring distances, testing the wind, lifting men, signaling, and communication for military operations.

Kite stories were brought to Europe by Marco Polo towards the end of the 13th century, and kites were brought back by sailors from Japan and Malaysia in the 16th and 17th centuries. Although initially regarded as curiosities, by the 18th and 19th centuries kites were used for scientific research.

Gliders and powered devices
Around 400 BC in Greece, Archytas was reputed to have designed and built the first self-propelled flying device, shaped like a bird and propelled by a jet of what was probably steam, said to have flown some 200 m. This machine may have been suspended during its flight.

One of the earliest attempts with gliders was by 11th-century monk Eilmer of Malmesbury, which failed. A 17th-century account states that 9th-century poet Abbas Ibn Firnas made a similar attempt, though no earlier sources record this event.

In 1799, Sir George Cayley laid out the concept of the modern airplane as a fixed-wing machine with systems for lift, propulsion, and control. Cayley was building and flying models of fixed-wing aircraft as early as 1803, and built a successful passenger-carrying glider in 1853. In 1856, Frenchman Jean-Marie Le Bris made the first powered flight, had his glider L'Albatros artificiel towed by a horse along a beach. In 1884, American John J. Montgomery made controlled flights in a glider as a part of a series of gliders he built between 1883 and 1886. Other aviators who made similar flights at that time were Otto Lilienthal, Percy Pilcher, and protégés of Octave Chanute.

In the 1890s, Lawrence Hargrave conducted research on wing structures and developed a box kite that lifted the weight of a man. His designs were widely adopted. He also developed a type of rotary aircraft engine, but did not create a powered fixed-wing aircraft.

Powered flight
Sir Hiram Maxim built a craft that weighed 3.5 tons, with a 110-foot (34-meter) wingspan powered by two 360-horsepower (270-kW) steam engines driving two propellers. In 1894, his machine was tested with overhead rails to prevent it from rising. The test showed that it had enough lift to take off. The craft was uncontrollable, and Maxim abandoned work on it. The Wright brothers' flights in 1903 with their Flyer I are recognized by the Fédération Aéronautique Internationale (FAI), the standard setting and record-keeping body for aeronautics, as "the first sustained and controlled heavier-than-air powered flight". By 1905, the Wright Flyer III was capable of fully controllable, stable flight for substantial periods. In 1906, Brazilian inventor Alberto Santos Dumont designed, built and piloted an aircraft that set the first world record recognized by the Aéro-Club de France by flying the 14 bis 220 m in less than 22 seconds. The flight was certified by the FAI.

The Bleriot VIII design of 1908 was an early aircraft design that had the modern monoplane tractor configuration. It had movable tail surfaces controlling both yaw and pitch, a form of roll control supplied either by wing warping or by ailerons and controlled by its pilot with a joystick and rudder bar. It was an important predecessor of his later Bleriot XI Channel-crossing aircraft of the summer of 1909.

World War I
World War I served initiated the use of aircraft as weapons and observation platforms. The earliest known aerial victory with a synchronized machine gun-armed fighter aircraft occurred in 1915, flown by German Luftstreitkräfte Lieutenant Kurt Wintgens. Fighter aces appeared; the greatest (by number of air victories) was Manfred von Richthofen.

Alcock and Brown crossed the Atlantic non-stop for the first time in 1919. The first commercial flights traveled between the United States and Canada in 1919.

Interwar aviation; the "Golden Age"
The so-called Golden Age of Aviation occurred between the two World Wars, during which updated interpretations of earlier breakthroughs. Innovations include Hugo Junkers' all-metal air frames in 1915 leading to multi-engine aircraft of up to 60+ meter wingspan sizes by the early 1930s, adoption of the mostly air-cooled radial engine as a practical aircraft power plant alongside V-12 liquid-cooled aviation engines, and longer and longer flights – as with a Vickers Vimy in 1919, followed months later by the U.S. Navy's NC-4 transatlantic flight; culminating in May 1927 with Charles Lindbergh's solo trans-Atlantic flight in the Spirit of St. Louis spurring ever-longer flight attempts.

World War II
Airplanes had a presence in the major battles of World War II. They were an essential component of military strategies, such as the German Blitzkrieg or the American and Japanese aircraft carrier campaigns of the Pacific.

Military gliders were developed and used in several campaigns, but were limited by the high casualty rate encountered. The Focke-Achgelis Fa 330 Bachstelze (Wagtail) rotor kite of 1942 was notable for its use by German U-boats.

Before and during the war, British and German designers worked on jet engines. The first jet aircraft to fly, in 1939, was the German Heinkel He 178. In 1943, the first operational jet fighter, the Messerschmitt Me 262, went into service with the German Luftwaffe. Later in the war the British Gloster Meteor entered service, but never saw action – top air speeds for that era went as high as 1130 km/h, with the early July 1944 unofficial record flight of the German Me 163B V18 rocket fighter prototype.

Postwar
In October 1947, the Bell X-1 was the first aircraft to exceed the speed of sound, flown by Chuck Yeager.

In 1948–49, aircraft transported supplies during the Berlin Blockade. New aircraft types, such as the B-52, were produced during the Cold War.

The first jet airliner, the de Havilland Comet, was introduced in 1952, followed by the Soviet Tupolev Tu-104 in 1956. The Boeing 707, the first widely successful commercial jet, was in commercial service for more than 50 years, from 1958 to 2010. The Boeing 747 was the world's biggest passenger aircraft from 1970 until it was surpassed by the Airbus A380 in 2005. The most successful aircraft is the Douglas DC-3, a medium twin engine passenger aircraft that has been in service since 1936 and is still used for skydiving and other recreational flights. Some of the thousands of versions found other purposes, like the AC-47, a Vietnam War era gunship, which is still used in some militaries.

Airplane/aeroplane
An airplane (aeroplane or plane) is a powered fixed-wing aircraft propelled by thrust from a jet engine or propeller. Planes come in many sizes, shapes, and wing configurations. Uses include recreation, transportation of goods and people, military, and research.

Seaplane
A seaplane (hydroplane) is capable of taking off and landing (alighting) on water. Seaplanes that can also operate from dry land are a subclass called amphibian aircraft. Seaplanes and amphibians divide into two categories: float planes and flying boats.

 * A float plane is similar to a land-based airplane. The fuselage is not specialized. The wheels are replaced/enveloped by floats, allowing the craft to make remain afloat for water landings.
 * A flying boat is a seaplane with a watertight hull for the lower (ventral) areas of its fuselage. The fuselage lands and then rests directly on the water's surface, held afloat by the hull. It does not need additional floats for buoyancy, although small underwing floats or fuselage-mounted sponsons may be used to stabilize it. Large seaplanes are usually flying boats, embodying most classic amphibian aircraft designs.

Powered gliders
Many forms of glider may include a small power plant. These include:
 * Motor glider – a conventional glider or sailplane with an auxiliary power plant that may be used when in flight to increase performance.
 * Powered hang glider – a hang glider with a power plant added.
 * Powered parachute – a paraglider type of parachute with an integrated air frame, seat, undercarriage and power plant hung beneath.
 * Powered paraglider or paramotor – a paraglider with a power plant suspended behind the pilot.

Ground effect vehicle
A ground effect vehicle (GEV) flies close to the terrain, making use of the ground effect – the interaction between the wings and the surface. Some GEVs are able to fly higher out of ground effect (OGE) when required – these are classed as powered fixed-wing aircraft.

Glider

A glider is a heavier-than-air craft whose free flight does not require an engine. A sailplane is a fixed-wing glider designed for soaring – gaining height using updrafts of air and to fly for long periods.

Gliders are mainly used for recreation but have found use for purposes such as aerodynamics research, warfare and spacecraft recovery.

Motor gliders are equipped with a limited propulsion system for takeoff, or to extend flight duration.

As is the case with planes, gliders come in diverse forms with varied wings, aerodynamic efficiency, pilot location, and controls.

Large gliders are most commonly born aloft by a tow-plane or by a winch. Military gliders have been used in combat to deliver troops and equipment, while specialized gliders have been used in atmospheric and aerodynamic research. Rocket-powered aircraft and spaceplanes have made unpowered landings similar to a glider.

Gliders and sailplanes that are used for the sport of gliding have high aerodynamic efficiency. The highest lift-to-drag ratio is 70:1, though 50:1 is common. After take-off, further altitude can be gained through the skillful exploitation of rising air. Flights of thousands of kilometers at average speeds over 200 km/h have been achieved.

One small-scale example of a glider is the paper airplane. An ordinary sheet of paper can be folded into an aerodynamic shape fairly easily; its low mass relative to its surface area reduces the required lift for flight, allowing it to glide some distance.

Gliders and sailplanes share many design elements and aerodynamic principles with powered aircraft. For example, the Horten H.IV was a tailless flying wing glider, and the delta-winged Space Shuttle orbiter glided during its descent phase. Many gliders adopt similar control surfaces and instruments as airplanes.

Types
The main application of modern glider aircraft is sport and recreation.

Sailplane
Gliders were developed in the 1920s for recreational purposes. As pilots began to understand how to use rising air, sailplane gliders were developed with a high lift-to-drag ratio. These allowed the craft to glide to the next source of "lift", increasing their range. This gave rise to the popular sport of gliding.

Early gliders were built mainly of wood and metal, later replaced by composite materials incorporating glass, carbon or aramid fibers. To minimize drag, these types have a streamlined fuselage and long narrow wings incorporating a high aspect ratio. Single-seat and two-seat gliders are available.

Initially, training was done by short "hops" in primary gliders, which have no cockpit and minimal instruments. Since shortly after World War II, training is done in two-seat dual control gliders, but high-performance two-seaters can make long flights. Originally skids were used for landing, later replaced by wheels, often retractable. Gliders known as motor gliders are designed for unpowered flight, but can deploy piston, rotary, jet or electric engines. Gliders are classified by the FAI for competitions into glider competition classes mainly on the basis of wingspan and flaps. A class of ultralight sailplanes, including some known as microlift gliders and some known as airchairs, has been defined by the FAI based on weight. They are light enough to be transported easily, and can be flown without licensing in some countries. Ultralight gliders have performance similar to hang gliders, but offer some crash safety as the pilot can strap into an upright seat within a deform-able structure. Landing is usually on one or two wheels which distinguishes these craft from hang gliders. Most are built by individual designers and hobbyists.

Military gliders
Military gliders were used during World War II for carrying troops (glider infantry) and heavy equipment to combat zones. The gliders were towed into the air and most of the way to their target by transport planes, e.g. C-47 Dakota, or by one-time bombers that had been relegated to secondary activities, e.g. Short Stirling. The advantage over paratroopers were that heavy equipment could be landed and that troops were quickly assembled rather than dispersed over a parachute drop zone. The gliders were treated as disposable, constructed from inexpensive materials such as wood, though a few were re-used. By the time of the Korean War, transport aircraft had become larger and more efficient so that even light tanks could be dropped by parachute, obsoleting gliders.

Research gliders
Even after the development of powered aircraft, gliders continued to be used for aviation research. The NASA Paresev Rogallo flexible wing was developed to investigate alternative methods of recovering spacecraft. Although this application was abandoned, publicity inspired hobbyists to adapt the flexible-wing airfoil for hang gliders.

Initial research into many types of fixed-wing craft, including flying wings and lifting bodies was also carried out using unpowered prototypes.

Hang glider
A hang glider is a glider aircraft in which the pilot is suspended in a harness suspended from the air frame, and exercises control by shifting body weight in opposition to a control frame. Hang gliders are typically made of an aluminum alloy or composite-framed fabric wing. Pilots can soar for hours, gain thousands of meters of altitude in thermal updrafts, perform aerobatics, and glide cross-country for hundreds of kilometers.

Paraglider
A paraglider is a lightweight, free-flying, foot-launched glider with no rigid body. The pilot is suspended in a harness below a hollow fabric wing whose shape is formed by its suspension lines. Air entering vents in the front of the wing and the aerodynamic forces of the air flowing over the outside power the craft. Paragliding is most often a recreational activity.

Unmanned gliders
A paper plane is a toy aircraft (usually a glider) made out of paper or paperboard.

Model glider aircraft are models of aircraft using lightweight materials such as polystyrene and balsa wood. Designs range from simple glider aircraft to accurate scale models, some of which can be very large.

Glide bombs are bombs with aerodynamic surfaces to allow a gliding flight path rather than a ballistic one. This enables stand-off aircraft to attack a target from a distance.

Kite
A kite is a tethered aircraft held aloft by wind that blows over its wing(s). High pressure below the wing deflects the airflow downwards. This deflection generates horizontal drag in the direction of the wind. The resultant force vector from the lift and drag force components is opposed by the tension of the tether.

Kites are mostly flown for recreational purposes, but have many other uses. Early pioneers such as the Wright Brothers and J.W. Dunne sometimes flew an aircraft as a kite in order to confirm its flight characteristics, before adding an engine and flight controls.

Military
Kites have been used for signaling, for delivery of munitions, and for observation, by lifting an observer above the field of battle, and by using kite aerial photography.

Science and meteorology
Kites have been used for scientific purposes, such as Benjamin Franklin's famous experiment proving that lightning is electricity. Kites were the precursors to the traditional aircraft, and were instrumental in the development of early flying craft. Alexander Graham Bell experimented with large man-lifting kites, as did the Wright brothers and Lawrence Hargrave. Kites had a historical role in lifting scientific instruments to measure atmospheric conditions for weather forecasting.

Radio aerials and light beacons
Kites can be used to carry radio antennas. This method was used for the reception station of the first transatlantic transmission by Marconi. Captive balloons may be more convenient for such experiments, because kite-carried antennas require strong wind, which may be not always available with heavy equipment and a ground conductor.

Kites can be used to carry light sources such as light sticks or battery-powered lights.

Kite traction
Kites can be used to pull people and vehicles downwind. Efficient foil-type kites such as power kites can also be used to sail upwind under the same principles as used by other sailing craft, provided that lateral forces on the ground or in the water are redirected as with the keels, center boards, wheels and ice blades of traditional sailing craft. In the last two decades, kite sailing sports have become popular, such as kite buggying, kite landboarding, kite boating and kite surfing. Snow kiting is also popular.

Kite sailing opens several possibilities not available in traditional sailing:

 * Wind speeds are greater at higher altitudes
 * Kites may be maneuvered dynamically, which dramatically increases the available force
 * Mechanical structures are not needed to withstand bending forces; vehicles/hulls can be light or eliminated.

Power generation
Research and development projects investigate kites for harnessing high altitude wind currents for electricity generation.

Cultural uses
Kite festivals are a popular form of entertainment throughout the world. They include local events, traditional festivals and major international festivals.

Designs

 * Bermuda kite
 * Bowed kite, e.g. Rokkaku
 * Cellular or box kite
 * Chapi-chapi
 * Delta kite
 * Foil, parafoil or bow kite
 * Malay kite see also wau bulan
 * Tetrahedral kite

Types

 * Expanded polystyrene kite
 * Fighter kite
 * Indoor kite
 * Inflatable single-line kite
 * Kytoon
 * Man-lifting kite
 * Rogallo parawing kite
 * Stunt (sport) kite
 * Water kite

Air frame
The structural element of a fixed-wing aircraft is the air frame. It varies according to the aircraft's type, purpose, and technology. Early airframes were made of wood with fabric wing surfaces, When engines became available for powered flight, their mounts were made of metal. As speeds increased metal became more common until by the end of World War II, all-metal (and glass) aircraft were common. In modern times, composite materials became more common.

Typical structural elements include:

 * One or more mostly horizontal wings, often with an airfoil cross-section. The wing deflects air downward as the aircraft moves forward, generating lifting force to support it in flight. The wing also provides lateral stability to stop the aircraft level in steady flight. Other roles are to hold the fuel and mount the engines.
 * A fuselage, typically a long, thin body, usually with tapered or rounded ends to make its shape aerodynamically slippery. The fuselage joins the other parts of the air frame and contains the payload, and flight systems.
 * A vertical stabilizer or fin is a rigid surface mounted at the rear of the plane and typically protruding above it. The fin stabilizes the plane's yaw (turn left or right) and mounts the rudder which controls its rotation along that axis.
 * A horizontal stabilizer, usually mounted at the tail near the vertical stabilizer. The horizontal stabilizer is used to stabilize the plane's pitch (tilt up or down) and mounts the elevators that provide pitch control.
 * Landing gear, a set of wheels, skids, or floats that support the plane while it is not in flight. On seaplanes, the bottom of the fuselage or floats (pontoons) support it while on the water. On some planes, the landing gear retracts during the flight to reduce drag.

Wings
The wings of a fixed-wing aircraft are static planes extending to either side of the aircraft. When the aircraft travels forwards, air flows over the wings that are shaped to create lift.

Structure
Kites and some lightweight gliders and airplanes have flexible wing surfaces that are stretched across a frame and made rigid by the lift forces exerted by the airflow over them. Larger aircraft have rigid wing surfaces.

Whether flexible or rigid, most wings have a strong frame to give them shape and to transfer lift from the wing surface to the rest of the aircraft. The main structural elements are one or more spars running from root to tip, and ribs running from the leading (front) to the trailing (rear) edge.

Early airplane engines had little power and light weight was critical. Also, early airfoil sections were thin, and could not support a strong frame. Until the 1930s, most wings were so fragile that external bracing struts and wires were added. As engine power increased, wings could be made heavy and strong enough that bracing was unnecessary. Such an unbraced wing is called a cantilever wing.

Configuration
The number and shape of wings vary widely. Some designs blend the wing with the fuselage, while left and right wings separated by the fuselage are more common.

Occasionally more wings have been used, such as the three-winged triplane from World War I. Four-winged quadruplanes and other multiplane designs have had little success.

Most planes are monoplanes, with one or two parallel wings. Biplanes and triplanes stack one wing above the other. Tandem wings place one wing behind the other, possibly joined at the tips. When the available engine power increased during the 1920s and 1930s and bracing was no longer needed, the unbraced or cantilever monoplane became the most common form.

The planform is the shape when seen from above/below. To be aerodynamically efficient, wings are straight with a long span, but a short chord (high aspect ratio). To be structurally efficient, and hence lightweight, wingspan must be as small as possible, but offer enough area to provide lift.

To travel at transonic speeds, variable geometry wings change orientation, angling backward to reduce drag from supersonic shock waves. The variable-sweep wing transforms between an efficient straight configuration for takeoff and landing, to a low-drag swept configuration for high-speed flight. Other forms of variable planform have been flown, but none have gone beyond the research stage. The swept wing is a straight wing swept backward or forwards.

The delta wing is a triangular shape that serves various purposes. As a flexible Rogallo wing, it allows a stable shape under aerodynamic forces, and is often used for kites and other ultralight craft. It is supersonic capable, combining high strength with low drag.

Wings are typically hollow, also serving as fuel tanks. They are equipped with flaps, which allow the wing to increase/decrease drag/lift, for take-off and landing, and acting in opposition, to change direction.

Fuselage
The fuselage is typically long and thin, usually with tapered or rounded ends to make its shape aerodynamically smooth. Most fixed-wing aircraft have a single fuselage. Others may have multiple fuselages, or the fuselage may be fitted with booms on either side of the tail to allow the extreme rear of the fuselage to be utilized.

The fuselage typically carries the flight crew, passengers, cargo, and sometimes fuel and engine(s). Gliders typically omit fuel andengines, although some variations such as motor gliders and rocket gliders have them for temporary or optional use.

Pilots of manned commercial fixed-wing aircraft control them from inside a cockpit within the fuselage, typically located at the front/top, equipped with controls, windows, and instruments, separated from passengers by a secure door. In small aircraft, the passengers typically sit behind the pilot(s) in the cabin, Occasionally, a passenger may sit beside or in front of the pilot. Larger passenger aircraft have a separate passenger cabin or occasionally cabins that are physically separated from the cockpit.

Aircraft often have two or more pilots, with one in overall command (the "pilot") and one or more "co-pilots". On larger aircraft a navigator is typically also seated in the cockpit as well. Some military or specialized aircraft may have other flight crew members in the cockpit as well.

Flying wing
A flying wing is a tailless aircraft that has no distinct fuselage, housing the crew, payload, and equipment inside.

The flying wing configuration was studied extensively in the 1930s and 1940s, notably by Jack Northrop and Cheston L. Eshelman in the United States, and Alexander Lippisch and the Horten brothers in Germany. After the war, numerous experimental designs were based on the flying wing concept. General interest continued into the 1950s, but designs did not offer a great advantage in range and presented technical problems. The flying wing is most practical for designs in the slow-to-medium speed range, and drew continual interest as a tactical airlifter design.

Interest in flying wings reemerged in the 1980s due to their potentially low radar cross-sections. Stealth technology relies on shapes that reflect radar waves only in certain directions, thus making it harder to detect. This approach eventually led to the Northrop B-2 Spirit stealth bomber (pictured). The flying wing's aerodynamics are not the primary concern. Computer-controlled fly-by-wire systems compensated for many of the aerodynamic drawbacks, enabling an efficient and stable long-range aircraft.

Blended wing body
Blended wing body aircraft have a flattened airfoil-shaped body, which produces most of the lift to keep itself aloft, and distinct and separate wing structures, though the wings are blended with the body.

Blended wing bodied aircraft incorporate design features from both fuselage and flying wing designs. The purported advantages of the blended wing body approach are efficient, high-lift wings and a wide, airfoil-shaped body. This enables the entire craft to contribute to lift generation with potentially increased fuel economy.

Lifting body

A lifting body is a configuration in which the body produces lift. In contrast to a flying wing, which is a wing with minimal or no conventional fuselage, a lifting body can be thought of as a fuselage with little or no conventional wing. Whereas a flying wing seeks to maximize cruise efficiency at subsonic speeds by eliminating non-lifting surfaces, lifting bodies generally minimize the drag and structure of a wing for subsonic, supersonic, and hypersonic flight, or, spacecraft re-entry. All of these flight regimes pose challenges for flight stability.

Lifting bodies were a major area of research in the 1960s and 1970s as a means to build small and lightweight manned spacecraft. The US built lifting body rocket planes to test the concept, as well as several rocket-launched re-entry vehicles. Interest waned as the US Air Force lost interest in the manned mission, and major development ended during the Space Shuttle design process when it became clear that highly shaped fuselages made it difficult to fit fuel tanks.

Empennage and foreplane
The classic airfoil section wing is unstable in flight. Flexible-wing planes often rely on an anchor line or the weight of a pilot hanging beneath to maintain the correct attitude. Some free-flying types use an adapted airfoil that is stable, or other mechanisms including electronic artificial stability.

In order to achieve trim, stability, and control, most fixed-wing types have an empennage comprising a fin and rudder that act horizontally, and a tailplane and elevator that act vertically. This is so common that it is known as the conventional layout. Sometimes two or more fins are spaced out along the tailplane.

Some types have a horizontal "canard" foreplane ahead of the main wing, instead of behind it. This foreplane may contribute to the trim, stability or control of the aircraft, or to several of these.

Kite control
Kites are controlled by one or more tethers.

Free-flying aircraft controls
Gliders and airplanes have sophisticated control systems, especially if they are piloted. The controls allow the pilot to direct the aircraft in the air and on the ground. Typically these are:
 * The yoke or joystick controls rotation of the plane about the pitch and roll axes. A yoke resembles a steering wheel. The pilot can pitch the plane down by pushing on the yoke or joystick, and pitch the plane up by pulling on it. Rolling the plane is accomplished by turning the yoke in the direction of the desired roll, or by tilting the joystick in that direction.
 * Rudder pedals control rotation of the plane about the yaw axis. Two pedals pivot so that when one is pressed forward the other moves backward, and vice versa. The pilot presses on the right rudder pedal to make the plane yaw to the right, and pushes on the left pedal to make it yaw to the left. The rudder is used mainly to balance the plane in turns, or to compensate for winds or other effects that push the plane about the yaw axis.
 * On powered types, an engine stop control ("fuel cutoff", for example) and, usually, a Throttle or thrust lever and other controls, such as a fuel-mixture control (to compensate for air density changes with altitude change).

Other common controls include:
 * Flap levers, which are used to control the deflection position of flaps on the wings.
 * Spoiler levers, which are used to control the position of spoilers on the wings, and to arm their automatic deployment in planes designed to deploy them upon landing. The spoilers reduce lift for landing.
 * Trim controls, which usually take the form of knobs or wheels and are used to adjust pitch, roll, or yaw trim. These are often connected to small airfoils on the trailing edge of the control surfaces and are called "trim tabs". Trim is used to reduce the amount of pressure on the control forces needed to maintain a steady course.
 * On wheeled types, brakes are used to slow and stop the plane on the ground, and sometimes for turns on the ground.

A craft may have two pilot seats with dual controls, allowing two to take turns.

The control system may allow full or partial automation, such as an autopilot, a wing leveler, or a flight management system. An unmanned aircraft has no pilot and is controlled remotely or via gyroscopes, computers/sensors or other forms of autonomous control.

Cockpit instrumentation
On manned fixed-wing aircraft, instruments provide information to the pilots, including flight, engines, navigation, communications, and other aircraft systems that may be installed. The six basic instruments, sometimes referred to as the six pack, are:
 * The airspeed indicator (ASI) shows the speed at which the plane is moving through the air.
 * The attitude indicator (AI), sometimes called the artificial horizon, indicates the exact orientation of the aircraft about its pitch and roll axes.
 * The altimeter indicates the altitude or height of the plane above mean sea level (AMSL).
 * The vertical speed indicator (VSI), or variometer, shows the rate at which the plane is climbing or descending.
 * The heading indicator (HI), sometimes called the directional gyro (DG), shows the magnetic compass orientation of the fuselage. The direction is affected by wind conditions and magnetic declination.
 * The turn coordinator (TC), or turn and bank indicator, helps the pilot to control the plane in a coordinated attitude while turning.

Other cockpit instruments include: Some or all of these instruments may appear on a computer display and be operated with touches, ala a phone.
 * A two-way radio, to enable communications with other planes and with air traffic control.
 * A horizontal situation indicator (HSI) indicates the position and movement of the plane as seen from above with respect to the ground, including course/heading and other information.
 * Instruments showing the status of the plane's engines (operating speed, thrust, temperature, and other variables).
 * Combined display systems such as primary flight displays or navigation aids.
 * Information displays such as onboard weather radar displays.
 * A radio direction finder (RDF), to indicate the direction to one or more radio beacons, which can be used to determine the plane's position.
 * A satellite navigation (satnav) system, to provide an accurate position.

title: Fixed-wing aircraft