GeometryGeometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
Euclidean geometryEuclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
Non-Euclidean geometryIn mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries.
Elliptic geometryElliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry.
Hyperbolic geometryIn mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct lines through P that do not intersect R. (Compare the above with Playfair's axiom, the modern version of Euclid's parallel postulate.) The hyperbolic plane is a plane where every point is a saddle point.
ArteryAn artery (: arteries) () is a blood vessel in humans and most animals that takes blood away from the heart to one or more parts of the body (tissues, lungs, brain etc.). Most arteries carry oxygenated blood; the two exceptions are the pulmonary and the umbilical arteries, which carry deoxygenated blood to the organs that oxygenate it (lungs and placenta, respectively). The effective arterial blood volume is that extracellular fluid which fills the arterial system.
Synthetic geometrySynthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulate, and at present called axioms. The term "synthetic geometry" has been coined only after the 17th century, and the introduction by René Descartes of the coordinate method, which was called analytic geometry.
Projective geometryIn mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "points at infinity") to Euclidean points, and vice-versa.
PigThe pig (Sus domesticus), often called swine (: swine), hog, or domestic pig when distinguishing from other members of the genus Sus, is an omnivorous, domesticated, even-toed, hoofed mammal. It is variously considered a subspecies of Sus scrofa (the wild boar or Eurasian boar) or a distinct species. The pig's head-plus-body length ranges from , and adult pigs typically weigh between , with well-fed individuals even exceeding this range. The size and weight of hogs largely depends on their breed.
Functional programmingIn computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which update the running state of the program. In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local identifiers), passed as arguments, and returned from other functions, just as any other data type can.
Pig farmingPig farming or pork farming or hog farming is the raising and breeding of domestic pigs as livestock, and is a branch of animal husbandry. Pigs are farmed principally for food (e.g. pork: bacon, ham, gammon) and skins. Pigs are amenable to many different styles of farming: intensive commercial units, commercial free range enterprises, or extensive farming (being allowed to wander around a village, town or city, or tethered in a simple shelter or kept in a pen outside the owner's house).
Purely functional data structureIn computer science, a purely functional data structure is a data structure that can be directly implemented in a purely functional language. The main difference between an arbitrary data structure and a purely functional one is that the latter is (strongly) immutable. This restriction ensures the data structure possesses the advantages of immutable objects: (full) persistency, quick copy of objects, and thread safety. Efficient purely functional data structures may require the use of lazy evaluation and memoization.
Data structureIn computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type.
StructureA structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as biological organisms, minerals and chemicals. Abstract structures include data structures in computer science and musical form. Types of structure include a hierarchy (a cascade of one-to-many relationships), a network featuring many-to-many links, or a lattice featuring connections between components that are neighbors in space.
Guinea pigThe guinea pig or domestic guinea pig (Cavia porcellus), also known as the cavy or domestic cavy ('keɪvi ), is a species of rodent belonging to the genus Cavia in the family Caviidae. Breeders tend to use the word cavy to describe the animal, while in scientific and laboratory contexts, it is far more commonly referred to by the common name guinea pig. Despite their common name, guinea pigs are not native to Guinea, nor are they closely related biologically to pigs, and the origin of the name is still unclear.
Pig slaughterPig slaughter is the work of slaughtering domestic pigs which is both a common economic activity as well as a traditional feast in some European and Asian countries. Pig slaughter is an activity performed to obtain pig meat (pork). It regularly happens as part of traditional and intensive pig farming. Pigs are slaughtered at different ages. Generally they can be divided into piglets, which are 1.5 to 3 months old; the fattening pigs, intended for pork and bacon, which are 4 months to one year old; and finally the older pigs, such as sows (female pigs) and boars (uncastrated male pigs).
Subclavian arteryIn human anatomy, the subclavian arteries are paired major arteries of the upper thorax, below the clavicle. They receive blood from the aortic arch. The left subclavian artery supplies blood to the left arm and the right subclavian artery supplies blood to the right arm, with some branches supplying the head and thorax. On the left side of the body, the subclavian comes directly off the aortic arch, while on the right side it arises from the relatively short brachiocephalic artery when it bifurcates into the subclavian and the right common carotid artery.
Persistent data structureIn computing, a persistent data structure or not ephemeral data structure is a data structure that always preserves the previous version of itself when it is modified. Such data structures are effectively immutable, as their operations do not (visibly) update the structure in-place, but instead always yield a new updated structure. The term was introduced in Driscoll, Sarnak, Sleator, and Tarjans' 1986 article. A data structure is partially persistent if all versions can be accessed but only the newest version can be modified.
Common carotid arteryIn anatomy, the left and right common carotid arteries (carotids) (pronkəˈrɒtɪd) are arteries that supply the head and neck with oxygenated blood; they divide in the neck to form the external and internal carotid arteries. The common carotid arteries are present on the left and right sides of the body. These arteries originate from different arteries but follow symmetrical courses. The right common carotid originates in the neck from the brachiocephalic trunk; the left from the aortic arch in the thorax.
